Publikationen
2024

Y. Karli, D.A. Vajner, F. Kappe, P.C.A. Hagen, L.M. Hansen, R. Schwarz, T.K. Bracht, C. Schimpf, S.F. Covre da Silva, P. Walther, A. Rastelli, V.M. Axt, J.C. Loredo, V. Remesh, T. Heindel, D.E. Reiter G. Weihs,
 Controlling the photon number coherence of solidstate quantum light sources for quantum cryptography
Abstract:
Quantum communication networks rely on quantum cryptographic protocols including quantum key distribution (QKD) based on single photons. A critical element regarding the security of QKD protocols is the photon number coherence (PNC), i.e., the phase relation between the vacuum and onephoton Fock state. To obtain single photons with the desired properties for QKD protocols, optimal excitation schemes for quantum emitters need to be selected. As emitters, we consider semiconductor quantum dots, that are known to generate ondemand single photons with high purity and indistinguishability. Exploiting twophoton excitation of a quantum dot combined with a stimulation pulse, we demonstrate the generation of highquality single photons with a controllable degree of PNC. The main tuning knob is the pulse area giving full control from minimal to maximal PNC, while without the stimulating pulse the PNC is negligible in our setup for all pulse areas. Our approach provides a viable route toward secure communication in quantum networks.
Supplementary Information

L. Nimmesgern, M. Cygorek, A. MielnikPyszczorski, D.E. Reiter, A. Vagov and V.M. Axt,
 Multiple wave packets running in the photon number space
Abstract:
If a twolevel system coupled to a singlemode cavity is strongly driven by an external laser, instead of a continuous accumulation of photons in the cavity, oscillations in the mean photon number occur. These oscillations correspond to peaks of finite width running up and down in the photon number distribution, reminiscent of wave packets in linear chain models. A single wave packet is found if the cavity is resonant to the external laser. Here, we show that for finite detuning, multiple packet structures can exist simultaneously, oscillating at different frequencies and amplitudes. We further study the influence of dissipative effects resulting in the formation of a stationary state, which, depending on the parameters, can be characterized by a bimodal photon number distribution. While we give analytical limits for the maximally achievable photon number in the absence of any dissipation, surprisingly, dephasing processes can push the photon occupations towards higher photon numbers.
2023

T.K. Bracht, M. Cygorek, T. Seidelmann, V.M. Axt and D.E. Reiter,
 Temperatureindependent almost perfect photon entanglement from quantum dots via the SUPER scheme
Abstract:
Entangled photon pairs are essential for quantum communication technology. They can be generated ondemand by semiconductor quantum dots, but several mechanisms are known to reduce the degree of entanglement. While some obstacles like the finite finestructure splitting of the exciton states can currently be overcome, the excitation scheme itself can impair the entanglement fidelity. Here, we demonstrate that the swingup of quantum emitter population (SUPER) scheme, using two reddetuned laser pulses applied to a quantum dot in a cavity, yields almost perfectly entangled photons. The entanglement remains robust against phonon influences even at elevated temperatures, due to decoupling of the excitation and emission process. With this achievement, quantum dots are ready to be used as entangled photon pair sources in applications requiring high degrees of entanglement up to temperatures of approximately 80 K.
Supplementary Information

A. Vagov, I.A. Larkin, M.D. Croitoru and V.M. Axt,
 Superanomalous skineffect and enhanced absorption of light scattered on conductive media
Abstract:
Light scattering spectroscopy is a powerful tool for studying various media, but interpretation of its results requires a detailed knowledge of how media excitations are coupled to electromagnetic waves. In electrically conducting media, an accurate description of propagating electromagnetic waves is a nontrivial problem because of nonlocal lightmatter interactions. Among other consequences, the nonlocality gives rise to the anomalous (ASE) and superanomalous (SASE) skin effects. As is well known, ASE is related to an increase in the electromagnetic field absorption in the radio frequency domain. This work demonstrates that the Landau damping underlying SASE gives rise to another absorption peak at optical frequencies. In contrast to ASE, SASE suppresses only the longitudinal field component, and this difference results in the strong polarization dependence of the absorption. The mechanism behind the suppression is generic and is observed also in plasma. Neither SASE, nor the corresponding light absorption increase can be described using popular simplified models for the nonlocal dielectric response.
Supplementary Information

B.U. Lehner, T. Seidelmann, G. Undeutsch, C. Schimpf, S. Manna, M. Gawełczyk, S.F. Covre da Silva, X. Yuan, S. Stroj, D.E. Reiter, V.M. Axt and A. Rastelli,
 Beyond the FourLevel Model: Dark and Hot States in Quantum Dots Degrade Photonic Entanglement
Abstract:
Entangled photon pairs are essential for a multitude of quantum photonic applications. To date, the best performing solidstate quantum emitters of entangled photons are semiconductor quantum dots operated around liquidhelium temperatures. To favor the widespread deployment of these sources, it is important to explore and understand their behavior at temperatures accessible with compact Stirling coolers. Here we study the polarization entanglement among photon pairs from the biexciton–exciton cascade in GaAs quantum dots at temperatures up to ∼65 K. We observe entanglement degradation accompanied by changes in decay dynamics, which we ascribe to thermal population and depopulation of hot and dark states in addition to the four levels relevant for photon pair generation. Detailed calculations considering the presence and characteristics of the additional states and phononassisted transitions support the interpretation. We expect these results to guide the optimization of quantum dots as sources of highly entangled photons at elevated temperatures.
Supporting Information

T. Seidelmann, M. Cosacchi, M. Cygorek, D.E. Reiter, A. Vagov and V.M. Axt,
 Phononinduced transition between entangled and nonentangled photon emission in constantly driven quantumdot–cavity systems
Abstract:
Entangled photon pairs are essential for many applications in quantum technologies. Recent theoretical studies demonstrated that different types of entangled Bell states can be created in a constantly driven fourlevel quantum emittercavity system. Unlike other candidates for the realization of the fourlevel emitter, semiconductor quantum dots unavoidably interact with their environment, resulting in carrierphonon interactions. Surprisingly, phonons change the entanglement of emitted photon pairs in a qualitative way, already at low temperatures on the order of 4 K. While one type of Bell state can still be generated using small driving strengths, the other type is suppressed due to phonon interactions in strongly conﬁned quantum dots. The degree of entanglement decreases with rising temperature and driving strength until it vanishes at a certain parameter value. Because it remains zero afterward, we encounter a phononinduced transition between entangled and nonentangled photon emission that resembles a phase transition. The transition occurs at temperatures below 30 K and, independent of the driving strength, the concurrence as a function of the reduced temperature is found to obey a power law with exponent one near the transition point.

T.K. Bracht, T. Seidelmann, Y. Karli, F. Kappe, V. Remesh, G. Weihs, V.M. Axt and D.E. Reiter,
 Dressedstate analysis of twocolor excitation schemes
Abstract:
To coherently control a fewlevel quantum emitter, typically pulses with an energy resonant to the transition energy are applied, making use of the Rabi mechanism, while a single offresonant pulse does not result in a population inversion. Surprisingly, a twocolor excitation with a combination of two offresonant pulses is able to invert the system. In this paper, we provide an indepth analysis of twocolor excitation schemes within the dressedstate picture. We show that such schemes can be understood as a driving of the transition between the dressed states. In the twolevel system this allows us to derive analytic expressions for the pulse parameters yielding a population inversion. We relate our findings to the SwingUP of quantum EmitteR population (SUPER) mechanism, where the two pulses are red detuned. Our interpretation also holds in the case where one pulse is red detuned while the other pulse is blue detuned, as in dichromatic excitation schemes. We extend our considerations of the SUPER mechanism to the threelevel system, where a strong mixing between the bare states takes place. The insights gained from these results help in finding accessible regimes for further experimental realizations of twocolor excitation schemes.

T. Seidelmann, T.K. Bracht, B.U. Lehner, C. Schimpf, M. Cosacchi, M. Cygorek, A. Vagov, A. Rastelli, D.E. Reiter and V.M. Axt,
 Twophoton excitation with finite pulses unlocks pure dephasinginduced degradation of entangled photons emitted by quantum dots
Abstract:
Semiconductor quantum dots have emerged as an especially promising platform for the generation of polarizationentangled photon pairs. However, it was demonstrated recently that the twophoton excitation scheme employed in stateoftheart experiments limits the achievable degree of entanglement by introducing whichpath information. In this work, the combined impact of twophoton excitation and longitudinal acoustic phonons on photon pairs emitted by stronglyconfining quantum dots is investigated. It is found that phonons further reduce the achievable degree of entanglement even in the limit of vanishing temperature due to phononinduced pure dephasing and phononassisted onephoton processes, which increase the reexcitation probability. In addition, the degree of entanglement, as measured by the concurrence, decreases with rising temperature and/or pulse duration, even if the excitonic finestructure splitting is absent and when higher electronic states are out of reach. Furthermore, in the case of finite finestructure splittings, phonons enlarge the discrepancy in concurrence for different laser polarizations.

F. Kappe, Y. Karli, T.K. Bracht, S. F. Covre da Silva, T. Seidelmann, V.M. Axt, A. Rastelli, G. Weihs, D.E. Reiter and V. Remesh,
 Collective excitation of spatiospectrally distinct quantum dots enabled by chirped pulses
Abstract:
Nanoscale bright sources that produce highpurity single photons and
highfidelity entangled photon pairs are the building blocks
to realize high security quantum communication devices. To
achieve high communication rates, it is desirable to have an
ensemble of quantum emitters that can be collectively excited,
despite their spectral variability. In case of semiconductor
quantum dots, Rabi rotations are the most popular method for
resonant excitation. However, these cannot assure a universal,
highly efficient excited state preparation, due to the
sensitivity to excitation parameters. In contrast, adiabatic
rapid passage (ARP), relying on chirped optical pulses, is
immune to quantum dot spectral inhomogeneity. Here, we show
that the robustness of ARP holds true for the simultaneous
excitation of the biexciton states in multiple, spatially
separated and spectrally different quantum dots. For positive
chirps, we also find a regime where the influence of phonons
relax the sensitivity to spectral detunings and lower the
needed excitation power. Being able to generate highpurity
photons from spatially multiplexed quantum dot sources using
the biexciton to ground state cascade is a big step towards
the implementation of high photon rate, entanglementbased
quantum key distribution protocols.
2022

M. Cygorek , M. Cosacchi, A. Vagov , V.M. Axt, B.W. Lovett,
J. Keeling and E.M. Gauger,
 Simulation of open quantum systems by automated compression of arbitrary environments
Abstract:
Studies of the dynamics of open quantum systems are limited by the large Hilbert space of typical environments, which is too large to be treated exactly. In some cases, approximate descriptions of the system are possible, for example, when the environment has a short memory time or only interacts weakly with the system. Accurate numerical methods exist, but these are typically restricted to baths with Gaussian correlations, such as noninteracting bosons. Here we present a method for simulating open quantum systems with arbitrary environments that consist of a set of independent degrees of freedom. Our approach automatically reduces the large number of environmental degrees of freedom to those which are most relevant. Specifically, we show how the process tensor describing the effect of the environment can be iteratively constructed and compressed using matrix product state techniques. We demonstrate the power of this method by applying it to a range of open quantum systems, including bosonic, fermionic and spin environments. The versatility and efficiency of our automated compression of environments method provides a practical generalpurpose tool for open quantum systems.
Supplementary Information
Universität Bayreuth Pressemitteilung/Press Release

T. Seidelmann, C. Schimpf, T.K. Bracht, M. Cosacchi, A. Vagov, A. Rastelli, D.E. Reiter and V.M. Axt,
 Twophoton excitation sets limit to entangled photon pair generation from quantum emitters
Abstract:
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of ondemand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic finestructure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a twophoton resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser pulse itself. Hence, in the setting explored here, the excitation process limits the achievable concurrence for entangled photons generated in an optically excited fourlevel quantum emitter.
Supplement

Y. Karli, F. Kappe, V. Remesh, T.K. Bracht, J. Münzberg,
S. Covre da Silva, T. Seidelmann, V.M. Axt, A. Rastelli, D.E. Reiter and G. Weihs,
 SUPER Scheme in Action: Experimental Demonstration of RedDetuned Excitation of a Quantum Emitter
Abstract:
The quest for the perfect singlephoton source includes finding the optimal protocol for exciting the quantum emitter. Coherent optical excitation was, up until now, achieved by tuning the laser pulses to the transition frequency of the emitter, either directly or in average. Recently, it was theoretically discovered that an excitation with two reddetuned pulses is also possible where neither of which would yield a significant upperlevel population individually. We show that the socalled swingup of quantum emitter population (SUPER) scheme can be implemented experimentally with similar properties to existing schemes by precise amplitude shaping of a broadband pulse. Because of its truly offresonant nature, this scheme has the prospect of powering highpurity photon sources with superior photon count rate.
Supporting Information
Universität Innsbruck Pressemitteilung/Press Release

M. Bozzio, M. Vyvlecka, M. Cosacchi, C. Nawrath, T. Seidelmann, J.C. Loredo, S.L. Portalupi, V.M. Axt, P. Michler and P. Walther,
 Enhancing quantum cryptography with quantum dot singlephoton sources
Abstract:
Quantum cryptography harnesses quantum light, in particular single photons, to provide security guarantees that cannot be
reached by classical means. For each cryptographic task, the security feature of interest is directly related to the
photons’ nonclassical properties. Quantum dotbased singlephoton sources are remarkable candidates, as they can
in principle emit deterministically, with high brightness and low multiphoton contribution. Here, we show that these sources provide additional security benefits, thanks to the tunabilityof coherence in the emitted photonnumber states. We identify the optimal optical pumping scheme for the main quantumcryptographic primitives, and benchmark their performance with respect to Poissondistributed sources such as attenuated laser states and downconversion sources. In particular, we elaborate on the advantage of using phononassisted and twophoton excitation rather than resonant excitation for quantum key distribution and other primitives. The presented results will guide future developments in solidstate and quantum information science for photon sources that are tailored to quantum communication tasks.
Supplementary Information

A. Völkel, L. Nimmesgern, A. MielnikPyszczorski, T. Wirth and G. Herink,
 Intracavity Raman scattering couples soliton molecules with terahertz phonons
Abstract:
Ultrafast atomic vibrations mediate heat transport, serve as fingerprints for chemical bonds and drive phase transitions in condensed matter systems. Light pulses shorter than the atomic oscillation period can not only probe, but even stimulate and control collective excitations. In general, such interactions are performed with freepropagating pulses. Here, we demonstrate intracavity excitation and timedomain sampling of coherent optical phonons inside an active laser oscillator. Employing realtime spectral interferometry, we reveal that Terahertz beats of Ramanactive optical phonons are the origin of soliton boundstates – also termed “Soliton molecules” – and we resolve a coherent coupling mechanism of phonon and intracavity soliton motion. Concurring electronic and nuclear refractive nonlinearities generate distinct soliton trajectories and, effectively, enhance the timedomain Raman signal. We utilize the intrinsic soliton motion to automatically perform highspeed Raman spectroscopy of the intracavity crystal. Our results pinpoint the impact of Ramaninduced soliton interactions in crystalline laser media and microresonators, and offer unique perspectives toward ultrafast nonlinear phononics by exploiting the coupling of atomic
Universität Bayreuth Pressemitteilung

Y.V. Zhumagulov, V.D. Neverov, A.E. Lukyanov, D.R. Gulevich, A.V. Krasavin, A. Vagov, and V. Perebeinos,
 Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides
Abstract:
Secondharmonic generation (SHG) is a wellknown nonlinear spectroscopy method to probe electronic structure, specifically, in transition metal dichalcogenide (TMDC) monolayers. This work investigates the nonlinear dynamics of a strongly excited TMDC monolayer by solving the time evolution equations for the density matrix. It is shown that the presence of excitons qualitatively changes the nonlinear dynamics leading, in particular, to a huge enhancement of the nonlinear signal as a function of the dielectric environment. It is also shown that the SHG polarization angular diagram and its dependence on the driving strength are very sensitive to the type of exciton state. This sensitivity suggests that SHG spectroscopy is a convenient tool for analyzing the fine structure of excitonic states.
Editor's Suggestion
Erratum: Phys. Rev. B 105, 239902(E) (2022)

M. Cosacchi, T. Seidelmann, A. MielnikPyszczorski,
M. Neumann, T.K. Bracht, M. Cygorek, A. Vagov, D.E. Reiter and V.M. Axt,
 Deterministic Photon Storage and Readout in a Semimagnetic Quantum Dot–Cavity System Doped with a Single Mn Ion
Abstract:
Light trapping is a crucial mechanism for synchronization in optical communication. Especially on the level of single photons, control of the exact emission time is desirable. In this paper, a singlephoton buffering device composed of a quantum dot doped with a single Mn atom in a cavity is theoretically proposed. A method to detain a single cavity photon as an excitation of the dot is presented. The storage scheme is based on bright to dark exciton conversion performed with an offresonant external optical field and mediated via a spinflip with the magnetic ion. The induced Stark shift brings both exciton states to resonance and results in an excitation transfer to the optically inactive one. The stored photon can be read out on demand in the same manner by repopulating the bright state, which has a short lifetime. The results indicate the possibility to suspend a photon for almost two orders of magnitude longer than the lifetime of the bright exciton.

J.M. Lia, P.I. Tamborenea, M. Cygorek and V.M. Axt,
 Dynamics of the angular momentum in narrow quantum rings with Rashba and Dresselhaus spinorbit interactions
Abstract:
The quantum dynamics of the electron's spin and orbital angular momenta in semiconductor quantum rings is analyzed. Both Rashba and Dresselhaus spinorbit interactions (SOIs) in their quasitwodimensional forms are taken into account. The narrow quantum rings are treated with models including one and two radial modes. We find that when either Rashba or Dresselhaus SOI acts alone, the different angular momentum states are coupled in blocks of two (for a single radial mode) or four (for two radial modes). We also show that the full Hilbert space splits into two disjoint subspaces, which are not coupled by either of the two SOIs, thereby decoupling accordingly the state evolution. When both SOI mechanisms are present, in principle infinitely many states are coupled, but we find by numerical computation of the quantum dynamics that for typical evolution times in practice only a few neighboring states are involved in the dynamics. Thus the exchange of angular momenta proceeds only via very few states. Furthermore, we find a trend that when initially high orbital momenta are prepared, the time evolution of spin and orbital momenta is almost unaffected by the availability of a second radial mode, in sharp contrast to the case of preparing the system in low orbital angular momentum states. The implications of our findings for the coherent control of angular momentum in quantum rings are pointed out.

M. Cosacchi, A. MielnikPyszczorski, T. Seidelmann, M. Cygorek, A. Vagov, D.E. Reiter and V.M. Axt,
 Nphoton bundle statistics on different solidstate platforms
Abstract:
The term Nphoton bundles has been coined for a specific type of photon emission, where light quanta are released from a cavity only in groups of N particles. This emission leaves a characteristic number distribution of the cavity photons that may be taken as one of their fingerprints. We study this characteristic Nphoton bundle statistics considering two solidstate cavity quantum electrodynamics (cQED) systems. As one example, we consider a semiconductor quantumdot–microcavity system coupled to longitudinal acoustic phonons. There, we find the environmental influence to be detrimental to the bundle statistics. The other example is a superconducting qubit inside a microwave resonator. In these systems, pure dephasing is not important and an experimentally feasible parameter regime is found, where the bundle statistics prevails.

V.D. Neverov, A.E. Lukyanov, A.V. Krasavin, A.Vagov and M.D. Croitoru ,
 Correlated disorder as a way towards robust superconductivity
Abstract:
Ordinary superconductors are widely assumed insensitive to small concentrations of random nonmagnetic impurities, whereas strong disorder suppresses superconductivity and even makes superconductorinsulator transition occur. In between these limiting cases, a most fascinating regime can take place where disorder enhances superconductivity. Hitherto, almost all theoretical studies have been conducted under the assumption that disorder is completely independent and random. In real materials, however, positions of impurities and defects tend to correlate with each other. This work shows that these correlations have a strong impact on superconductivity making it more robust and less sensitive to the disorder potential. Superconducting properties can therefore be controlled not only by the overall density of impurities and defects, but by their spatial correlations as well.

A.A. Shanenko, T.T. Saraiva, A. Vagov, A.S. Vasenko, and A. Perali,
 Suppression of fluctuations in a twoband superconductor with a quasionedimensional band
Abstract:
Chainlike structured superconductive materials (such as A2Cr3As3, with A=K,Rb,Cs) exhibit the multiband electronic structure of singleparticle states, where coexisting quasionedimensional (Q1D) and conventional higherdimensional energy bands take part in the creation of the aggregate superconducting condensate. When the chemical potential approaches the edge of a Q1D band in a singleband superconductor, the corresponding meanfield critical temperature increases significantly but the superconductivity is quenched by fluctuations. However, recent investigation has revealed that when a Q1D band is coupled to a higherdimensional one by the interband Cooperpair transfer, the thermal superconductive fluctuations can be suppressed so that the resulting critical temperature can be close to its meanfield value. In the present work, we calculate the meanfield Tc0 and fluctuationshifted Tc critical temperatures for a twoband superconductor where a Q1D band coexists with a higherdimensional band, and investigate how the thermal fluctuations are sensitive to the system parameters. We find that Tc is close to Tc0 in a wide range of microscopic parameters, and even the dimensionality of the higherdimensional band does not play an essential role. Thus, the screening mechanism for suppressing fluctuations via the pairexchange coupling between the bands is indeed relevant for a large class of Q1D multiband superconducting materials, encouraging further experiments aimed at reaching larger critical temperatures in such multiband superconductors.

X.S. Brems, S.Mühlbauer, W.Y. CórdobaCamacho, A.A. Shanenko, A.Vagov, J. Albino Aguiar and R. Cubitt,
 Currentinduced selforganisation of mixed superconducting states
Abstract:
Smallangle neutron scattering is used in combination with transport measurements to investigate the currentinduced effects on the morphology of the intermediate mixed state (IMS) domains in the intertype superconductor niobium. We report the robust selforganisation of the vortex lattice domains to elongated parallel stripes perpendicular to the applied current in a steadystate. The experimental results for the formation of the superstructure are supported by theoretical calculations, which highlight important details of the vortex matter evolution. The investigation demonstrates a mechanism of a spontaneous pattern formation that is closely related to the universal physics governing the IMS in lowκ superconductors.

T.K. Bracht, T. Seidelmann, T. Kuhn, V.M. Axt and D.E. Reiter,
 Phonon wave packet emission during state preparation of a semiconductor quantum dot using different schemes
Abstract:
The carrier–phonon interaction in semiconductor quantum dots (QDs) can greatly affect the optical preparation of the excited state. For resonant excitation used in the Rabi preparation scheme, the polaron is formed accompanied by the emission of a phonon wave packet, leading to a degradation of preparation ﬁdelity. In this article, phonon wave packets for different coherent excitation schemes are analyzed. One example is the adiabatic rapid passage scheme relying on a chirped excitation. Herein, also a phonon wave packet is emitted, but the preparation ﬁdelity can still be approximately unity. A focus is on the phonon impact on a recently proposed swingup scheme, induced by two detuned pulses. Similar to the Rabi scheme, a degradation and a phonon wave packet emission are found, despite the detuning. If the swingup frequency coincides with the maximum of the phonon spectral density, a series of wave packets is emitted yielding an even stronger degradation. The insight gained from our results further helps in designing an optimal preparation scheme for QDs.
60 Years Physica Status Solidi Anniversary Edition
2021

T.K. Bracht , M. Cosacchi, T. Seidelmann, M. Cygorek, A.
Vagov, V.M. Axt, T. Heindel and D.E. Reiter,
 SwingUp of quantum emitter population using detuned pulses
Abstract:
The controlled preparation of the excited state in a quantum emitter is a prerequisite for its usage as a
singlephoton source—a key building block for quantum technologies. In this paper, we propose a coherent
excitation scheme using oﬀresonant pulses. In the usual Rabi scheme, these pulses would not lead to a
signiﬁcant occupation. This is overcome by using a frequencymodulated pulse to swing up the excited
state population. The same eﬀect can be obtained using two pulses with diﬀerent strong detunings of the
same sign. We theoretically analyze the applicability of the scheme to a semiconductor quantum dot. In
this case, the excitation is several millielectronvolts below the band gap, i.e., far away from the detection
frequency, allowing for easy spectral ﬁltering, and does not rely on any auxiliary particles such as phonons.
Our scheme has the potential to lead to the generation of closetoideal photons.
Editor's Suggestion
Universität Münster Pressemitteilung/Press Release

M. Cosacchi, T. Seidelmann, M. Cygorek, A. Vagov, D.E. Reiter and V.M. Axt,
 Accuracy of the Quantum Regression Theorem for Photon Emission from a Quantum Dot
Abstract:
The quantum regression theorem (QRT) is the most widely used tool for calculating multitime
correlation functions for the assessment of quantum emitters. It is an approximate method based on a
Markov assumption for environmental coupling. In this Letter we quantify properties of photons emitted
from a single quantum dot coupled to phonons. For the singlephoton purity and the indistinguishability,
we compare numerically exact pathintegral results with those obtained from the QRT. It is demonstrated
that the QRT systematically overestimates the influence of the environment for typical quantum dots used
in quantum information technology.
Supplement
Erratum: Phys. Rev. Lett. 128, 079901(E) (2022)

T. Seidelmann, D.E. Reiter, M. Cosacchi, M. Cygorek, A. Vagov and V.M. Axt,
 Timedependent switching of the photon entanglement type using a driven quantum emitter–cavity system
Abstract:
The cascaded decay in a fourlevel quantum emitter is a wellestablished mechanism to generate polarizationentangled photon pairs, the building blocks of many applications in quantum technologies. The four most prominent maximally entangled photon pair states are the Bell states. In a typical experiment based on an undriven emitter, only one type of Bell state entanglement can be observed in a given polarization basis. Other types of Bell state entanglement in the same basis can be created by continuously driving the system by an external laser. In this work, we propose a protocol for timedependent entanglement switching in a fourlevel quantum emitter–cavity system that can be operated by changing the external driving strength. By selecting different twophoton resonances between the laserdressed states, we can actively switch back and forth between the different types of Bell state entanglement in the same basis as well as between entangled and nonentangled photon pairs. This remarkable feature demonstrates the possibility to achieve a controlled, timedependent manipulation of the entanglement type that could be used in many innovative applications.

T. Seidelmann, M. Cosacchi, M. Cygorek, D.E. Reiter,
A. Vagov and V.M. Axt,
 Different Types of Photon Entanglement from a Constantly Driven Quantum Emitter Inside a Cavity
Abstract:
Bell states are the most prominent maximally entangled photon states. In a
typical fourlevel emitter, like a semiconductor quantum dot, the photon
states exhibit only one type of Bell state entanglement. By adding an external
driving to the emitter system, also other types of Bell state entanglement are
reachable without changing the polarization basis. In this work, it is shown
under which conditions the diﬀerent types of entanglement occur and
analytical equations are given to explain these ﬁndings. Furthermore, special
points are identiﬁed, where the concurrence, being a measure for the degree
of entanglement, drops to zero, while the coherences between the twophoton
states stay strong. Results of this work pave the way to achieve a controlled
manipulation of the entanglement type in practical devices.
Erratum: Adv. Quantum Technol. 5, 2200058 (2022)

M. Cosacchi, T. Seidelmann, J. Wiercinski, M. Cygorek,
A. Vagov, D. E. Reiter and V.M. Axt,
 Schrödinger cat states in quantumdotcavity systems
Abstract:
A Schrödingercat state is a coherent superposition of macroscopically distinguishable quantum states, in
quantum optics usually realized as superposition of coherent states. Protocols to prepare photonic cats have been
presented for atomic systems. Here we investigate in what manner and how well the preparation protocols can
be transferred to a solidstate platform, namely, a semiconductor quantumdot–cavity system. In quantumdot–
cavity systems there are many disruptive inﬂuences like cavity losses, the radiative decay of the quantum dot,
and the coupling to longitudinal acoustic phonons. We show that for one of the protocols these inﬂuences kill
the quantum coherence between the states forming the cat, while for a second protocol a parameter regime can
be identiﬁed where the essential characteristics of Schrödingercat states survive the environmental inﬂuences
under conditions that can be realized with current equipment.

W.Y. CórdobaCamacho, A. Vagov, A.A. Shanenko, J. Albino Aguiar, A.S. Vasenko and V.S. Stolyarov,
 Vortex Interactions and Clustering in Thin Superconductors
Abstract:
Cluster formation is a focus of interdisciplinary research in both chemistry and physics. Here we discuss the exotic example of this phenomenon in the vortex matter of a thin superconductor. In superconducting films, the clustering takes place because of particular properties of the vortex interactions in the crossover or intertype regime between superconductivity types I and II. These interactions are controlled by the two parameters that are responsible for the crossover, Ginzburg–Landau parameter κ, which specifies the superconducting material of the film, and film thickness d, which controls effects due to stray magnetic fields outside the sample. We demonstrate that their competition gives rise to a complex spatial dependence of the interaction potential between vortices, favoring the formation of chainlike vortex clusters.

M. Neumann, F. Kappe, T.K. Bracht , M. Cosacchi , T. Seidelmann , V.M. Axt, G. Weihs and D.E. Reiter,
 Optical Stark shift to control the dark exciton occupation of a quantum dot in a tilted magnetic ﬁeld
Abstract:
When a detuned and strong laser pulse acts on an optical transition, a Stark shift of the corresponding
energies occurs. We analyze how this optical Stark effect can be used to prepare and control the dark exciton
occupation in a semiconductor quantum dot. The coupling between the bright and dark exciton states is facilitated
by an external magnetic ﬁeld. Using sequences of laser pulses, we show how the dark exciton and different
superposition states can be prepared. We give simple analytic formulas, which yield a good estimate for optimal
preparation parameters. The preparation scheme is quite robust against the inﬂuence of acoustic phonons. We
further discuss the experimental feasibility of the used Stark pulses. Giving a clear physical picture, our results
will stimulate the usage of dark excitons in schemes to generate photons from quantum dots.
2020

T.T. Saraiva, P.J.F. Cavalcanti, A. Vagov, A.S. Vasenko, A. Perali, L. Dell’Anna and A.A. Shanenko,
 Multiband Material with a Quasi1D Band as a Robust HighTemperature Superconductor
Abstract:
It is well known that superconductivity in quasionedimensional (Q1D) materials is hindered by large fluctuations of the order parameter. They reduce the critical temperature and can even destroy the superconductivity altogether. Here it is demonstrated that the situation changes dramatically when a Q1D pair condensate is coupled to a higherdimensional stable one, as in recently discovered multiband Q1D superconductors. The fluctuations are suppressed even by vanishingly small pairexchange coupling between different band condensates and the superconductor is well described by the mean field theory. In this case the low dimensionality effects enhance the coherence of the system instead of suppressing it. As a result, the critical temperature of the multiband Q1D superconductor can increase by orders of magnitude when the system is tuned to the Lifshitz transition with the Fermi level close to the edge of the Q1D band.
Supplement

M. Cosacchi, J. Wiercinski, T. Seidelmann, M. Cygorek,
A. Vagov, D. E. Reiter and V.M. Axt,
 Ondemand generation of higherorder Fock states in quantumdotcavity systems
Abstract:
The ondemand preparation of higherorder Fock states is of fundamental importance in quantum information
sciences. We propose and compare different protocols to generate higherorder Fock states in solid state
quantumdot–cavity systems. The protocols make use of a series of laser pulses to excite the quantum dot
exciton and offresonant pulses to control the detuning between dot and cavity. Our theoretical studies include
dot and cavity loss processes as well as the puredephasing type coupling to longitudinal acoustic phonons in
a numerically complete fashion. By going beyond the twolevel approximation for quantum dots, we study the
impact of a ﬁnite exchange splitting, the impact of a higher energetic exciton state, and an excitation with linearly
polarized laser pulses leading to detrimental occupations of the biexciton state. We predict that under realistic conditions, a protocol which keeps the cavity at resonance with the quantum dot until the desired target state is reached is able to deliver fidelities to the Fock state 5> well above 40%.

A.E. Lukyanov, V. D. Neverov, Y.V. Zhumagulov, A.P. Menushenkov, A.V. Krasavin and A. Vagov,
 Laserinduced ultrafast insulatormetal transition in BaBiO3
Abstract:
We investigate ultrafast coherent quantum dynamics of undoped BaBiO3 driven by a strong laser pulse. Our calculations demonstrate that in a wide range of radiation frequencies and intensities the system undergoes a transient change from the insulating to the metallic state, where the charge density wave and the corresponding energy spectrum gap vanish. The transition takes place on the ultrafast timescale of tens femtoseconds, comparable to the period of the corresponding lattice vibrations. The dynamics are determined by a complex interplay of the particlehole excitation over the gap and of the tunneling through it, giving rise to the highly nontrivial time evolution which comprises high harmonics and reveals periodic reappearance of the gap. The time evolution is obtained by solving the dynamical meanfield theory equations with the realistic parameters for the system and radiation. Results are summarized in the phase diagram, helpful for a possible experimental setup to achieve a dynamical control over the conduction state of this and other materials with the similarly strong electronphonon interaction.
Supplement

F. Trybel , M. Cosacchi, T. Meier, V.M. Axt and G. SteinleNeumann,
 Proton dynamics in highpressure iceVII from density functional theory
Abstract:
Using a density functional theory based approach, we explore the symmetrization and proton dynamics in
iceVII, for which recent highpressure NMR experiments indicate signiﬁcant proton dynamics in the pressure
range of 20–95 GPa. We directly sample the potential seen by the proton and ﬁnd a continuous transition from
double to singlewell character over the pressure range of 2 to 130 GPa accompanied by proton dynamics, in
agreement with the NMR experiments.
Supplement

M.D. Croitoru, A.A. Shanenko, Y. Chen, A. Vagov and J. Albino Aguiar,
 Microscopic description of surface superconductivity
Abstract:
In this work, we revisit the problem of superconductivity under the influence of boundary effects. By solving the Bogoliubovde Gennes (BdG) equations for the tightbinding model, we demonstrate that the critical temperature of the nucleation of superconductivity near a sample surface can be considerably enhanced as compared to its bulk value. To bring to light this effect, we investigate different methods to solve numerically the BdG equations, including the continuous and Anderson approximations, and perform the calculations for a wide range of the system parameters. We obtain that all the selfconsistent BdG eigenstates are delocalized and occupy the entire volume of the sample. Our results reveal that the enhancement of the surface critical temperature originates from the quantum interference of different BdG states contributing to the order parameter. We also find that the surface enhancement is the largest when the conduction band is symmetric with respect to the Fermi level, particularly, the half filling is an important proviso for the pronounced surface effect on the critical temperature. The approximate continuous model as well as the Anderson approximation do not capture the main feature of the surface effect. In addition, our study of this effect versus surface roughness reveals its fragile character.

Y.V. Zhumagulov, A. Vagov, N.Yu. Senkevich, D.R. Gulevich and V. Perebeinos,
 Threeparticle states and brightening of intervalley excitons in a doped MoS2 monolayer
Abstract:
Optical spectra of twodimensional transitionmetal dichalcogenides (TMDC) are influenced by complex multiparticle excitonic states. Their theoretical analysis requires solving the manybody problem, which in most cases, is prohibitively complicated. In this work, we calculate the optical spectra by exact diagonalization of the threeparticle Hamiltonian within the TammDancoff approximation where the doping effects are accounted for via the Pauli blocking mechanism, modelled by a discretized mesh in the momentum space. The singleparticle basis is extracted from the ab initio calculations. Obtained threeparticle eigenstates and the corresponding transition dipole matrix elements are used to calculate the linear absorption spectra as a function of the doping level. Results for negatively doped MoS2 monolayer (ML) are in excellent quantitative agreement with the available experimental data, validating our approach. The results predict additional spectral features due to the intervalley exciton that is optically dark in an undoped ML but is brightened by the doping. Our approach can be applied to a plethora of other atomically thin semiconductors, where the doping induced brightening of the manyparticle states is also anticipated.

A. Vagov, S. Wolf, M.D. Croitoru and A.A. Shanenko,
 Universal flux patterns and their interchange in superconductors between types I and II
Abstract:
Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic ﬂux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such conﬁgurations has not been presented. We solve this oldstanding fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic conﬁgurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the selfduality of the theory that is universal and not sensitive to the microscopic details.

M. Cosacchi, T. Seidelmann, F. Ungar, M. Cygorek, A. Vagov and V.M. Axt,
 Transiently changing shape of the photon number distribution in a quantumdotcavity system driven by chirped laser pulses
Abstract:
We have simulated the time evolution of the photon number distribution in a semiconductor quantumdot–microcavity system driven by chirped laser pulses and compare with unchirped results. When phonon interactions with the dot are disregarded—thus corresponding to the limit of atomic cavity systems—chirped pulses generate photon number distributions that change their shape drastically in the course of time. Phonons have a strong and qualitative impact on the photon statistics. The asymmetry between phonon absorption and emission destroys the symmetry of the photon distributions obtained for positive and negative chirps. While for negative chirps transient distributions resembling thermal ones are observed, for positive chirps the photon
number distribution still resembles its phononfree counterpart but with overall smoother shapes. In sharp contrast, using unchirped pulses of the same pulse area and duration wave packets are found that move up and down the JaynesCummings ladder with a bell shape that changes little in time. For shorter pulses and lower driving strength Rabilike oscillations occur between low photon number states. For all considered excitation conditions transitions between sub and superPoissonian statistics are found at certain times. For resonant driving with low intensity the Mandel parameter oscillates and is mostly negative, which indicates a nonclassical state in the cavity ﬁeld. Finally, we show that it is possible that the Mandel parameter dynamically approaches zero and still the photon distribution exhibits two maxima and thus is far from being a Poissonian.

A.A. VargasParedes, A.A. Shanenko, A. Vagov, M.V. Milošević and A. Perali,
 Crossband versus intraband pairing in superconductors: Signatures and consequences of the interplay
Abstract:
We analyze the paradigmatic competition between intraband and crossband Cooperpair formation in twoband superconductors, neglected in most works to date. We derive the phasesensitive gap equations and describe the crossover between the intrabanddominated and the crossbanddominated regimes, delimited by a “gapless” state. Experimental signatures of crosspairing comprise notable gap splitting in the excitation spectrum, nonBCS behavior of gaps versus temperature, as well as changes in the pairing symmetry as a function of temperature. The consequences of these findings are illustrated on the examples of MgB2 and Ba0.6K0.4Fe2As2.

P.J. F. Cavalcanti, T.T. Saraiva, J. Albino Aguiar, A. Vagov, M.D. Croitoru and A.A. Shanenko,
 Multiband superconductors with degenerate excitation gaps
Abstract:
There is a tacit assumption that multiband superconductors are essentially the same as multigap superconductors. More precisely, it is usually assumed that the number of excitation gaps in the singleparticle energy spectrum of a uniform superconductor (i.e. number of peaks in the density of states of the superconducting electrons) determines the number of contributing bands in the corresponding superconducting model. Here we demonstrate that contrary to this widely accepted viewpoint, the superconducting magnetic properties are sensitive to the number of contributing bands even when the spectral gaps are degenerate and cannot be distinguished. In particular, we find that the crossover between superconductivity types I and II—the intertype regime—is strongly affected by the difference between characteristic lengths of multiple contributing condensates. The reason for this is that condensates with diverse characteristic lengths, when coexisting in one system, interfere constructively or destructively, which results in multicondensate magnetic phenomena regardless of the presence/absence of the multigap spectrum of a superconducting multiband material.

W.Y. CórdobaCamacho, R.M. da Silva, A.A. Shanenko , A. Vagov, A.S. Vasenko, B.G. Lvov and J. Albino Aguiar,
 Spontaneous pattern formation in superconducting films
Abstract:
Superconducting films are usually regarded as type II superconductors even when they are made of a type I material. The reason is the presence of stray magnetic fields that stabilize the vortex matter by inducing longrange repulsive interactions between vortices. While very thin films indeed reach this limit, there is a large interval of thicknesses where magnetic properties of superconducting films cannot be classified as either of the two conventional superconductivity types. Recent calculations revealed that in this interval the system exhibits spontaneous formation of magnetic fluxcondensate patterns and superstructures appearing due to the interplay between the longrange stray field effects and proximity to the Bogomolnyi selfduality point. These calculations were based on the periodic inplane boundary conditions which, as is well known from classical electrodynamics, for systems with longrange interactions can lead to field distortions and considerable discrepancies between results of different calculation methods. Here we demonstrate that similar spontaneous patterns are obtained for superconducting films with open inplane boundary conditions (vanishing inplane currents perpendicular to the edges of the finite film) and thus the phenomenon is not an artefact of chosen boundary conditions.

Y.V. Zhumagulov, A.Vagov, D.R. Gulevich, P.E. Faria Junior and V. Perebeinos,
 Trion induced photoluminescence of a doped MoS2 monolayer
Abstract:
We demonstrate that the temperature and doping dependencies of the photoluminescence (PL) spectra of a doped MoS_{2} monolayer have several peculiar characteristics defined by the trion radiative decay. While only zeromomentum exciton states are coupled to light, radiative recombination of nonzero momentum trions is also allowed. This leads to an asymmetric broadening of the trion spectral peak and redshift of the emitted light with increasing temperature. The lowest energy trion state is dark, which is manifested by the sharply nonmonotonic temperature dependence of the PL intensity. Our calculations combine the Dirac model for the singleparticle states, with parameters obtained from the firstprinciples calculations, and the direct solution of the threeparticle problem within the Tamm–Dancoff approximation. The numerical results are well captured by a simple model that yields analytical expressions for the temperature dependencies of the PL spectra
2019

D.E. Reiter, T. Kuhn and V.M. Axt,
 Distinctive characteristics of carrierphonon interactions in optically driven semiconductor quantum dots
Abstract:
We review distinct features arising from the unique nature of the carrierphonon coupling in selfassembled semiconductor quantum dots. Because of the discrete electronic energy structure, the pure dephasing coupling usually dominates the phonon effects, of which two properties are of key importance: The resonant nature of the dotphonon coupling, i.e. its nonmonotonic behavior as a function of energy, and the fact that it is of superOhmic type. Phonons do not only act destructively in quantum dots by introducing dephasing, they also offer new opportunities, e.g. in state preparation protocols. Apart from being an interesting model systems for studying fundamental physical aspects, quantum dot and quantum dotmicrocavity systems are a hotspot for many innovative applications. We discuss recent developments related to the decisive impact of phonons on key figures of merit of photonic devices like single or entangled photon sources under aspects like indistinguishability, purity and brightness. All in all it follows that understanding and controlling the carrierphonon interaction in semiconductor quantum dots is vital for their usage in quantum information technology.

T. Seidelmann, F. Ungar, A.M. Barth, A. Vagov, V.M. Axt, M. Cygorek and T. Kuhn,
 PhononInduced Enhancement of Photon Entanglement in Quantum DotCavity Systems
Abstract:
We report on simulations of the degree of polarization entanglement of photon pairs simultaneously
emitted from a quantum dotcavity system that demand revisiting the role of phonons. Since coherence is a
fundamental precondition for entanglement and phonons are known to be a major source of decoherence, it
seems unavoidable that phonons can only degrade entanglement. In contrast, we demonstrate that phonons
can cause a degree of entanglement that even surpasses the corresponding value for the phononfree case. In
particular, we consider the situation of comparatively small biexciton binding energies and either finite
exciton or cavity mode splitting. In both cases, combinations of the splitting and the dotcavity coupling
strength are found where the entanglement exhibits a nonmonotonic temperature dependence which
enables entanglement above the phononfree level in a finite parameter range. This unusual behavior can be
explained by phononinduced renormalizations of the dotcavity coupling g in combination with a
nonmonotonic dependence of the entanglement on g that is present already without phonons.
Supplement

M. Cosacchi, F. Ungar, M. Cygorek, A. Vagov and V.M. Axt,
 EmissionFrequency Separated High Quality SinglePhoton Sources Enabled by Phonons
Abstract:
We demonstrate theoretically that the singlephoton purity of photons emitted from a quantum dot exciton prepared by phononassisted offresonant excitation can be significantly higher in a wide range of parameters than that obtained by resonant preparation for otherwise identical conditions. Despite the offresonant excitation, the brightness stays on a high level. These surprising findings exploit the fact that the phononassisted preparation is a twostep process where phonons first lead to a relaxation between laserdressed states while high exciton occupations are reached only with a delay to the laser pulse maximum by adiabatically undressing the dot states. Due to this delay, possible subsequent processes, in particular multiphoton excitations, appear at a time when the laser pulse is almost gone. The resulting suppression of reexcitation processes increases the singlephoton purity. Due to the spectral separation of the signal photons from the laser frequencies this enables the emission of high quality single photons not disturbed by a laser background while taking advantage of the robustness of the phonon assisted scheme.
Supplement

F. Ungar, P.I. Tamborenea and V.M. Axt,
 Spin dynamics of hot excitons in diluted magnetic semiconductors with spinorbit interaction
Abstract:
We explore the impact of a Rashbatype spinorbit interaction in the conduction band on the spin dynamics of hot excitons in diluted magnetic semiconductor quantum wells. In materials with strong spinorbit coupling, we identify parameter regimes where spinorbit effects greatly accelerate the spin decay and even change the dynamics qualitatively in the form of damped oscillations. Furthermore, we show that the application of a small external magnetic field can be used to either mitigate the influence of spinorbit coupling or entirely remove its effects for fields above a materialdependent threshold.
Erratum: Phys. Rev. B 100, 089901(E) (2019)

F. Ungar, M. Cygorek and V.M. Axt,
 Origins of overshoots in the exciton spin dynamics in semiconductors
Abstract:
We investigate the origin of overshoots in the exciton spin dynamics after resonant optical excitation. As a material system, we focus on diluted magnetic semiconductor quantum wells as they provide a strong spinflip scattering for the carriers. Our study shows that overshoots can appear as a consequence of radiative decay even on the singleparticle level in a theory without any memory. The magnitude of the overshoots in this case depends strongly on the temperature as well as the doping fraction of the material. If manybody effects beyond the singleparticle level become important so that a quantumkinetic description is required, a spin overshoot appears already without radiative decay and is much more robust against variations of system parameters. We show that the origin of the spin overshoot can be determined either via its temperature dependence or via its behavior for different doping fractions. The results can be expected to apply to a wide range of semiconductors as long as radiative decay and a spinflip mechanism are present.
Erratum: Phys. Rev. B 100, 049902(E) (2019)

F. Ungar, M. Cygorek and V.M. Axt,
 Phononinduced quantum ratchet in the exciton spin dynamics in diluted magnetic semiconductors in a magnetic field
Abstract:
Magnetically doped semiconductors are well known for their giant Zeeman splittings which can reach several meV even in relatively small external magnetic fields. After preparing a nonequilibrium exciton distribution via optical excitation, the spin dynamics in diluted magnetic semiconductor quantum wells is typically governed by spinflip scattering processes due to the excitonimpurity exchange interaction. Our theoretical calculations show that the giant Zeeman splitting in these materials in combination with the influence of longitudinal acoustic phonons lead to a quantum ratchettype dynamics, resulting in an almost complete reversal of the carrier spin polarization at very low temperatures. Furthermore, we find that the predictions of a much simpler rateequation approach qualitatively agree with a more advanced and numerically demanding quantumkinetic description of the spin dynamics for a wide range of temperatures, although quantitative differences are noticeable.

T. Seidelmann, F. Ungar, M. Cygorek, A. Vagov, A.M. Barth, T. Kuhn and V.M. Axt,
 From strong to weak temperature dependence of the twophoton entanglement resulting from the biexciton cascade inside a cavity
Abstract:
We investigate the degree of entanglement quantified by the concurrence of photon pairs that are simultaneously emitted in the biexcitonexciton cascade from a quantum dot in a cavity. Four dotcavity configurations are compared that differ with respect to the detuning between the cavity modes and the quantum dot transitions, corresponding to different relative weights of direct twophoton and sequential singlephoton processes. The dependence of the entanglement on the exciton finestructure splitting δ is found to be significantly different for each of the four configurations. For a finite splitting and low temperatures, the highest entanglement is found when the cavity modes are in resonance with the twophoton transition between the biexciton and the ground state and, in addition, the biexciton has a finite binding energy of a few meV. However, this widely used configuration is rather strongly affected by phonons such that other dotcavity configurations, that are commonly regarded as less suited for obtaining high degrees of entanglement, become more favorable already at temperatures on the order of 10K and above. If the cavity modes are kept in resonance with one of the excitontogroundstate transitions and the biexciton binding energy is finite, the entanglement drastically drops for positive δ with rising temperatures when T is below ≃4K, but is virtually independent of the temperature for higher T.

F. Ungar, M. Cygorek and V.M. Axt,
 Role of excited states in the dynamics of excitons and their spins in diluted magnetic semiconductors
Abstract:
We theoretically investigate the impact of excited states on the dynamics of the exciton ground state in diluted magnetic semiconductor quantum wells. Exploiting the giant Zeeman shift in these materials, an external magnetic ﬁeld is used to bring transitions between the exciton ground state and excited states close to resonance. It turns out that, when treating the exciton dynamics in terms of a quantum kinetic theory beyond the Markov approximation, higher exciton states are populated already well below the critical magnetic ﬁeld required to bring the exciton ground state in resonance to an excited state. This behavior is explained by excitonimpurity correlations that can bridge energy differences on the order of a few meV and require a quantum kinetic description beyond the independentparticle picture. Of particular interest is the signiﬁcant spin transfer toward
states on the optically dark 2p exciton parabola which are protected against radiative decay.

F. Ungar, M. Cygorek and V.M. Axt,
 Phonon impact on the dynamics of resonantly excited and hot excitons in diluted magnetic semiconductors
Abstract:
Phonons are well known to be the main mechanism for the coupling between bright and dark excitons in
nonmagnetic semiconductors. Here, we investigate diluted magnetic semiconductors where this process is in
direct competition with the scattering at localized magnetic impurities. To this end, a recently developed quantum
kinetic description of the exciton spin dynamics in diluted magnetic semiconductor quantum wells is extended
by the scattering with longitudinal acoustic phonons. A strong phonon impact is found in the redistribution
of exciton momenta on the exciton parabola that becomes especially prominent for high temperatures and
exciton distributions further away from the exciton resonance which are optically dark. Despite their impact
on the energetic redistribution, acoustic phonons virtually do not affect the exciton spin dynamics as the
excitonimpurity interaction always dominates. Furthermore, it turns out that the exciton spin lifetime increases
by roughly one order of magnitude for nonequilibrium hot exciton distributions and, in addition, pronounced
quantum kinetic signatures in the exciton spin dynamics appearing after resonant optical excitation are drastically
reduced.

L. Salasnich, A.A. Shanenko, A. Vagov, J. Albino Aguiar and A. Perali,
 Screening of pair fluctuations in superconductors with coupled shallow and deep bands: A route to highertemperature superconductivity
Abstract:
A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize highTc superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with the Josephsonlike pair transfer between the bands to couple the two condensates, realizes an optimal multicomponent superconductivity regime: it preserves strong pairing to generate large gaps and a very high critical temperature but screens the detrimental superconducting fluctuations, thereby suppressing the pseudogap state. Surprisingly, we find that the screening is very efficient even when the interband coupling is very small. Thus, a multiband superconductor with a coherent mixture of condensates in the BCS regime (deep band) and in the BCSBEC crossover regime (shallow band) offers a promising route to higher critical temperatures.

T.T. Saraiva, A. Vagov, V.M. Axt, J. Albino Aguiar and A.A. Shanenko,
 Anisotropic superconductors between types I and II
Abstract:
Selfduality or matching between the magnetic and the condensate coherence lengths is a fundamental property of isotropic superconductors at the critical Bogomolnyi point (B point). The selfdual state of the condensate is infinitely degenerate, which is the core reason for the sharp transition between the superconductivity types in the nearest vicinity of the critical temperature Tc. Below Tc nonlocal interactions in the condensate remove the degeneracy, which leads to the appearance of a finite intertype (IT) domain between types I and II. This domain exhibits the mixed state with exotic fieldcondensate configurations and nonstandard magnetic response, which cannot be understood within the dichotomy of the conventional superconductivity types. At a first glance, this picture does not apply to an anisotropic system because no spatial matching between the condensate and magnetic field can be generally expected for directiondependent characteristic lengths. However, contrary to these expectations, here we demonstrate that anisotropic superconductors follow the same scenario of the interchange between types I and II. In anisotropic materials the IT domain is governed by the B point of the effective isotropic model obtained by the appropriate scaling transformation of the initial anisotropic formalism. This transformation depends on the direction of the applied magnetic field, and thus the superconductivity type of strongly anisotropic materials can be dependent on this direction.

D.R. Gulevich, Ya.V. Zhumagulov, A. Vagov and V. Perebeinos,
 Nonadiabatic electron dynamics in timedependent density functional theory at the cost of adiabatic local density approximation
Abstract:
We propose a computationally efficient approach to account for the nonadiabatic effects in timedependent density functional theory (TDDFT) based on a representation of the frequencydependent exchangecorrelation kernel as a response of a set of damped oscillators. The requirements to computational resources needed to implement our approach do not differ from those of the standard realtime TDDFT in the adiabatic local density approximation. Thus, our result offers an exciting opportunity to take into account temporal nonlocality and memory effects in calculations with TDDFT in quantum chemistry and solid state physics for unprecedentedly low costs.
2018

F. Ungar, M. Cygorek and V.M. Axt,
 Manybody correlations brought to light in absorption spectra of diluted magnetic semiconductors
Abstract:
Diluted magnetic semiconductors are materials well known to exhibit strong correlations which typically manifest in carriermediated magnetic ordering. In this Rapid Communication, we show that the interaction between excitons and magnetic impurities in these materials is even strong enough to cause a significant deviation from the bare exciton picture in linear absorption spectra of quantum well nanostructures. It is found that excitonimpurity correlations induce a characteristic fingerprint in the form of an additional feature close to the exciton resonance in combination with a shift of the main exciton line of up to a few meV. We trace back these features to the form of the selfenergy and demonstrate that reliable values of the average correlation energy per exciton can be extracted directly from the spectra. Since the only requirement for our findings is sufficiently strong correlations, the results can be generalized to other strongly correlated systems.
Supplement

M. Cosacchi, M. Cygorek, F. Ungar, A.M. Barth, A. Vagov and V.M. Axt,
 Pathintegral approach for nonequilibrium multitime correlation functions of open quantum systems coupled to Markovian and nonMarkovian environments
Abstract:
Using a realtime path integral approach we develop an algorithm to calculate multitime correlation functions of open fewlevel quantum systems that is applicable to highly nonequilibrium dynamics. The calculational scheme fully keeps the nonMarkovian memory introduced by the puredephasing type coupling to a continuum of oscillators. Furthermore, we discuss how to deal consistently with the simultaneous presence of nonMarkovian and Markovian system reservoir interactions. We apply the method to a crucial test case, namely the evaluation of emission spectra of a laserdriven twolevel quantum dot coupled to a continuum of longitudinal acoustic phonons, which give rise to nonMarkovian dynamics. Here, we also account for the coupling to a photonic environment, which models radiative decay and can be treated as a Markovian bath. The phonon side bands are found on the correct side of the zero phonon line in our calculation, in contrast to known results where the quantum regression theorem is applied naively to nonMarkovian dynamics. Combining our algorithm with a recently improved iteration scheme for performing the required sum over paths we demonstrate the numerical feasibility of our approach to systems with more than two levels. Results are shown for the secondorder photonic twotime correlation function of a quantum dotcavity system with seven states on the JaynesCummings ladder taken into account.
Editors' Suggestion

S. Hannibal, P. Kettmann, M.D. Croitoru, V.M. Axt and T. Kuhn,
 Persistent oscillations of the order parameter and interaction quench phase diagram for a confined BardeenCooperSchrieffer Fermi gas
Abstract:
We present a numerical study of the interaction quench dynamics in a superfluid ultracold Fermi gas confined in a threedimensional cigarshaped harmonic trap. In the present paper, we investigate the amplitude mode of the superfluid order parameter after interaction quenches, which start deep in the BCS phase and end in the BCSBECcrossover regime. To this end, we exploit the Bogoliubov–de Gennes formalism, which takes the confinement potential explicitly into account and provides a microscopic fully coherent description of the system. We find an anharmonic nonlinear oscillation of the modulus of the superfluid order parameter, i.e., of the Higgs mode. This oscillation persists for large times with only a small amplitude modulation being visible. We connect the frequency and the mean value of this oscillation with the breaking of Cooper pairs in the superfluid phase. Additionally, we demonstrate that the occurrence of this persistent oscillation is connected to the onset of chaotic dynamics in our model. Finally, we calculate an interaction quench phase diagram of the Higgs mode for quenches on the BCS side of the BCSBEC crossover and discuss its properties as a function of the aspect ratio of the cigarshaped trap.

M. Cygorek, F. Ungar, T. Seidelmann, A.M. Barth, A. Vagov, V.M. Axt and T. Kuhn,
 Comparison of different concurrences characterizing photon pairs generated in the biexciton cascade in quantum dots coupled to microcavities
Abstract:
We compare three different notions of concurrence to measure the polarization entanglement of twophoton states generated by the biexciton cascade in a quantum dot embedded in a microcavity. The focus of the paper lies on the oftendiscussed situation of a dot with ﬁnite biexciton binding energy in a cavity tuned to the twophoton resonance. Apart from the timedependent concurrence, which can be assigned to the twophoton density matrix at any point in time, we study single and doubletime integrated concurrences commonly used in the literature that are based on different quantum state reconstruction schemes. In terms of the photons detected in coincidence measurements, we argue that the singletime integrated concurrence can be thought of as the concurrence of photons simultaneously emitted from the cavity without resolving the common emission time, while the more widely studied doubletime integrated concurrence refers to photons that are neither ﬁltered with respect to the emission time of the ﬁrst photon nor with respect to the delay time between the two emitted photons. Analytic and numerical calculations reveal that the singletime integrated concurrence indeed agrees well with the typical value of the timedependent concurrence at long times, even when the interaction between the quantum dot and longitudinal acoustic phonons is accounted for. Thus the more easily measurable singletime integrated concurrence gives access to the physical information represented by the timedependent concurrence. However, the doubletime integrated concurrence shows a different behavior with respect to changes in the exciton ﬁne structure splitting and even displays a completely different trend when the ratio between the cavity loss rate and the ﬁne structure splitting is varied while keeping their product constant. This implies the nonequivalence of the physical information contained in the timedependent and singletime integrated concurrence on the one hand and the doubletime integrated concurrence on the other hand.

S. Hannibal, P. Kettmann, M.D. Croitoru, V.M. Axt and T. Kuhn,
 Dynamical vanishing of the order parameter in a confined BardeenCooperSchrieffer Fermi gas after an interaction quench
Abstract:
We present a numerical study of the Higgs mode in an ultracold confined Fermi gas after an interaction quench and find a dynamical vanishing of the superfluid order parameter. Our calculations are done within a microscopic densitymatrix approach in the Bogoliubov–de Gennes framework which takes the threedimensional cigarshaped confinement explicitly into account. In this framework, we study the amplitude mode of the order parameter after interaction quenches starting on the BCS side of the BECBCS crossover close to the transition and ending in the BCS regime. We demonstrate the emergence of a dynamically vanishing superfluid order parameter in the spatiotemporal dynamics in a threedimensional trap. Further, we show that the signal averaged over the whole trap mirrors the spatiotemporal behavior and allows us to systematically study the effects of the system size and aspect ratio on the observed dynamics. Our analysis enables us to connect the confinementinduced modifications of the dynamics to the pairing properties of the system. Finally, we demonstrate that the signature of the Higgs mode is contained in the dynamical signal of the condensate fraction, which, therefore, might provide a new experimental access to the nonadiabatic regime of the Higgs mode.

F. Ungar, M. Cygorek and V.M. Axt,
 Trend reversal in the magneticfield dependence of exciton spintransfer rates in diluted magnetic semiconductors due to nonMarkovian dynamics
Abstract:
We investigate theoretically the influence of an external magnetic field on the spin dynamics of excitons in diluted magnetic semiconductor quantum wells. To this end, we apply a quantum kinetic theory beyond the Markov approximation which reveals that nonMarkovian effects can significantly influence the exciton spin dynamics. If the magnetic field is oriented parallel to the growth direction of the well, the Markovian spintransfer rate decreases monotonically with increasing field as predicted by Fermi's golden rule. The quantum kinetic theory follows this result qualitatively but predicts pronounced quantitative differences in the spintransfer rate as well as in the longtime spin polarization. However, for an inplane magnetic field, where the Markovian spintransfer rate first drops and then increases again, quantum kinetic effects become so pronounced that the Markovian trend is completely reversed. This is made evident by a distinct maximum of the rate followed by a monotonic decrease. The deviations can be traced back to a redistribution of carriers in energy space caused by correlations between excitons and magnetic dopants. The same effect leads to a finite electronspin polarization at long times in longitudinal as well as transverse fields which is much larger than the corresponding Markovian prediction.

W.Y. CórdobaCamacho, R.M. da Silva, A. Vagov, A.A. Shanenko and J. Albino Aguiar,
 Quasionedimensional vortex matter in superconducting nanowires
Abstract:
It is well known that superconducting films made of a typeI material can demonstrate a typeII magnetic response, developing stable vortex configurations in a perpendicular magnetic field. Here we show that the superconducting state of a typeI nanowire undergoes more complex transformations, depending on the nanowire thickness. Sufficiently thin nanowires deviate from type I and develop multiquantum vortices and vortex clusters similar to intertype (IT) vortex states in bulk superconductors between conventional superconductivity types I and II. When the nanowire thickness decreases further, the quasionedimensional vortex matter evolves towards type II so that the IT vortex configurations gradually disappear in favor of the standard Abrikosov lattice (chain) of singlequantum vortices. However, type II is not reached. Instead, an ultrathin nanowire reenters abruptly the typeI regime while vortices tend to be suppressed by the boundaries, eventually becoming onedimensional phaseslip centers. Our results demonstrate that arrays of nanowires can be used to construct composite superconducting materials with a widely tunable magnetic response.
2017

I.A. Larkin, K. Keil, A. Vagov, M.D. Croitoru and V.M. Axt,
 Superanomalous Skin Effect for Surface Plasmon Polaritons
Abstract:
It is commonly assumed that surface plasmonpolariton (SPP) excitations on a metaldielectric interface decay exponentially inside the metallic sample. Here, we show that in a wide spectral interval the SPP field decays much slower, being inversely proportional to the distance to the interface modified by an additional logarithmic factor. This dependence differs from the standard anomalous skin effect and is provisionally referred to as superanomalous. Its origin is the nonlocality and the logarithmic singularity of the dielectric permittivity in metals. This type of decay is pronounced for SPP modes of higher frequencies, but it is suppressed for light waves.
Editors' Suggestion

T. Papenkort, V.M. Axt and T. Kuhn,
 Stationary Phonon Squeezing by Optical Polaron Excitation
Abstract:
We demonstrate that a stationary squeezed phonon state can be prepared by a pulsed optical excitation of a semiconductor quantum well. Unlike previously discussed scenarios for generating squeezed phonons, the corresponding uncertainties become stationary after the excitation and do not oscillate in time. The effect is caused by twophonon correlations within the excited polaron. We demonstrate by quantum kinetic simulations and by a perturbation analysis that the energetically lowest polaron state comprises twophonon correlations which, after the pulse, result in an uncertainty of the lattice momentum that is continuously lower than in the ground state of the semiconductor. The simulations show the dynamics of the polaron formation process and the resulting timedependent lattice uncertainties.

M. Cygorek, A.M. Barth, F. Ungar, A. Vagov and V.M. Axt,
 Nonlinear cavity feeding and unconventional photon statistics in solidstate cavity QED revealed by manylevel realtime pathintegral calculations
Abstract:
The generation of photons in a microcavity coupled to a laserdriven quantum dot interacting with longitudinal acoustic (LA) phonons is studied in the regime of simultaneously strong driving and strong dotcavity coupling. The stationary cavity photon number is found to depend in a nontrivial way on the detuning between the laser and the exciton transition in the dot. In particular, the maximal efficiency of the cavity feeding is obtained for detunings corresponding to transition energies between cavitydressed states with excitation numbers larger than one. Phonons significantly enhance the cavity feeding at large detunings. In the strongdriving, strongcoupling limit, the photon statistics is highly nonPoissonian. While without phonons a doublepeaked structure in the photon distribution is predicted, phonons make the photon statistics thermallike with very high effective temperatures ∼105 K, even for low phonon temperatures ∼4 K. These results were obtained by numerical calculations where the driving, the dotcavity coupling, and the dotphonon interactions are taken into account without approximations. This is achieved by a reformulation of an exact iterative pathintegral scheme which is applicable to a large class of quantumdissipative systems and which in our case reduces the numerical demands by 15 orders of magnitude.
Supplement
Erratum: Phys. Rev. B 99, 079906(E) (2019)

A. Vagov, M.D. Croitoru, I.A. Larkin and V.M. Axt,
 NonLocality Effects in Excitation and Spatial Propagation of Surface PlasmonPolaritons
Abstract:
This work investigates the influence of nonlocality in the dielectric response on the spatiotemporal evolution of surface plasmonpolaritons (SPP). SPP excitations are coherently generated by a quantum scatterer in the vicinity of a flat metal interface. It is demonstrated that the excited nonequilibrium SPP population eventually splits into two coherent localized wave packets. One packet propagates along the interface and the other is centered in the vicinity of the scatter. The amplitude of both waves slowly decreases due to several relaxation mechanisms, with the Landau damping being the strongest. The nonlocality of the metallic dielectric response considerably influences spatial profiles of the plasmon field intensity, in particular, leading to coherent spatiotemporal oscillations between the two wave packets.

S. Wolf, A. Vagov, A.A. Shanenko, V.M. Axt and J. Albino Aguiar,
 Vortex matter stabilized by manybody interactions
Abstract:
This work investigates interactions of vortices in superconducting materials between standard types I and II, in the domain of the socalled intertype (IT) superconductivity. Contrary to common expectations, the manybody (manyvortex) contribution is not a correction to the pairvortex interaction here but plays a crucial role in the formation of the IT vortex matter. In particular, the manybody interactions stabilize vortex clusters that otherwise could not exist. Furthermore, clusters with large numbers of vortices become more stable when approaching the boundary between the intertype domain and type I. This indicates that IT superconductors develop a peculiar unconventional type of the vortex matter governed by the manybody interactions of vortices.

A.S. Mosquera Polo, R.M. da Silva, A. Vagov, A.A. Shanenko, C.E. Deluque Toro and J. Albino Aguiar,
 Nonequilibrium interband phase textures induced by vortex splitting in twoband superconductors
Abstract:
We demonstrate that in a weakcoupled twoband superconducting slab the interaction between vortices penetrating the sample and its boundaries leads to the phenomenon of vortex splitting, which divides composite vortices and creates fractional ones. The interaction between vortices, attractive for different bands and repulsive for the same band, which is controlled by the electric current density flowing through the system, leads to an ordered alternating arrangement of the vortices. This arrangement creates nonequilibrium interband phase textures or domains with different signs of the Josephson energy of the interaction between the band condensates. Such phase textures have a significant effect on the dissipation caused by the vortex motion. In particular, in the phasetexture regime the onset of the dissipation is shifted to higher current densities.

P. Kettmann, S. Hannibal, M.D. Croitoru, V.M. Axt and T. Kuhn,
 Pure Goldstone mode in the quench dynamics of a confined ultracold Fermi gas in the BCSBEC crossover regime
Abstract:
We present a numerical study of the dynamic response of a confined superfluid Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic timedependent densitymatrix approach within the full Bogoliubov–de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigarshaped 6Li gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potential but that it is determined by the details of the quench. Thus we report the emergence of a pure Goldstone mode of the BCS gap that—in contrast to situations in many previous studies—maintains its gapless excitation spectrum predicted by the Goldstone theorem. Furthermore, we observe that the sizedependent superfluid resonances resulting from the atypical BCSBEC crossover have a direct impact on this Goldstone mode. Finally, we find that the interaction quenchinduced Goldstone mode leads to a lowfrequency inphase oscillation of the singleparticle occupations with complete inversion of the lowestlying singleparticle states which could provide a convenient experimental access to the pure gapless Goldstone mode.

F. Ungar, M. Cygorek and V.M. Axt,
 Quantum kinetic equations for the ultrafast spin dynamics of excitons in diluted magnetic semiconductor quantum wells after optical excitation
Abstract:
Quantum kinetic equations of motion for the description of the exciton spin dynamics in IIVI diluted magnetic semiconductor quantum wells with laser driving are derived. The model includes the magnetic as well as the nonmagnetic carrierimpurity interaction, the Coulomb interaction, Zeeman terms, and the lightmatter coupling, allowing for an explicit treatment of arbitrary excitation pulses. Based on a dynamicscontrolled truncation scheme, contributions to the equations of motion up to second order in the generating laser field are taken into account. The correlations between the carrier and the impurity subsystems are treated within the framework of a correlation expansion. For vanishing magnetic field, the Markov limit of the quantum kinetic equations formulated in the exciton basis agrees with existing theories based on Fermi's golden rule. For narrow quantum wells excited at the 1s exciton resonance, numerical quantum kinetic simulations reveal pronounced deviations from the Markovian behavior. In particular, the spin decays initially with approximately half the Markovian rate and a nonmonotonic decay in the form of an overshoot of up to 10% of the initial spin polarization is predicted.
Erratum: Phys. Rev. B 96, 239904(E) (2017)

M. Cosacchi, M. Cygorek, F. Ungar, and V. M. Axt,
 Nonexponential spin decay in a quantum kinetic description of the D'yakonovPerel' mechanism mediated by impurity scattering
Abstract:
The electron spin dynamics in an optically excited narrow quantum well is studied, where the electron spins precess in a kdependent magnetic field, while the electrons scatter at localized impurities. For the resulting spin decay, which is commonly known as the D'yakonovPerel' mechansim, analytical expressions in the strong and weakscattering limits are available. It is found by the numerical solution of quantum kinetic equations in a broad range of parameters that, in situations that are typically relevant for ultrafast optical experiments, the dynamics of the total spin polarization significantly deviates from the pertinent analytical results. This is attributed to the broad spectral width of the optically excited spinpolarized electron distribution, which gives rise to a spin dephasing due to inhomogeneous broadening. Furthermore, it is found that the decay of the spin polarization need not be exponential. The notion of a spin decay time becomes ambiguous and different definitions of spin decay times can lead to different outcomes. The longterm dynamics of the decay of the spin polarization is even dominated by an algebraically decaying component. These findings highlight the importance of the effects of the broad spectral distribution of optically excited carriers in ultrashort magnetooptical experiments.

S. Wolf, A. Vagov, A.A. Shanenko, V.M. Axt, A. Perali and J. Albino Aguiar,
 BCSBEC crossover induced by a shallow band: Pushing standard superconductivity types apart
Abstract:
The appearance of a shallow band(s) drives a superconductor towards the BCSBEC crossover, conventionally associated with notable changes in singleparticle properties and an elevated critical temperature. Here we demonstrate that the proximity to the crossover induced by a shallow band has also a dramatic effect on the phase diagram of the superconducting magnetic properties. When the system passes from the BCS to BEC regime, the intertype domain between superconductivity types I and II enlarges systematically, being inversely proportional to the square of the Cooperpair radius, the main parameter that controls the BCSBEC superconductivity. We also show that despite the presence of a shallow band, the condensate fluctuations are suppressed when it coexists in one material with standard deep bands, as in recent iron chalcogenides FeSexTe1−x and FeSe.

M. Cygorek, F. Ungar, P.I. Tamborenea and V.M. Axt,
 Influence of nonmagnetic impurity scattering on spin dynamics in diluted magnetic semiconductors
Abstract:
The doping of semiconductors with magnetic impurities gives rise not only to a spinspin interaction between quasifree carriers and magnetic impurities but also to a local spinindependent disorder potential for the carriers. Based on a quantum kinetic theory for the carrier and impurity density matrices as well as the magnetic and nonmagnetic carrierimpurity correlations, the influence of the nonmagnetic scattering potential on the spin dynamics in DMS after optical excitation with circularly polarized light is investigated using the example of Mndoped CdTe. It is shown that nonMarkovian effects, which are predicted in calculations where only the magnetic carrierimpurity interaction is accounted for, can be strongly suppressed in the presence of nonmagnetic impurity scattering. This effect can be traced back to a significant redistribution of carriers in kspace which is enabled by the buildup of large carrierimpurity correlation energies. A comparison with the Markov limit of the quantum kinetic theory shows that, in the presence of an external magnetic field parallel to the initial carrier polarization, the asymptotic value of the spin polarization at long times is significantly different in the quantum kinetic and the Markovian calculations. This effect can also be attributed to the formation of strong correlations, which invalidates the semiclassical Markovian picture and it is stronger when the nonmagnetic carrierimpurity interaction is accounted for. In an external magnetic field perpendicular to the initial carrier spin, the correlations are also responsible for a renormalization of the carrier spin precession frequency. Considering only the magnetic carrierimpurity interaction, a significant renormalization is predicted for a very limited set of material parameters and excitation conditions. Accounting also for the nonmagnetic interaction, a relevant renormalization of the precession frequency is found to be more ubiquitous.

I.A. Larkin and A. Vagov,
 Resonant scattering and energy relaxation in quantum dot systems
Abstract:
We propose a new Augerlike mechanism for energy relaxation in quantum dots (QD) driven by resonant scattering of delocalized wetting layer (WL) carriers. It is demonstrated that resonant scattering leads to a considerable increase in the relaxation rate that can explain experimentally obtained relaxation rates. Analytical results for the relaxation rate are obtained for rectangular dots revealing a weak logarithmic dependence on the dot depth and level density. Comparing results for a rectangular and a parabolic QD model we conclude that the relaxation rate is not very sensitive to a chosen model.

P. Kettmann, S. Hannibal, M.D. Croitoru, A. Vagov, V.M. Axt and T. Kuhn,
 Spectral characteristics of the coherent dynamics of the order parameter in superconducting nanorods
Abstract:
Within the densitymatrix formalism based on the Bogoliubovde Gennes equations approach we investigate the dynamics of the nonequilibrium BCS pairing induced by a sudden change of the coupling constant in quasi1D and quasi0D samples. We demonstrate that two different dynamical regimes of the amplitude of the BCS gap can be distinguished: an initially damped oscillation in the case of short quantum wires and purely irregular dynamics in the case of nanorods.
2016

A.M. Barth, A. Vagov and V.M. Axt,
 Pathintegral description of combined Hamiltonian and nonHamiltonian dynamics in quantum dissipative systems
Abstract:
We present a numerical pathintegral iteration scheme for the lowdimensional reduced density matrix of a timedependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled puredephasingtype coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing nonHamiltonian dynamics in the inner system represented, e.g., by Lindbladtype dissipation or relaxation. Our formulation of the pathintegral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Editor's Suggestion
Erratum: Phys. Rev. B 96, 119901(E) (2017)

A. Vagov, A.A. Shanenko, M.V. Milošević, V.M. Axt, V.M. Vinokur, J. Albino Aguiar and F.M. Peeters,
 Superconductivity between standard types: Multiband versus singleband materials
Abstract:
In the nearest vicinity of the critical temperature, types I and II of conventional singleband superconductors interchange at the GinzburgLandau parameter
κ=1/2√ . At lower temperatures this point unfolds into a narrow but finite interval ofκ 's, shaping an intertype (transitional) domain in the(κ,T) plane. In the present work, based on the extended GinzburgLandau formalism, we show that the same picture of the two standard types with the transitional domain in between applies also to multiband superconductors. However, the intertype domain notably widens in the presence of multiple bands and can become extremely large when the system has a significant disparity between the band parameters. It is concluded that many multiband superconductors, such as recently discovered borides and ironbased materials, can belong to the intertype regime.

A. Vagov, I.A. Larkin, M.D. Croitoru and V.M. Axt,
 Role of nonlocality and Landau damping in the dynamics of a quantum dot coupled to surface plasmons
Abstract:
We investigate the dynamics of a quantum emitter (quantum dot) placed in the vicinity of a flat metal surface. The dynamics is induced by the coupling between the emitter and surface plasmonpolaritons. The plasmonpolariton modes are described within a continuous media model with a nonlocal Lindhardtype dielectric response of the metal. The analytic solution of the dynamical equations is obtained in the rotating wave approximation. The results demonstrate a considerable influence of the nonlocality of the electromagnetic response and the Landau damping in the metal. In particular, the relaxation dynamics is characterized by two distinct times that may differ by large amounts as a consequence of the nonlocality of the response. It is also shown that one of the contributions to the relaxation can have a powerlaw longtime asymptote, leading to notable changes in the dynamical pattern.

M. Cygorek, P.I. Tamborenea and V.M. Axt,
 Carrierimpurity spin transfer dynamics in paramagnetic IIVI diluted magnetic semiconductors in the presence of a wavevectordependent magnetic field
Abstract:
Quantum kinetic equations of motion for carrier and impurity spins in paramagnetic IIVI diluted magnetic semiconductors in a
k dependent effective magnetic field are derived, where the carrierimpurity correlations are taken into account. In the Markov limit, rates for the electronimpurity spin transfer can be derived for electron spins parallel and perpendicular to the impurity spins corresponding to measurable decay rates in Kerr experiments in Faraday and Voigt geometry. Our rigorous microscopic quantum kinetic treatment automatically accounts for the fact that, in an individual spin flipflop scattering process, a spin flip of an electron is necessarily accompanied by a flop of an impurity spin in the opposite direction and the corresponding change of the impurity Zeeman energy influences the final energy of the electron after the scattering event. This shift in the electron energies after a spin flipflop scattering process, which usually has been overlooked in the literature, turns out to be especially important in the case of extremely diluted magnetic semiconductors in an external magnetic field. As a specific example for ak dependent effective magnetic field the effects of a Rashba field on the dynamics of the carrierimpurity correlations in aHg1−x−yCdyMnxTe quantum well are described. It is found that, although accounting for the Rashba interaction in the dynamics of the correlations leads to a modifiedk space dynamics, the time evolution of the total carrier spin is not significantly influenced. Furthermore, a connection between the present theory and the description of collective carrierimpurity precession modes is presented.

F. Liu, L.M.P. Martins, A.J. Brash, A.M. Barth, J.H. Quilter, V.M. Axt, M.S. Skolnick and A.M. Fox,
 Ultrafast depopulation of a quantum dot by LAphononassisted stimulated emission
Abstract:
We demonstrate ultrafast incoherent depopulation of a quantum dot from above to below the transparency point using LAphononassisted emission stimulated by a redshifted laser pulse. The QD is turned from a weakly vibronic system into a strongly vibronic one by laser driving which enables the phononassisted relaxation between the excitonic components of two dressed states. The depopulation is achieved within a laser pulsewidthlimited time of 20 ps and exhibits a broad tuning range of a few meV. Our experimental results are well reproduced by pathintegral calculations.
Supplement

A.M. Barth, S. Lüker, A. Vagov, D.E. Reiter, T. Kuhn and V.M. Axt,
 Fast and selective phononassisted state preparation of a quantum dot by adiabatic undressing
Abstract:
We investigate theoretically the temporal behavior of a quantum dot under offresonant optical excitation targeted at fast acoustic phononassisted state preparation. We demonstrate that in a preparation process driven by short laser pulses, three processes can be identified: a dressing of the states during the switchon of the laser pulse, a subsequent phononinduced relaxation, and an undressing at the end of the pulse. By analyzing excitation scenarios with different pulse shapes we highlight the decisive impact of an adiabatic undressing on the final state in shortpulse protocols. Furthermore, we show that in excitonbiexciton systems the laser characteristics such as the pulse detuning and the pulse length as well as the biexciton binding energy can be used to select the targeted quantum dot state.

M. Cygorek, P.I. Tamborenea and V.M. Axt,
 Nonperturbative correlation effects in diluted magnetic semiconductors
Abstract:
The effects of carrierimpurity correlations due to a Kondolike spinspin interaction in diluted magnetic semiconductors are investigated. These correlations are not only responsible for a transfer of spins between the carriers and the impurities, but also produce nonperturbative effects in the spin dynamics such as renormalization of the precession frequency of the carrier spins, which can reach values of several percent in CdMnTe quantum wells. In twodimensional systems, the precession frequency renormalization for a single electron spin with defined wave vector shows logarithmic divergences similar to those also known from the Kondo problem in metals. For smooth electron distributions, however, the divergences disappear due to the integrability of the logarithm. A possible dephasing mechanism caused by the wavevector dependence of the electron spin precession frequencies is found to be of minor importance compared to the spin transfer from the carrier to the impurity system. In the Markov limit of the theory, an expression for the stationary carrierimpurity correlation energy can be deduced indicating the formation of weakly correlated carrierimpurity states with binding energies in the
μeV range.
Erratum: Phys. Rev. B 94, 079906(E) (2016)

W.Y. CórdobaCamacho, R.M. da Silva, A. Vagov, A.A. Shanenko and J. Albino Aguiar,
 Between types I and II: Intertype flux exotic states in thin superconductors
Abstract:
The Bogomolnyi point separates superconductivity types I and II while itself hiding infinitely degenerate magnetic flux configurations, including very exotic states (referred to here as flux “monsters”). When the degeneracy is removed, the Bogomolnyi point unfolds into a finite, intertype domain in the phase diagram between types I and II. One can expect that in this case the flux monsters can escape their “prison” at the Bogomolnyi point, occupying the intertype domain and shaping its internal structure. Our calculations reveal that such exotic flux distributions are indeed stable in the intertype regime of thin superconductors made of a typeI material, where the Bogomolnyi degeneracy is removed by stray magnetic fields. They can be classified into three typical patterns that are qualitatively different from those in types I and II: superconducting islands separated by vortex chains; stripes/worms/labyrinths patterns; and mixtures of giant vortices and vortex clusters. Our findings shed light on the problem of the interchange between types I and II, raising important questions on the completeness of the textbook classification of the superconductivity types.

A.J. Brash, L.M.P.P. Martins, A.M. Barth, F. Liu, J.H. Quilter, M. Glässl, V.M. Axt, A.J. Ramsay, M.S. Skolnick and A.M. Fox ,
 Dynamic vibronic coupling in InGaAs quantum dots
Abstract:
The electron–phonon coupling in selfassembled InGaAs quantum dots is relatively weak at low light intensities, which means that the zerophonon line in emission is strong compared to the phonon sideband. However, the coupling to acoustic phonons can be dynamically enhanced in the presence of an intense optical pulse tuned within the phonon sideband. Recent experiments have shown that this dynamic vibronic coupling can enable population inversion to be achieved when pumping with a blueshifted laser and for rapid deexcitation of an inverted state with red detuning. In this paper we confirm the incoherent nature of the phononassisted pumping process and explore the temperature dependence of the mechanism. We also show that a combination of blueshifted and redshifted pulses can create and destroy an exciton within a timescale of
∼20 ps as determined by the pulse duration and ultimately limited by the phonon thermalization time.

M.D. Croitoru, A.A. Shanenko, A. Vagov, A.S. Vasenko, M.V. Milošević, V.M. Axt and F.M. Peeters
,
 Influence of Disorder on Superconducting Correlations in Nanoparticles
Abstract:
We investigate how the interplay of quantum confinement and level broadening caused by disorder affects superconducting correlations in ultrasmall metallic grains. We use the electronphonon interactioninduced electron mass renormalization and the reduced staticpath approximation of the BCS formalism to calculate the critical temperature as a function of the grain size. We show how the strong electronimpurity scattering additionally smears the peak structure in the electronic density of states of a metallic grain and imposes additional limits on the critical temperature under strong quantum confinement.

D. Wigger, H. Gehring, V.M. Axt, D.E. Reiter and T. Kuhn
,
 Quantum dynamics of optical phonons generated by optical excitation of a quantum dot
Abstract:
The study of the fundamental properties of phonons is crucial to understand their role in applications in quantum information science, where the active use of phonons is currently highly debated. A genuine quantum phenomenon associated with the fluctuation properties of phonons is squeezing, which is achieved when the fluctuations of a certain variable drop below their respective vacuum values. We consider a semiconductor quantum dot (QD) in which the exciton is coupled to phonons. We review the fluctuation properties of the phonons, which are generated by optical manipulation of the QD, in the limiting case of ultrashort pulses. Then, we discuss the phonon properties for an excitation with finite pulses. Within a generating function formalism, we calculate the corresponding fluctuation properties of the phonons and show that phonon squeezing can be achieved by the optical manipulation of the QD exciton for certain conditions even for a singlepulse excitation where neither for short nor for long pulses squeezing occurs. To explain the occurrence of squeezing, we employ a Wigner function picture providing a detailed understanding of the induced quantum dynamics.

M. Cygorek, F. Ungar, P.I. Tamborenea and V.M. Axt,
 Dependence of quantum kinetic effects in the spin dynamics of diluted magnetic semiconductors on the excitation conditions
Abstract:
NonMarkovian quantum kinetic features, that cannot be captured by rate equations, have been predicted theoretically in the spin dynamics in diluted magnetic semiconductors excited with a circularly polarized laser. In order to identify situations which are most promising for detecting the genuine quantum kinetic effects in future experiments, we study numerically the strength of these effects for a number of different excitation conditions. In particular, we show that laser pulse durations of the order of the spintransfer rate or longer are well suited for studying the nonMarkovian effects. Furthermore, in the presence of an external magnetic field, the quantum kinetic theory predicts a significantly different stationary value for the carrier spin polarization than Markovian rate equations, which can be attributed to the buildup of strong carrierimpurity correlations.
2015

M.D. Croitoru, A.A. Shanenko, A. Vagov, M.V. Milošević, V.M. Axt and F.M. Peeters,
 Phonon limited superconducting correlations in metallic nanograins
Abstract:
Conventional superconductivity is inevitably suppressed in ultrasmall metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. In addition, there is experimental evidence that whether an enhancement or a reduction is found depends on the strength of the electronphonon interaction in the bulk. We reveal how the strength of the eph interaction interplays with the quantumsize effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data. We demonstrate that strong eph scattering smears the peak structure in the electronic densityofstates of a metallic grain and enhances the electron mass, and thereby limits the highest T_{c} achievable by quantum confinement.

J.H. Quilter, A.J. Brash, F. Liu, M. Glässl, A.M. Barth, V.M. Axt, A.J. Ramsay, M.S. Skolnick and A.M. Fox,
 PhononAssisted Population Inversion of a Single InGaAs/GaAs Quantum Dot by Pulsed Laser Excitation
Abstract:
We demonstrate a new method to realize the population inversion of a single
InGaAs/GaAs quantum dot excited by a laser pulse tuned within the neutral exciton phonon sideband. In contrast to the conventional method of inverting a twolevel system by performing coherent Rabi oscillation, the inversion is achieved by rapid thermalization of the optically dressed states via incoherent phononassisted relaxation. A maximum exciton population of0.67±0.06 is measured for a laser tuned 0.83 meV to higher energy. Furthermore, the phonon sideband is mapped using a twocolor pumpprobe technique, with its spectral form and magnitude in very good agreement with the result of pathintegral calculations.
Supplement
featured as Editor's suggestion, Physics Viewpoint (Open Access): Crystal Vibrations Invert Quantum Dot Exciton

S. Bounouar, M. Müller, A.M. Barth, M. Glässl, V.M. Axt and P. Michler,
 Phononassisted robust and deterministic twophoton biexciton preparation in a quantum dot
Abstract:
We investigate both experimentally and theoretically a simple yet more robust and flexible alternative to Rabi oscillationtype biexciton preparation protocols traditionally used for semiconductor quantum dots. The quantum dot is excited by a strong laser pulse positively detuned from the twophoton resonance yielding an on demand initialization of the biexciton state by making use of the phononinduced thermalization of the photon dressed states. It is shown that for excitation pulses in the picosecond range, a stable and high occupation of up to
CXX=0.95±0.02 is reached. Notably, the generated photons show similar coherence properties as measured in the resonant twophoton scheme. This protocol is a powerful tool for the control of complex solid state systems combining radiative cascades, entanglement, and resonant cavity modes.
Supplement

M. Cygorek, P.I. Tamborenea and V.M. Axt,
 Insensitivity of spin dynamics to the orbital angular momentum transferred from twisted light to extended semiconductors
Abstract:
We study the spin dynamics of carriers due to the Rashba interaction in semiconductor quantum disks and wells after excitation with light with orbital angular momentum. We find that although twisted light transfers orbital angular momentum to the excited carriers and the Rashba interaction conserves their total angular momentum, the resulting electronic spin dynamics is essentially the same for excitation with light with orbital angular momentum
l=+l andl=−l . The differences between cases with different values ofl are due to the excitation of states with slightly different energies and not to the different angular momenta per se and vanish for samples with large radii where ak space quasicontinuum limit can be established. These findings apply not only to the Rashba interaction but also to all other envelopefunctionapproximation spinorbit Hamiltonians like the Dresselhaus coupling.

F. Ungar, M. Cygorek, P.I. Tamborenea and V.M. Axt,
 Ultrafast spin dynamics in IIVI diluted magnetic semiconductors with spinorbit interaction
Abstract:
We study theoretically the ultrafast spin dynamics of IIVI diluted magnetic semiconductors in the presence of spinorbit interaction. Our goal is to explore the interplay or competition between the exchange
sd coupling and the spinorbit interaction in both bulk and quantumwell systems. For bulk materials we concentrate onZn1−xMnxSe and take into account the Dresselhaus interaction, while for quantum wells we examineHg1−x−yMnxCdyTe systems with a strong Rashba coupling. Our calculations were performed with a recently developed formalism which incorporates electronic correlations beyond meanfield theory originating from the exchangesd coupling. For both bulk and quasitwodimensional systems we find that, by varying the system parameters within realistic ranges, either of the two interactions can be chosen to play a dominant role or they can compete on an equal footing with each other. The most notable effect of the spinorbit interaction in both types of system is the appearance of strong oscillations where the exchangesd coupling by itself causes only an exponential decay of the mean electronic spin components. The meanfield approximation is also studied and an analytical interpretation is given as to why it shows a strong suppression of the spinorbitinduced dephasing of the spin component parallel to the Mn magnetic field.

C. Hopfmann, A. Musiał, M. Strauß, A.M. Barth, M. Glässl, A. Vagov, M. Strauß, C. Schneider, S. Höfling, M. Kamp, V.M. Axt and S. Reitzenstein,
 Compensation of phononinduced renormalization of vacuum Rabi splitting in large quantum dots: Towards temperaturestable strong coupling in the solid state with quantum dotmicropillars
Abstract:
We study experimentally the influence of temperature on the emission characteristics of quantum dotmicropillars in the strong coupling regime of cavity quantum electrodynamics (cQED). In particular, we investigate its impact on the vacuum Rabi splitting (VRS) and we address the important question of the temperature stability of the coherent coupling regime in a semiconductor system, which is relevant in view of both fundamental study and future applications. To study the temperature dependence we investigate an unprecedentedly large number of strong coupling cases (89) in a wide temperature range from 10 up to 50 K, which constitutes a good basis for statistical analysis. The experiment indicates a statistically significant increase of the VRS with temperature in contrast to an expected decrease of the VRS due to the dephasing induced by acoustic phonons. From the theoretical point of view, the phononinduced renormalization of the VRS is calculated using a realtime pathintegral approach for strongly confined quantum dots (QDs), which allows for a numerical exact treatment of the coupling between the QD and a continuum of longitudinal acoustic phonons. The absence of the expected decrease of the VRS with temperature in our experimental data can be attributed to a unique optical property of laterally extended
In0.4Ga0.6As QDs used in this study. Their electronic structure facilitates an effective temperaturedriven increase of the oscillator strength of the excitonic state by up to 40% in the given temperature range. This leads to enhanced lightmatter interaction and overcompensates the phononrelated decrease of the VRS. The observed persistence of strong coupling in the presence of phononinduced decoherence demonstrates the appealing possibility to counteract detrimental phonon effects in the cQED regime via engineering the electronic structure of QDs.

D. Wigger, S. Lüker, V.M. Axt, D.E. Reiter and T. Kuhn,
 Squeezed Phonon Wave Packet Generation by Optical Manipulation of a Quantum Dot
Abstract:
In solidstate physics, the quantized lattice vibrations, i.e., the phonons, play a vital role. Phonons, much like photons, satisfy bosonic commutation relations, and therefore, various concepts wellknown in quantum optics can be transferred to the emerging field of phononics. Examples are nonclassical states and, in particular, squeezed states. We discuss the generation of phonon squeezing by optically exciting a quantum dot and show that by excitation with detuned continuous wave laser fields, sequences of squeezed phonon wave packets are created, which are emitted from the quantum dot region into the surrounding material.

M. Cygorek and V.M. Axt ,
 Effective equations for the precession dynamics of electron spins and electron–impurity correlations in diluted magnetic semiconductors
Abstract:
Starting from a quantum kinetic theory for the spin dynamics in diluted magnetic semiconductors, we derive simplified equations that effectively describe the spin transfer between carriers and magnetic impurities for an arbitrary initial impurity magnetization. Taking the Markov limit of these effective equations, we obtain good quantitative agreement with the full quantum kinetic theory for the spin dynamics in bulk systems at high magnetic doping. In contrast, the standard rate description where the carrier–dopant interaction is treated according to Fermi's golden rule, which involves the assumption of a short memory as well as a perturbative argument, has been shown previously to fail if the impurity magnetization is nonzero. The Markov limit of the effective equations is derived, assuming only a short memory, while higher order terms are still accounted for. These higher order terms represent the precession of the carrier–dopant correlations in the effective magnetic field due to the impurity spins. Numerical calculations show that the Markov limit of our effective equations reproduces the results of the full quantum kinetic theory very well. Furthermore, this limit allows for analytical solutions and for a physically transparent interpretation.

A. Brand, B. Kaiser, A. Vagov, V.M. Axt and U. Pietsch,
 Model study on how an ordered grouping of atoms affects their innershell photoionization
Abstract:
We show that the photoionization dynamics from the innermost shell of atoms changes significantly when instead of single atoms an ordered group of atoms or a crystal is considered. We find that the electronic current away from a given atom induced by pulsed photoionization is strongly suppressed in ordered groups of atoms although the overlap of the groundstate orbitals of neighboring atoms is negligible. The effect occurs even when the electronelectron interaction is disregarded in our model and thus impact ionization as well as the trapping due to the charging of the environment cannot be the cause of the suppression. Even when a reflectionless potential is used for the modeling of the atomic potential, the suppression is still profound. We interpret this localization of photoionized electrons as appearing due to quantum interference between the partial electron wave packets emitted from different atoms.

S. Hannibal, P. Kettmann, M.D. Croitoru, A. Vagov, V.M. Axt and T. Kuhn,
 Quench dynamics of an ultracold Fermi gas in the BCS regime: Spectral properties and confinementinduced breakdown of the Higgs mode
Abstract:
The Higgs amplitude mode of the order parameter of an ultracold confined Fermi gas in the BCS regime after a quench of the coupling constant is analyzed theoretically. A characteristic feature is a damped oscillation which at a certain transition time changes into a rather irregular dynamics. We compare the numerical solution of the full set of nonlinear equations of motion for the normal and anomalous Bogoliubov quasiparticle excitations with a linearized approximation. In doing so the transition time as well as the difference between resonant systems, i.e., systems where the Fermi energy is close to a subband minimum, and offresonant systems can be well understood and traced back to the system and geometry parameters.

V. Zalipaev, C.M. Linton, M.D. Croitoru and A. Vagov,
 Resonant tunneling and localized states in a graphene monolayer with a mass gap
Abstract:
We study tunneling of quasiparticles through potential barriers in a graphene monolayer with the mass gap using a semiclassical (WKB) approach. The main equations are derived in a way similar to the WKB theory for the Schrödinger equation, which allows for explicit solutions at all orders. The analog of the classical action is used to distinguish types of possible stationary states in the system. The analysis focuses on the resonant scattering and the hole states localized in the vicinity of a barrier that are often overlooked. The scattering coefficients for the physically interesting limits are obtained by matching the WKB approximation with the known solutions at turning points. The localized states demonstrate unconventional properties and lead to alterations of the single particle density of states.

A.A. Shanenko, J. Albino Aguiar, A. Vagov, M.D. Croitoru and M.V. Milošević,
 Atomically flat superconducting nanofilms: multiband properties and meanfield theory
Abstract:
Recent progress in materials synthesis enabled fabrication of superconducting atomically flat singlecrystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nanothin systems is attracted by the dimensional 3D–2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin–Wagner–Hohenberg theorem and concerns frustration of the longrange order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri–Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the meanfield behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg–Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband meanfield formalism which allows for numerical and even analytical treatment of nanothin superconductors in applied magnetic fields.

D.E. Reiter, D. Wigger, S. Lüker, V.M. Axt, P. Machnikowski and T. Kuhn ,
 Generating sequences of phonon wave packets by optical excitation of a quantum dot
Abstract:
Phonons can play an active role in controlling solid state systems or in the transport of energy and information. Thus, it is vital to understand generation processes and properties of phonons. By optical excitation of a semiconductor quantum dot, a sequence of phonon wave packets can be created. In this paper we focus on the fluctuation properties of lattice displacement and momentum of these phonon wave packets. For detuned excitation the fluctuations may fall below their respective vacuum values and squeezing occurs.

F. Ungar, M. Cygorek, P.I. Tamborenea and V.M. Axt,
 Relaxation and coherent oscillations in the spin dynamics of IIVI diluted magnetic quantum wells
Abstract:
We study theoretically the ultrafast spin dynamics of IIVI diluted magnetic quantum wells in the presence of spinorbit interaction. We extend a recent study where it was shown that the spinorbit interaction and the exchange sd coupling in bulk and quantum wells can compete resulting in qualitatively new dynamics when they act simultaneously. We concentrate on Hg_{1xy}Mn_{x}Cd_{y}Te quantum wells, which have a highly tunable Rashba spinorbit coupling. Our calculations use a recently developed formalism which incorporates electronic correlations originating from the exchange sdcoupling. We find that the dependence of electronic spin oscillations on the excess energy changes qualitatively depending on whether or not the spinorbit interaction dominates or is of comparable strength with the sd interaction.

M. Cygorek and V.M. Axt,
 NonMarkovian Effects in the Spin Transfer Dynamics in Diluted Magnetic Semiconductors due to Excitation in Proximity to the Band Edge
Abstract:
The nonMarkovian effects in the spin dynamics in diluted magnetic semiconductors found in quantum kinetic calculations can be reproduced very well by a much simpler effective single electron theory, if a finite memory is accounted for. The resulting integrodifferential equation can be solved by a differential transform method, yielding the Taylor series of the solution. From the comparison of both theories it can be concluded that the nonMarkovian effects are due to the spectral proximity of the excited electrons to the band edge.

A.J. Brash, J.H. Quilter, F. Liu, M. Glässl, A.M. Barth, V.M. Axt,
A.J. Ramsay, M.S. Skolnick and A.M. Fox
,
 PhononAssisted Population Inversion of a Single Quantum Dot
Abstract:
We demonstrate a new method to produce a population inversion in an InGaAs quantum dot by quasiresonant, incoherent excitation within the LA phonon sideband. A maximum exciton population of 0.67 is measured; applications include single photon sources and single QD lasers.
2014

D.E. Reiter, T. Kuhn, M. Glässl and V.M. Axt,
 The role of phonons for exciton and biexciton generation in an optically driven quantum dot
Abstract:
Topical Review
For many applications of semiconductor quantum dots in quantum technology, wellcontrolled state preparation of the quantum dot states is mandatory. Since quantum dots are embedded in the semiconductor matrix, their interaction with phonons often plays a major role in the preparation process. In this review, we discuss the influence of phonons on three basically different optical excitation schemes that can be used for the preparation of exciton, biexciton and superposition states: a resonant excitation leading to Rabi rotations in the excitonic system, an excitation with chirped pulses exploiting the effect of adiabatic rapid passage and an offresonant excitation giving rise to a phononassisted state preparation. We give an overview of experimental and theoretical results, showing the role of phonons and compare the performance of the schemes for state preparation.

M. Müller, S. Bounouar, K. D. Jöns, M. Glässl and P. Michler,
 Ondemand generation of indistinguishable polarizationentangled photon pairs
Abstract:
An ondemand source of indistinguishable and entangled photon pairs is a fundamental component of various quantum information applications, including optical quantum computing, quantum repeaters, quantum teleportation and quantum communication. Parametric downconversion and fourwave mixing sources of entangled photons have shown high degrees of entanglement and indistinguishability, but the probabilistic nature of their generation process also creates zero or multiple photon pairs following a Poissonian distribution. This limits their use in complex algorithms where many qubits and gate operations are required. Here, we simultaneously show ultrahigh purity (g((2))(0) < 0.004), high entanglement fidelity (0.81 +/ 0.02), high twophoton interference nonpost selective visibilities (0.86 +/ 0.03 and 0.71 +/ 0.04) and ondemand generation (efficiency epsilon(pair) = 0.86 +/ 0.08) of polarizationentangled photon pairs from a single semiconductor quantum dot. Through a twophoton resonant excitation scheme, the biexciton population is deterministically prepared by a pipulse (epsilon(biexciton) = 0.98 +/ 0.07). Applied on a quantum dot showing no exciton finestructure splitting, this results in the deterministic generation of indistinguishable entangled photon pairs.

A. Brand, B. Kaiser, A. Vagov, V.M. Axt and U. Pietsch,
 NonMarkovian behavior of ultrafast coherent ionization dynamics in a crystal exposed to a seeded freeelectronlaser pulse
Abstract:
We investigate the ionization dynamics of a crystal structure driven by ultrafast coherent xray pulses of moderate to high intensities for excitations where dipoleallowed, singlephoton ionization dominates. Using a simple model of the crystal, we demonstrate that quantum coherences may already play an important role at moderate pulse intensities, leading to qualitatively novel features which cannot be described by rate equations. In particular, the ionization may exhibit a minimum as a function of the pulse duration, where the ionization drops to almost zero, although during the pulse a noticeable fraction of the electrons is promoted to unbound states. For higher intensities, the qualitative deviations between the coherent quantummechanical treatment and the rate description is even more pronounced. In particular, due to the presence of quantummechanical coherences, the full theory predicts, even for the singlephoton transitions to a continuum of freeelectron states, a Rabitype behavior similar to what is known for twolevel systems.

M. Cygorek and V.M. Axt ,
 Comparison between a quantum kinetic theory of spin transfer dynamics in Mndoped bulk semiconductors and its Markov limit for nonzero Mn magnetization
Abstract:
We investigate the transfer between carrier and Mn spins due to the
s d exchange interaction in a Mndoped bulk semiconductor within a microscopic quantum kinetic theory. We demonstrate that the spin transfer dynamics is qualitatively different for components of the carrier spin parallel and perpendicular to the Mn magnetization. From our quantum kinetic equations we have worked out the corresponding Markov limit, which is equivalent to rate equations based on Fermi's golden rule. The resulting equations resemble the widely used LandauLifshitzGilbert equations, but also describe genuine spin transfer due to quantum corrections. Although it is known that the Markovian rate description works well for bulk systems when the initial Mn magnetization is zero, we find large qualitative deviations from the full quantum kinetic theory for finite initial Mn magnetizations. These deviations mainly reflect corrections of higher than leading order in the interaction, which are not accounted for in goldenruletype rates.

A. Vagov, M. Glässl, M.D. Croitoru, V.M. Axt and T. Kuhn ,
 Competition between pure dephasing and photon losses in the dynamics of a dotcavity system
Abstract:
We demonstrate that in quantumdot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both dephasing mechanisms strongly affects the transition from the weak to the strongcoupling regime as well as the shape of the spectral triplet that represents the quantumdot occupation in Fourier space. The width of the central peak in the triplet is expected to decrease with rising temperature, while the widths and heights of the side peaks depend nonmonotonically on the dotcavity coupling.

A.A. Shanenko, A. Vagov, F.M. Peeters, J. Albino Aguiar,
 Nanoﬁlms as effectively multiband superconductors: Intrabandpairing approximation and GinzburgLandau theory
Abstract:
It is wellknown that the Ginzburg–Landau (GL) theory is a reliable and powerful theoretical tool to investigate the magnetic response of a superconducting state. However, in its standard form, this approach is not applicable to atomically uniform nanothin superconducting films which are effective multiband superconductors. Here we discuss a relevant generalization of the GL theory, focusing on the underlying intrabandpairing approximation.

D. Wigger, S. Lüker, D.E. Reiter, V.M. Axt, P. Machnikowski and T. Kuhn,
 Energy transport and coherence properties of acoustic phonons generated by optical excitation of a quantum dot
Abstract:
The energy transport of acoustic phonons generated by the optical excitation of a quantum dot as well as the coherence properties of these phonons are studied theoretically both for the case of a pulsed excitation and for a continuous wave (CW) excitation switched on instantaneously. For a pulsed excitation, depending on pulse area and pulse duration, a finite number of phonon wave packets is emitted, while for the case of a CW excitation a sequence of wave packets with decreasing amplitude is generated after the excitation has been switched on. We show that the energy flow associated with the generated phonons is partly related to coherent phonon oscillations and partly to incoherent phonon emission. The efficiency of the energy transfer to the phonons and the details of the energy flow depend strongly and in a nonmonotonic way on the Rabi frequency exhibiting a resonance behavior. However, in the case of CW excitation it turns out that the total energy transferred to the phonons is directly linked in a monotonic way to the Rabi frequency.

M.D. Croitoru, M. Zachmann, A. Vagov, V.M. Axt,
A.A. Shanenko, P. Kettmann, T. Papenkort and T. Kuhn
,
 Coherent dynamics of confinementinduced multiband superconductors
Abstract:
We study the coherent dynamics of pairing in a nanoscale superconductor, that is intrinsically multiband, after an external perturbation in the nonadiabatic regime. The description of the dynamics of the pairing order is within the densitymatrix approach based on the BCS model and the Bogoliubov–de Gennes equations. We find that for certain resonant wire widths the superconducting order parameter exhibits two oscillatory frequencies which are determined by the longtime asymptotic values of the subgaps. This in turn leads to a pronounced beating phenomenon.
2013

M. Glässl, A.M. Barth and V.M. Axt ,
 Proposed robust and highfidelity preparation of excitons and biexcitons in semiconductor quantum dots making active use of phonons
Abstract:
It is demonstrated how the exciton and the biexciton state of a quantum dot can be prepared with high fidelity on a picosecond time scale by driving the dot with a strong laser pulse that is tuned above the exciton resonance for exciton preparation and in resonance with the exciton transition for biexciton preparation. The proposed protocols make use of the phononinduced relaxation towards photon dressed states in optically driven quantum dots and combine the simplicity of traditional Rabi oscillation schemes with the robustness of adiabatic rapid passage schemes. Our protocols allow for an ondemand, fast, and almost perfect state preparation even at strong carrierphonon interaction where other schemes fail. In fact, the performance of the presented protocols is shown to be better the stronger the carrierphonon interaction is.

A.A. Shanenko, N.V. Orlova, A. Vagov, M.V. Milošević, V.M. Axt and F. M. Peeters,
 Nanofilms as quantumengineered multiband superconductors: The GinzburgLandau theory
Abstract:
Recently fabricated singlecrystalline atomically flat metallic nanofilms are in fact quantumengineered multiband superconductors. Here the multiband structure is dictated by the nanofilm thickness through the size quantization of the electron motion perpendicular to the nanofilm. This opens the unique possibility to explore superconductivity in wellcontrolled multiband systems. However, a serious obstacle is the absence of a convenient and manageable theoretical tool to access new physical phenomena in such quasi–twodimensional systems, including interplay of quantum confinement and fluctuations. Here we cover this gap and construct the appropriate multiband GinzburgLandau functional for nanothin superconductors.

C.Thurn, M. Cygorek, V.M. Axt and T. Kuhn ,
 Coherent spintransfer dynamics in diluted magnetic semiconductor quantum wells even after optical excitation with zero net angular momentum
Abstract:
A quantum kinetic study of correlated spin transfer between optically excited electrons and Mn atoms in a
ZnMnSe quantum well is presented. The simulations predict genuine signatures of nonMarkovian spin dynamics which are particularly pronounced for special twocolor laser excitations with a zero net angular momentum where a Markovian theory predicts an almost zero total electron spin for all times. In contrast, in the quantum kinetic simulations a sizable total electron spin builds up. Subsequently, a coherent oscillatory exchange of spin between the electron and Mn subsystems is observed.

B. Kaiser, A. Brand, M. Glässl, A. Vagov, V.M. Axt and U. Pietsch,
 Photoionization of resonantly driven atomic states by an extreme ultravioletfreeelectron laser: intensity dependence and renormalization of Rabi frequencies
Abstract:
We analyze theoretically the high intensity photoionization dynamics of a system with two atomic states resonantly coupled by coherent extreme ultraviolet laser radiation that also gives rise to the ionization. The ground state occupation of such a system is shown to exhibit damped Rabi oscillations. The corresponding ionization, which is responsible for the damping, scales almost linearly with the field intensity when the pulse length exceeds the Rabi period. For shorter pulses a quadratic scaling is found. The Rabi frequency is shifted compared to its value for an isolated twolevel system. The shift increases with excitation intensity and can acquire a high percentage of the unrenormalized frequency at high intensities. Analytical results obtained within a simplified solvable model demonstrate that the damping and the shift both result from the coupling of the discrete states to the ionization continuum and are therefore closely related. Numerical simulations for a twoelectron system reveal at high intensities the importance of offresonant ionization channels.

M. Zachmann, M.D. Croitoru, A. Vagov, V.M. Axt, T. Papenkort and T. Kuhn,
 Ultrafast terahertzfieldinduced dynamics of superconducting bulk and quasi1D samples
Abstract:
Within a densitymatrix formalism based on the Bardeen–Cooper–Schrieffer (BCS) model and the Bogoliubov–de Gennes equations we provide a description of the dynamics of the nonequilibrium superconducting pairing induced by a terahertz (THz) laser pulse in bulk and quasionedimensional (1D) samples of conventional (BCStype) superconductors. A crossover from an adiabatic to a nonadiabatic regime takes place for short and intense THz pulses. In the nonadiabatic regime, the order parameter performs a damped oscillation. We discuss how the parameters of the THz pulse influence the amplitude and the mean value of the oscillation in bulk samples. It is demonstrated that for high intensities the nonadiabatic regime can be reached even for pulses longer than the oscillation period. For the 1D samples we find that the oscillation may attenuate with a different power law. This is analysed by comparing the THzinduced dynamics with the dynamics induced by a sudden switching of the pairing strength, which exhibits essentially the same behaviour. The numerical calculations show that the exponent of the power law depends critically on the density of states in the Debye window and therefore changes in an oscillatory way with the confinement strength. Irregularities in the decay of the oscillation are predicted when the 1D quantum wire is cut short to an elongated zerodimensional quantum dot structure.

D. Thuberg, D.E. Reiter, V.M. Axt and T. Kuhn,
 Switching between ground states of an InAs quantum dot doped with a single Mn atom
Abstract:
The ultrafast lightinduced dynamics in an InAs quantum dot doped with a single Mn atom is studied
theoretically. Due to the exchange interaction between the Mn atom and the acceptor hole in the quantum
dot, an effective twolevel system is formed in the groundstate manifold. We show that this twolevel system can
be controlled coherently on a picosecond time scale. The control involves an optical manipulation of the quantum
dot exciton by using either a series of two ultrafast pulses or a single extended laser pulse. For the excitation
with two pulses, we discuss the optical signals that could be used in timeresolved spectroscopy to monitor the
dynamics. We compare these results to the spin dynamics in a CdTe quantum dot doped with a single Mn atom.
Ein Bild dieses Artikels wurde ausgewählt für das: Phys. Rev. B Kaleidoscope Aug. 2013

C.Thurn, M. Cygorek, V.M. Axt and T. Kuhn ,
 NonMarkovian spin transfer dynamics in magnetic semiconductors despite short memory times
Abstract:
A quantum kinetic theory of the spin transfer between carriers and Mn atoms in a Mndoped diluted magnetic semiconductor is presented. It turns out that the typical memory time associated with these processes is orders of magnitude shorter than the time scale of the spin transfer. Nevertheless, Markovian rate equations, which are obtained by neglecting the memory, work well only for bulk systems. For quantum wells and wires the quantum kinetic results qualitatively deviate from the Markovian limit under certain conditions. Instead of a monotonic decay of an initially prepared excess electron spin, an overshoot or even coherent oscillations are found. It is demonstrated that these features are caused by energetic redistributions of the carriers due to the energytime uncertainty.

N.V. Orlova, A.A. Shanenko, M.V. Milošević, F.M. Peeters, A.V. Vagov and V.M. Axt ,
 GinzburgLandau theory for multiband superconductors: Microscopic derivation
Abstract:
A procedure to derive the GinzburgLandau (GL) theory from the multiband BCS Hamiltonian is developed in a general case with an arbitrary number of bands and arbitrary interaction matrix. It combines the standard Gor'kov truncation and a subsequent reconstruction in order to match accuracies of the obtained terms. This reconstruction recovers the phenomenological GL theory as obtained from the Landau model of phase transitions but offers explicit microscopic expressions for the relevant parameters. Detailed calculations are presented for a threeband system treated as a prototype multiband superconductor. It is demonstrated that the symmetry in the coupling matrix may lead to the chiral ground state with the phase frustration, typical for systems with broken timereversal symmetry.

D.E. Reiter, V.M. Axt and T. Kuhn,
 Optical signals of spin switching using the optical Stark effect in a Mndoped quantum dot
Abstract:
The optically induced spin dynamics of a single Mn atom embedded into a single semiconductor quantum dot can be strongly influenced by using the optical Stark effect. The exchange interaction gives rise to simultaneous spin flips between the quantum dot electron and Mn. In the time domain, these flips correspond to exchange induced Rabi oscillations, which are typically offresonant. By applying a detuned laser pulse, the states involved in the flipping can be brought into resonance by means of the optical Stark effect increasing the amplitude of the Rabi oscillations to one. In this paper, we study theoretically how this spin dynamics can be monitored in timeresolved spectroscopy. In the spectrum, the exchange interaction leads to a splitting of the exciton line into six lines, each corresponding to one of the six Mn spin states. The dynamical behavior of the Mn spin is reflected by the strength of the individual lines as a function of time. When an offresonant optical pulse is applied, the spectral positions of the lines shift, but still the flipping dynamics is visible.

M. Glässl, A.M. Barth, K. Gawarecki, P. Machnikowski, M.D. Croitoru, S. Lüker, D.E. Reiter, T. Kuhn and V.M. Axt ,
 Biexciton state preparation in a quantum dot via adiabatic rapid passage: Comparison between two control protocols and impact of phononinduced dephasing
Abstract:
We investigate theoretically under what conditions a stable and highfidelity preparation of the biexciton state in a quantum dot can be realized by means of adiabatic rapid passage in the presence of acoustic phonon coupling. Our analysis is based on a numerically complete realtime pathintegral approach and comprises two different schemes of optical driving using frequencyswept (chirped) pulses. We show that depending on the size of the biexciton binding energy, resonant twophoton excitations or twocolor schemes can be favorable. It is demonstrated that the carrierphonon interaction strongly affects the efficiency of both protocols and that a robust preparation of the biexciton is restricted to positive chirps and low temperatures. A considerable increase of the biexciton yield can be achieved realizing temperatures below 4 K.
Ein Bild dieses Artikels wurde ausgewählt für das: Phys. Rev. B Kaleidoscope Feb. 2013

D. Wigger, D.E. Reiter, V.M. Axt and T. Kuhn,
 Fluctuation properties of acoustic phonons generated by ultrafast optical excitation of a quantum dot
Abstract:
We study theoretically the fluctuation properties of acoustic phonons created in a semiconductor quantum dot after ultrafast optical excitation. An excitation with a single ultrafast pulse creates an exciton confined to the quantum dot, which is coupled to longitudinal acoustic phonons. This leads to the formation of a polaron in the quantum dot accompanied by the emission of a phonon wave packet. We show that the fluctuations of the lattice displacement associated with the wave packet after a single laser pulse excitation in resonance with the exciton transition are always larger than their respective vacuum values. Manipulation of the exciton with a second pulse can result in a reduction of the fluctuations below their vacuum limit, which means that the phonons are squeezed. We show that the squeezing properties of the wave packet strongly depend on the relative phase and the time delay between the two laser pulses.

K. Gawarecki, S. Lüker, D.E. Reiter, T. Kuhn, M. Glässl, V.M. Axt, A. GrodeckaGrad and P. Machnikowski,
 Adiabatic rapid passage in quantum dots: phononassisted decoherence and biexciton generation
Abstract:
We study the evolution of a quantum dot controlled by a frequencyswept (chirped), linearly polarized laser pulse in the presence of carrierphonon coupling. The final occupation of the exciton state is limited both due to phononinduced transitions between the adiabatic spectral branches and because of phononassisted transitions to the biexciton state.
When the biexciton shift is large enough, the quantum dot can be modeled as a twolevel system, which corresponds to excitation with circularly polarized light. For this case, we compare different methods of simulations: (i) a time convolutionless method, (ii) correlation expansion and (iii) path integrals. We show that results obtained from these methods agree perfectly at low temperatures.
Ein Bild dieses Artikels wurde als Titelbild des zugehöigen Phys. Stat. Sol. (c) Bandes ausgewählt
2012

M. Glässl and V.M. Axt,
 Polarization dependence of phonon inﬂuences in excitonbiexciton quantum dot systems
Abstract:
We report on a strong dependence of the phononinduced damping of Rabi dynamics in an optically driven excitonbiexciton quantum dot system on the polarization of the exciting pulse. While for a ﬁxed pulse intensity the damping is maximal for linearly polarized excitation, it decreases with increasing ellipticity of the polarization. This ﬁnding is most remarkable considering that the carrierphonon coupling is spin independent. In addition to simulations based on a numerically exact realtime pathintegral approach, we present an analysis within a weakcoupling theory that allows for analytical expressions for the pertinent damping rates. We demonstrate that an efﬁcient coupling to the biexciton state is of central importance for the reported polarization dependencies. Further, we discuss inﬂuences of various system parameters and show that, for ﬁnite biexciton binding energies, Rabi scenarios differ qualitatively from the widely studied twolevel dynamics.

A.A. Shanenko, M.D. Croitoru, A.V. Vagov, V.M. Axt, A. Perali and F.M. Peeters,
 Atypical BCSBEC crossover induced by quantumsize effects
Abstract:
Quantumsize oscillations of the basic physical characteristics of a conﬁned fermionic condensate are a wellknown phenomenon. Its conventional understanding is based on the singleparticle physics, whereby the oscillations follow variations in the singleparticle density of states driven by the size quantization. Here we present a study of a cigarshaped ultracold superﬂuid Fermi gas, which demonstrates an important manybody aspect of the quantumsize coherent effects, overlooked previously. The manybody physics is revealed here in the atypical crossover from the BardeenCooperSchrieffer (BCS) superﬂuid to the BoseEinstein condensate (BEC) induced by the size quantization of the particle motion. The singleparticle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasifree dispersion. This results in the formation of a series of singleparticle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCSBEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEClike components.

A. Vagov, A.A. Shanenko, M.V. Milošević, V.M. Axt and
F.M. Peeters,
 Twoband superconductors: Extended GinzburgLandau formalism by a systematic expansion in small deviation from the critical temperature
Abstract:
We derive the extended GinzburgLandau (GL) formalism for a clean swave twoband superconductor by employing a systematic expansion of the freeenergy functional and the corresponding matrix gap equation in powers of the small deviation from the critical temperature τ=1−T/T_{c}. The two lowest orders of this expansion produce the equation for T_{c} and the standard GL theory. It is shown that in agreement with previous studies, this twoband GL theory maps onto the singleband GL model and thus fails to describe the difference in the spatial profiles of the twoband condensates. We prove that this difference appears already in the leading correction to the standard GL theory, which constitutes the extended GL formalism. We derive linear differential equations that determine the leading corrections to the band order parameters and magnetic field, discuss the validity of these equations, and consider examples of an important interplay between the band condensates. Finally, we present numerical results for the thermodynamic critical magnetic field and temperaturedependent band gaps for recent materials of interest, which are in very good agreement with those obtained from the full BCS approach in a wide temperature range. To this end, we emphasize the advantages of our extended GL theory in comparison with the often used twocomponent GLlike model based on an unreconstructed twoband generalization of the Gor'kov derivation.

M. Glässl, L. Sörgel, A. Vagov, M.D. Croitoru, T. Kuhn and V.M. Axt,
 Interaction of a quantumdot cavity system with acoustic phonons: Stronger lightmatter coupling can reduce the visibility of strong coupling effects
Abstract:
We present a numerically complete study of the combined dynamics of a quantum dot exciton coupled to a single quantized cavity mode and a continuum of acoustic phonons. We demonstrate that acoustic phonons have a pronounced impact on effects characteristic of the strong lightmatter coupling regime, such as vacuum Rabi oscillations and collapse and revival scenarios. This impact is considerable already at zero temperature, where initially no phonons are present. Counterintuitively it is found that an increase of the lightmatter coupling does not necessarily enhance the visibility of strongcoupling effects. In fact, for typical experimental situations, a stronger lightmatter coupling will considerably reduce the visibility.

M. Glässl, M.D. Croitoru, A. Vagov, V.M. Axt and T. Kuhn,
 Impact of dark superpositions on the relaxation dynamics of an optically driven phononcoupled excitonbiexciton quantumdot system
Abstract:
Within a numerically complete realtime path integral approach we identify the realization of dark superpositions as a general mechanism that strongly modifies the quantum dissipative relaxation of an optically driven quantum dot coupled to acoustic phonons. The presence of dark superpositions in an excitonbiexciton system that can be controlled by varying the laser polarization is shown to have a significant impact on the stationary values of the electronic occupations as well as on the precedent relaxation dynamics. Similar to the critical slowing down that is known to occur near phase transitions the time to reach a stationary state rises with no limit for polarizations that nearly realize a dark superposition. Interestingly, this time may show a nonmonotonic temperature dependence caused by a crossover between coherent and incoherent relaxation dynamics.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 11, Issue 6, Condensed Matter Physics (Jun 2012)
sowie auch für: Virt. J. Nan. Sci. & Tech., Vol. 25, Issue 21, Optical Properties and Quantum Optics (May 2012)

S. Lüker, K. Gawarecki, D.E. Reiter, A. GrodeckaGrad, V.M. Axt, P. Machnikowski and T. Kuhn ,
 Influence of acoustic phonons on the optical control of quantum dots driven by adiabatic rapid passage
Abstract:
The role of phonons for adiabatic rapid passage in semiconductor quantum dots is studied theoretically. While in an ideal system adiabatic rapid passage results in a full inversion of the quantum dot occupation, phonons hamper this behavior drastically. We show that the transitions between the adiabatic states lead to a temperaturedependent decrease of the final exciton occupation. In contrast to the ideal evolution, the phononrelated perturbation induces dependencies on the pulse power and on the sign of the chirp.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 11, Issue 4, Photonics (Apr 2012)
sowie auch für: Virt. J. Nan. Sci. & Tech., Vol. 25, Issue 13, Optical Properties and Quantum Optics (Mar 2012)

K. Gawarecki, S. Lüker, D.E. Reiter, T. Kuhn, M. Glässl, V. M. Axt,
A. Grodecka–Grad and P. Machnikowski ,
 Dephasing in the adiabatic rapid passage in quantum dots: Role of phononassisted biexciton generation
Abstract:
We study the evolution of an exciton conﬁned in a quantum dot adiabatically controlled by a frequencyswept (chirped) laser pulse in the presence of carrierphonon coupling. We focus on the dynamics induced by a linearly polarized beam and analyze the decoherence due to phononassisted biexciton generation. We show that if the biexciton state is shifted down by a few meV, as is typically the case, then the resulting decoherence is strong even at low temperatures. As a result, efﬁcient state preparation is restricted to a small parameter area corresponding to low temperatures, positive chirps, and moderate pulse areas.

C. Thurn and V.M. Axt,
 Quantum kinetic description of spin transfer in diluted magnetic semiconductors
Abstract:
We derive quantum kinetic equations of motion that describe laserdriven Mndoped diluted semiconductors and account for the carrier Mn exchange interaction beyond the meanfield theory. We treat a spatially inhomogeneous system with arbitrary given positions of Mn dopants as well as an ensemble of randomly distributed Mn atoms in an infinite crystal, which represents an on average spatially homogeneous system. In the latter case, special care is taken of the interplay between higherorder correlations and the random positioning of Mn atoms. For the ensembleaveraged system, we explicitly identify the terms responsible for a spin transfer between spinpolarized carriers and Mn atoms in the special case valid, e.g., for paramagnetic samples without external magnetic field, where initially the total Mn magnetization vanishes. It turns out that here the meanfield approach as well as the virtual crystal approximation predict a vanishing spin transfer, in contrast to our quantum kinetic equations. Moreover, in our approach, the exchange interaction with the localized Mn atoms leads to a significant redistribution of the carrier momenta even in an on average spatially homogeneous system. The latter feature can not be described in the virtual crystal approximation.

D.E. Reiter, T. Kuhn and V.M. Axt,
 Spin switching in a Mndoped quantum dot using the optical Stark effect
Abstract:
In a single quantum dot doped with a single Mn atom, ultrafast optical control can be used to coherently manipulate the Mn spin state. Here we show that due to the optical Stark effect induced by a detuned laser pulse the Mn spin can be efficiently flipped by one during the action of the pulse. We discuss the influence of different pulse envelopes on the flipping process. We then show how this flipping mechanism can be used in a switching protocol to address all Mn spin states selectively and point out the advantage of exploiting the optical Stark effect compared to previously proposed methods.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 25, Issue 4, Nanomagnetism and Spintronics (Jan 2012)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 11, Issue 2, Condensed Matter Physics (Feb 2012)

T. Papenkort, V.M. Axt and T. Kuhn ,
 Optical excitation of squeezed longitudinal optical phonon states in an electrically biased quantum well
Abstract:
We present quantum kinetic calculations showing how squeezed phonon states can be generated in a biased quantum well by optical driving. In such states the uncertainty of the lattice displacement or momentum is reduced below its zeropoint value. It is shown that quantitative results that are meaningful for real observations require accounting for the inevitably limited spatial resolution. Our simulations yield results for the strength of the squeezing and predict under which conditions it can occur: Optical excitations on the lowest absorption line need at least two pulses to generate squeezing, while a single pulse below the band gap may produce a squeezed state which has an almost minimumvalue uncertainty product.

A.V. Vagov, A.A. Shanenko, M.V. Milošević, V.M. Axt and F.M. Peeters,
 Extended GinzburgLandau formalism: Systematic expansion in small deviation from the critical temperature
Abstract:
Based on the Gor'kov formalism for a clean swave superconductor, we develop an extended version of the singleband GinzburgLandau (GL) theory by means of a systematic expansion in the deviation from the critical temperature T_{c}, i.e., τ=1−T/T_{c}. We calculate different contributions to the order parameter and the magnetic field: the leading contributions (~τ^{1/2} in the order parameter and ~τ in the magnetic field) are controlled by the standard GL theory, while the nexttoleading terms (~τ^{3/2} in the gap and ~τ^{2} in the magnetic field) constitute the extended GL (EGL) approach. We derive the freeenergy functional for the extended formalism and the corresponding expression for the current density. To illustrate the usefulness of our formalism, we calculate, in a semianalytical form, the temperaturedependent correction to the GL parameter at which the surface energy becomes zero, and analytically, the temperature dependence of the thermodynamic critical field. We demonstrate that the EGL formalism is not just a mathematical extension to the theory: variations of both the gap and the thermodynamic critical field with temperature calculated within the EGL theory are found in very good agreement with the full BCS results down to low temperatures, which dramatically improves the applicability of the formalism compared to its standard predecessor.

M.D. Croitoru, A. Vagov, A.A. Shanenko and V.M. Axt,
 The Cooper problem in nanoscale: enhancement of the coupling due to confinement
Abstract:
In 1956 Cooper demonstrated (1956 Phys. Rev. 104 1189) that, no matter how weak the attraction is, two electrons in threedimensional (3D) space just above the Fermi sea could be bound. In this work we investigate the inﬂuence of conﬁnement on the binding energy of a Cooper pair. We show that conﬁnementinduced modiﬁcation of the Fermi sea results in a signiﬁcant increase of the binding energy, when the bottom of an energy subband is very close to the Fermi surface.

A. Vagov, M. Glässl, M. D. Croitoru, V. M. Axt, P. Machnikowski and
T. Kuhn,
 Laser driven dynamics of a quantum dot coupled to phonons: Dependence of the reappearance of Rabi rotations on the pulse length and shape
Abstract:
We study the dynamics of a semiconductor quantum dot coupled to phonons and laser light in the limit of strong electronic confinement. Using real time path integrals our numerical results are nonperturbative with respect to both, the carrierlight and the carrierphonon coupling. As it is known the damping of Rabi rotations is a nonmonotonic function of the pulse area.
Here, we analyze how pulse parameters affect the resulting decayreappearance of Rabi rotations, which arises from the resonant nature of carrierphonon coupling. For longer pulses, the maximal reduction of the amplitude of Rabi rotations is shifted to higher pulse areas. In addition, for Gaussian pulses the reappearance rate is significantly reduced compared to rectangular profiles.

D.E. Reiter, V.M. Axt and T. Kuhn,
 Spectral characteristics and dynamics of a light hole type quantum dot doped with a single Mn atom
Abstract:
For a single semiconductor quantum dot doped with a single Mn atom we study theoretically the spectral characteristics and dynamics under optical excitation. Because the Mn spin couples to the electron and hole spin of the quantum dot exciton via the exchange interaction, in the absorption spectrum instead of a single exciton line a set of lines appears. Here we consider a quantum dot with one conduction band and one light hole type valence band. Due to this untypical valence band structure a spectrum of twelve lines is seen at zero magnetic field. When a magnetic field is applied, the lines shift, cross and anticross. By an analysis of the corresponding eigenvalues and eigenfunctions as functions of the magnetic field more insight into the spectral behavior can be achieved. The exchange interaction furthermore opens the possibility for ultra fast control of the Mn spin via optical manipulation of the exciton. We analyze whether switching of the Mn spin can be optimized by the application of an external magnetic field.

D.E. Reiter, S. Lüker, K. Gawarecki, A. GrodeckaGrad,
P. Machnikowski, V.M. Axt and T. Kuhn ,
 Phonon Effects on Population Inversion in Quantum Dots: Resonant, Detuned and FrequencySwept Excitations
Abstract:
The effect of acoustic phonons on different lightinduced excitations of a semiconductor quantum dot is investigated. Resonant excitation of the quantum dot leads to the Rabi oscillations, which are damped due to the phonon interaction. When the excitation frequency is detuned, an occupation can only occur due to phonon absorption or emission processes. For frequencyswept excitations a population inversion is achieved through adiabatic rapid passage, but the inversion is also damped by phonons. For all three scenarios the influence of the phonons depends nonmonotonically on the pulse area.
2011

A.A. Shanenko, M.V. Milošević, F.M. Peeters and A.V. Vagov ,
 Extended GinzburgLandau formalism for twoband superconductors
Abstract:
Recent observation of unusual vortex patterns in MgB_{2} single crystals raised speculations about possible “type1.5” superconductivity in twoband materials, mixing the properties of both typeI and typeII superconductors. However, the strict application of the standard twoband GinzburgLandau (GL) theory results in simply proportional order parameters of the two bands—and does not support the “type1.5” behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small τ=1T/Tc parameter) for a twoband clean swave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T→Tc. The extended version of the twoband GL formalism improves the validity of GL theory below Tc and suggests revisiting the earlier calculations based on the standard model.
ausgewählt für: Virt. J. Appl. Superconductivity, Vol. 20, Issue 3, Materials important for applications (Feb 2011)

B. Kaiser, A. Vagov, V.M. Axt and U. Pietsch,
 Ultrafast photoionization dynamics at high laser intensities in the xuv regime
Abstract:
We study the ionization dynamics in the softxray regime for high intensities and short pulses for excitations near the ionization threshold. Using a onedimensional helium atom model, we compare exact numerical solutions with timedependent HartreeFock results in order to identify the role of electronelectron correlations. At moderate intensities but still in the xray and shortpulse regime, we find that the HartreeFock theory reproduces well the dynamics of the groundstate occupation, while at high intensities strong correlation effects occur for excitations close to the threshold. From their characteristic momentum distributions, we can identify contributions to the double ionization from sequential threephoton and nonsequential or sequential twophoton processes. At elevated intensities these contributions deviate from their usual intensity scaling due to saturation effects, even though the total doubleionization probability stays below 10%. Furthermore, analysis of the time evolution of the momentum distribution reveals signatures of the energytime uncertainty which indicate a coherent regime of the dynamics.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 10, Issue 11, Atomic and Molecular Physics (Nov 2011)

A. Vagov, M.D. Croitoru, M. Glässl, V.M. Axt and T. Kuhn ,
 Realtime path integrals for quantum dots: Quantum dissipative dynamics with superohmic environment coupling
Abstract:
Based on a representation of the functional integral as the time evolution of the augmented density matrix we have worked out an implementation of the realtime path integral approach that is applicable to the dynamics of quantum dissipative systems with superohmic coupling to the environment. As a prototype for such a system we consider a laserdriven strongly confined semiconductor quantum dot coupled to acoustic phonons. First applications of this approach to quantum dot systems have already been published. Here, we provide a detailed description of the implementation, including a discussion of numerical issues and extend the formalism from twolevel quantum dot models with a puredephasing type carrierphonon coupling to the case of multiple electronic levels. The method allows for numerically exact calculations of the dot dynamics at strong dotphonon and dotlaser coupling and at long times, usually inaccessible by other approaches.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 23, Issue 12, Optical Properties and Quantum Optics (Mar 2011)

D.E. Reiter, T. Kuhn and V.M. Axt,
 Coherent control of a single Mn spin in a quantum dot via optical manipulation of the light hole exciton
Abstract:
Due to the strong exchange interaction between a single Mn spin embedded in a single semiconductor quantum dot and the quantum dot exciton, the spin state of the Mn atom can be controlled via optical manipulation of the exciton. When the hole of the exciton is of light hole type, both electron and hole can induce spin flips and thus change the Mn spin. We propose switching protocols to selectively address the Mn spin states. Depending on the polarization of the laser pulses the Mn spin can be switched by different switching schemes into all eigenstates. In contrast to previous studies involving heavy holes, we can find faster and more stable switching sequences. We discuss in detail the absorption spectrum of the lowest light hole exciton transition, which is strongly modified by the presence of the Mn spin. Furthermore, we show that spectrally resolved pumpprobe measurements provide a suitable technique to monitor the Mn spin dynamics.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 10, Issue 5, Photonics (May 2011)

D.E. Reiter, D. Wigger, V.M. Axt and T. Kuhn ,
 Generation and dynamics of phononic cat states after optical excitation of a quantum dot
Abstract:
We study theoretically the fluctuation properties of optical phonons generated after optical excitation of a quantum dot. If the quantum dot exciton is optically manipulated by ultrafast laser pulses, the electronic system and the phonon system can become entangled, which strongly influences the fluctuation properties of the phonons. When reduced to the phonon system, such an entanglement corresponds to a mixed phonon state. We discuss excitations with one or two ultrafast laser pulses. For a single pulse excitation, in general, a statistical mixture of two coherent states is found. For more pulses, a statistical mixture of superpositions of coherent states builds up in the phonon system. With the help of the Wigner function, which provides an intuitive picture of the generated phonon states, we explain how these states are formed depending on the excitation conditions and illustrate their time evolution. From this the fluctuation properties of the corresponding states can be well interpreted and the conditions for obtaining phonon squeezing are identified.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 24, Issue 24, Quantum Coherence, Computing and Inf. Stor. (Dec 2011)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 10, Issue 12, Photonics (Dec 2011)
sowie auch für: Virt. J. Quantum Inf., Vol. 11, Issue 12, Entanglement (Dec 2011)

M. Glässl, M.D. Croitoru, A. Vagov, V.M. Axt and T. Kuhn ,
 Influence of the pulse shape and the dot size on the decay and reappearance of Rabi rotations in laser driven quantum dots
Abstract:
We study the dynamics of strongly confined semiconductor quantum dots coupled to acoustic phonons and driven by external laser pulses by a numerical path integral method. The fielddependent damping, caused by the nonMarkovian processes of pure dephasing and manifesting itself in the peculiar decay and reappearance phenomenon of Rabi rotations is found to depend notably on the dot size and the shape of the applied laser pulses. In the limit of strong fields rectangular pulses yield a significant weaker damping than Gaussian or other bellshaped profiles. As a consequence, the undamping of Rabi rotations at high pulse areas is most clearly visible for rectangular pulses.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 24, Issue 12, Electronic Structure and Transport (Sep 2011)

M. Glässl, A. Vagov, S. Lüker, D.E. Reiter, M.D. Croitoru, P. Machnikowski, V.M. Axt and T. Kuhn,
 Longtime dynamics and stationary nonequilibrium of an optically driven strongly confined quantum dot coupled to phonons
Abstract:
We study the longtime dynamics and the stationary nonequilibrium state of an optically driven quantum dot coupled to acoustic phonons using numerically exact realtime path integrals and a fourthorder correlation expansion. By exploring wide ranges of temperatures, carrierphonon and carrierlight coupling strengths, we characterize the stationary nonequilibrium state and compare the exact solution to known, approximatively derived results. It is found that analytical calculations tend to overestimate the influence of the carrierphonon coupling, particularly at low temperatures and in the weakcoupling regime. The possibility of controlling the dot occupation in the stationary nonequilibrium by varying the laser detuning is discussed. A comparison between the numerical methods identifies the range of validity of the correlation expansion, which in the longtime limit is found to be surprisingly wide.

J.M. Daniels, T. Papenkort, D.E. Reiter, T. Kuhn and V.M. Axt,
 Quantum kinetics of squeezed lattice displacement generated by phonon down conversion
Abstract:
We study the fluctuation properties of longitudinal acoustic (LA) phonons generated by the anharmonic decay of coherent longitudinal optical phonons in a bulk semiconductor and a quantum dot. This process is comparable to the down conversion of photons, which is well known to generate squeezed photons. We use a quantum kinetic model to calculate the fluctuations of lattice displacement and momentum. This allows us to analyze the strength and the spatial distribution of the fluctuations. It is shown that the fluctuations may fall below their vacuum value, i.e., squeezing occurs. The squeezing only persists for short times due to fast dephasing of the different LA phonon modes and the increasing LA phonon population. In the quantum dot case, it is found that although LA phonon wave packets travel out of the quantum dot, the squeezing does not leave the vicinity of the dot but remains confined.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 24, Issue 16, Structural Properties (Oct 2011)

M.D. Croitoru, A.A. Shanenko, F.M. Peeters and V.M. Axt,
 Parityfluctuation induced enlargement of the ratio ΔE/kBTc in metallic grains
Abstract:
We investigate how the interplay of quantum confinement and particle numberparity fluctuations affects superconducting correlations in ultrasmall metallic grains. Using the numberparity projected BCS formalism we calculate the critical temperature and the excitation gap as a function of the grain size for grains with even and odd number of confined carriers. We show that the experimentally observed anomalous increase of the coupling ratio Δ_{E}/k_{B}T_{c} with decreasing superconducting grain size can be attributed to an enhancement of the numberparity fluctuations in ultrasmall grains.

M.D. Croitoru, A.A. Shanenko, C.C. Kaun and F.M. Peeters,
 Metallic nanograins: Spatially nonuniform pairing induced by quantum confinement
Abstract:
It is well known that the formation of discrete electron levels strongly influences the pairing in metallic nanograins. Here, we focus on another effect of quantum confinement in superconducting grains that was not studied previously, i.e., spatially nonuniform pairing. This effect is very significant when singleelectron levels form bunches and/or a kind of shell structure. We find that, in highly symmetric grains, the order parameter can exhibit variations with position by an order of magnitude. Nonuniform pairing is closely related to a quantumconfinementinduced modification of the pairinginteraction matrix elements and sizedependent pinning of the chemical potential to groups of degenerate or nearly degenerate levels. For illustrative purposes, we consider spherical metallic nanograins and also rectangular shapes. We show that the relevant matrix elements are, as a rule, enhanced in the presence of quantum confinement, which favors spatial variations of the order parameter, compensating the corresponding energy cost. The sizedependent pinning of the chemical potential further increases the spatial variation of the pair condensate. The role of nonuniform pairing is smaller in less symmetric confining geometries and/or in the presence of disorder. However, it always remains of importance when the energy spacing between discrete electron levels δ is approaching the scale of the bulk gap ΔB, i.e., δ>0.1–0.2 ΔB.

A . Vagov, M.D. Croitoru, V.M. Axt, P. Machnikowski and T. Kuhn
,
 Dynamics of quantum dots with strong electron phonon coupling: Correlation expansion vs. path integrals
Abstract:
We have simulated coherent control signals from quantum dots for carrier phonon interactions covering the low as well as the strong coupling limit. Calculations using the correlation expansion for phonon assisted density matrices are compared with numerically exact results obtained from a time dependent pathintegral approach. Even at elevated coupling strengths both calculations agree well for not too high temperatures. For pulse lengths and delay times shorter than the phonon induced memory time the correlation expansion gives good results in almost all cases. For strong coupling and/or high temperatures drastic discrepancies emerge. Interestingly, the correlation expansion works better at high pulse areas, which is related to a dynamic decoupling of electron and phonon dynamics in strongly confined systems.

D.E. Reiter, D. Wigger, J.M. Daniels, T. Papenkort, A. Vagov, V.M. Axt and T. Kuhn,
 Fluctuation properties of phonons generated by ultrafast optical excitation of a quantum dot
Abstract:
In this paper, the fluctuation properties of phonons after the optical excitation of a quantum dot with an ultrashort laser pulse are studied theoretically. When a single pulse with pulse area π creates an exciton in the system, a coherent phonon state builds up. Fluctuations of coherent states are time independent and equal to the vacuum fluctuations. By an excitation with a π/2 pulse a superposition of ground and exciton state is created. In this case the phonon system becomes entangled with the electronic system. In the phonon subsystem this leads to the formation of a statistical mixture of the vacuum and the coherent state. The fluctuations of this mixture oscillate in time with both the single and the double phonon frequency, but never exhibit squeezing. The discrepancies with the predictions made in a Raman tensor model are briefly discussed. All scenarios are illustrated using the Wigner function.

T. Papenkort, T. Kuhn and V.M. Axt,
 Generation of coherent LO phonons in optically driven biased quantum wells
Abstract:
We present a theoretical analysis and numerical simulations of the resonant generation of coherent LO phonons in an electrically biased quantum well. The system is driven by a laser pulse short enough to simultaneously excite two transitions, which leads to a quantum beat that can resonantly create coherent phonons. The generation of incoherent phonons is also calculated on a quantum kinetic level and found to be dominant in terms of the energy transferred to the lattice. The simulations successfully reproduce the main features found in recent experiments [Mizoguchi et al., Appl. Phys. Lett. 94, 171105 (2009)]. Depending on the excitation conditions different generation mechanisms can be discerned. We discuss their characteristics and their relative efficiency in the special case of the quantum well model under consideration.
2010

S. Sauer, J.M. Daniels, D.E. Reiter, T. Kuhn, A. Vagov and V.M. Axt,
 Lattice fluctuations at a double phonon frequency with and without squeezing: An exactly solvable model of an optically excited quantum dot
Abstract:
Timedependent lattice fluctuations of an optically excited strongly confined quantum dot are investigated with the aim to analyze the characteristics commonly used for identifying the presence of squeezed phonon states. It is demonstrated that the appearance of fluctuations oscillating with twice the phonon frequency, commonly regarded as a clear indication of squeezed states, cannot be considered as such. The source of the discrepancy with earlier investigations is discussed. Conditions for generating a squeezed state by using a twopulse excitation are analyzed.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 22, Issue 16, Optical Properties and Quantum Optics (Oct 2010)

A.A. Shanenko, M.D. Croitoru, A. Vagov and F.M. Peeters,
 Giant drop in the BardeenCooperSchrieffer coherence length induced by quantum size effects in superconducting nanowires
Abstract:
The BCS coherence length in lowdimensional superconductors is dramatically modified by quantumsize effects. In particular, for nanowires made of conventional superconducting materials, we show that the longitudinal zerotemperature coherence length exhibits widthdependent drops by 2–3 orders of magnitude each time when the bottom of one of singleelectron subbands formed due to the transverse quantization of electron motion is situated in a close vicinity to the Fermi level. This phenomenon has strong similarities to the wellknown BCSBEC BoseEinstein condensation crossover in ultracold fermionic condensates but with an important exception: it is driven by the transverse quantization of the electron motion rather than by the externally controlled strength of the fermionfermion interaction.

T. Papenkort, T. Kuhn and V.M. Axt,
 Resonant generation of coherent LO phonons by charge oscillations in a biased quantum well
Abstract:
A theoretical analysis of the generation of coherent and incoherent LO phonons after optical excitation of an electrically biased quantum well is presented. We show numerical calculations based on the densitymatrix formalism where both coherent and incoherent phonons are included on a fully quantum kinetic level. Bulk phonon modes are used as is appropriate for the wide quantum well studied here. The generation of coherent phonons is resonantly enhanced when two exciton lines with the splitting tuned to the phonon energy are simultaneously excited; such a tuning is achievable by the quantumconfined Stark effect, where the exciton lines are shifted by varying the electric bias. However, there is also a strong emission of incoherent LO phonons due to intersubband transitions of the excited carriers; even in the resonant case this by far dominates the energy transfer to the lattice. The different contributions of the impulsive and the resonant coherent phonon generation mechanism are discussed. A good agreement with recent experiments is found.

D.E. Reiter, T. Kuhn and V.M. Axt,
 Optically controlled spin dynamics in a magnetically doped quantum dot
Abstract:
The optically induced spin dynamics in a single quantum dot doped with a single Mn atom are studied theoretically both for the case of a magnetic field applied in Faraday configuration and in Voigt configuration. When the magnetic field is applied in Faraday configuration, the zcomponent of the angular momentum remains a good quantum number. We show that using a series of ultra short laser pulses manipulating both heavy and light hole excitons allows us to coherently switch the Mn spin from a given initial state into all other spin eigenstates on a picosecond time scale. By modifying the pulse sequence coherent superposition states can be prepared as well. Possible detection schemes are discussed. When the magnetic field is applied in Voigt configuration, the ultrafast optical excitation of an exciton changes the direction of the effective magnetic field acting on the Mn spin on a femtosecond time scale. This induces a precession of the Mn spin which can be efficiently controlled by the application of additional optical pulses.

V.M. Axt, D.E. Reiter and T. Kuhn ,
 Ultrafast dynamics and optical spincontrol in single magnetic quantum dots
Abstract:
An alloptical magnetization switching protocol is presented where the magnetization associated with a single Mn atom embedded in a single CdTe quantum dot is controlled on a picosecond time scale. Even though there is no direct optical coupling to the Mn spin, the control may be achieved by the optical excitation and manipulation of spinpolarized carriers that couple to the Mn spin via the exchange interaction. It is shown that the Mn spin can be selectively driven into each of its spin eigenstates. By suitably chosen pulse sequences also well defined superposition states can be prepared. The Mn spin dynamics is directly reflected in pump probe type signals.

J. Huneke, T. Kuhn, I. D’Amico and V.M. Axt,
 A theoretical analysis of instantaneous Coulomb renormalizations in a single quantum dot pumpprobe experiment
Abstract:
We present a theoretical analysis of Coulombcorrelation effects on the optical spectra of a single negatively charged quantum dot. The considered initial and final many particle states are adapted and motivated by a recent twocolor pumpprobe experiment. We demonstrate that the lowest energy transition is noticeably affected by exchange interactions if the initial state consists of a hot trion. It turns out that for initial states as obtained after spinconserving carrier relaxation new absorption and emission lines emerge.

D.E. Reiter, V.M. Axt and T. Kuhn,
 Fast preparation and detection of Mn spin states in a magnetically doped quantum dot
Abstract:
The spin dynamics of a single Mn spin in a single quantum dot under the excitation with ultra fast laser pulses is studied. We develop a switching protocol that is able to prepare stable superpositions of states with different Mn spin quantum numbers. Furthermore the optical signal in a pumpprobe type setup is calculated which can be used to read out the Mn spin state.

T. Papenkort, T. Kuhn and V.M. Axt ,
 Interplay between coherent and incoherent phonons in optically excited biased quantum wells
Abstract:
We present numerical simulations of the generation of coherent LO phonons in an electrically biased quantum well. An ultrashort laser pulse is used to simultaneously excite two exciton levels, which leads to an oscillating dipole moment that couples to the polar lattice and drives the phonons. The generation of coherent phonons becomes resonantly enhanced if the splitting of the two exciton levels is tuned to the LO phonon energy. In this case relaxation by emission of incoherent phonons becomes also possible. Our calculation therefore takes into account incoherent phonons on a quantum kinetic level as well. The intersubband relaxation by excitation of incoherent phonons competes with the generation of coherent phonons and is dominant in terms of the energy transferred.

D.E. Reiter, G. Hemmert, T. Kuhn, V.M. Axt and P. Machnikowski,
 Alloptical spin switching in neutral or charged magnetic quantum dots
Abstract:
The spin dynamics in a single semiconductor quantum dot doped with a single Mn atom are analyzed. We consider a neutral and a negatively charged dot and in both cases we concentrate on the light holetoconduction band transition. Both electrons and light holes couple to the Mn spin via the strong exchange interaction. After the excitation by an ultra short laser pulse oscillatory spin dynamics take place, where electron or hole can flip their spin accompanied by a change of the Mn spin. The Mn spin dynamics can be controlled by excitation with additional pulses. Starting from a given initial state we demonstrate that the Mn spin can be flipped alloptically into a steady final state in both neutral or charged quantum dots.

J. Huneke, T. Kuhn and V.M. Axt,
 Detecting strain wave propagation through quantum dots by pumpprobe spectroscopy: A theoretical analysis
Abstract:
The influence of strain waves traveling across a quantum dot structure on its optical response is studied for two different situations: First, a strain wave is created by the optical excitation of a single quantum dot near a surface which, after reflection at the surface, reenters the dot; second, a phonon wave packet is emitted by the excitation of a nearby second dot and then travels across the quantum dot. Pumpprobe type excitations are simulated for quantum dots in the strong confinement limit. We show that the optical signals allow us to monitor crossing strain waves for both structures in the realtime response as well as in the corresponding pumpprobe spectra. In the timederivative of the phase of the polarization a distinct trace reflects the instantaneous shifts of the transition energy during the passage while in the spectra pronounced oscillations reveal the passage of the strain waves.

K. Roszak, P. Machnikowski, V. M. Axt and T. Kuhn,
 Spin decoherence of a confined exciton due to one and twophonon assisted transitions
Abstract:
Exciton spin decay in a selfassembled InAs/GaAs quantum dot is studied. The spin relaxation results from an interplay of two factors: the BirPikus Hamiltonian and the shortrange exchange interaction, leading to one and twophonon assisted transitions. We establish a hierarchy between the resulting transition rates; the onephonon assisted transition to dark states is the fastest process. We also show the dominating role of transverse phonons for all of the transitions.
2009

D.E. Reiter, T. Kuhn and V.M. Axt,
 Alloptical spin manipulation of a single manganese atom in a quantum dot
Abstract:
For a CdTe quantum dot doped with a single Mn atom we analyze the dynamics of the Mn spin when the dot is excited by ultrashort laser pulses. Because of the exchange interaction with the Mn atom, electron and hole spins can flip and induce a change of the Mn spin. Including both heavy and lighthole excitons and using suitable pulse sequences, angular momentum can be transferred from the light to the Mn system while the exciton system returns to its ground state. We show that by a series of ultrashort laser pulses the Mn spin can be selectively driven into each of its six possible orientations on a picosecond timescale. By applying a magnetic field the total switching time and the required number of pulses can be strongly reduced.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 19, Issue 19, Optical Properties and Quantum Optics (May 2009)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 8, Issue 6, Condensed Matter Physics (Jun 2009)

C. Thurn, V.M. Axt, A. Winter, H. Pascher, H. Krenn, X. Liu,
J.K. Furdyna and T. Wojtowicz
,
 Origin of resonance structures in magnetooptical spectra of InSb and In_{1−x}Mn_{x}Sb
Abstract:
InSb and InMnSb samples have been investigated by means of magnetooptical Kerr effect and magnetic circular dichroism. In binary semiconductor compounds such as InSb the observed magnetooptical spectra exhibit narrow and distinct resonances which can be associated with dipoleallowed transitions between the Landau levels in conduction and valence bands. With increasing magnetic field the Landau splitting increases and the observed peaks change their position and amplitude accordingly. In contrast to this observation, the magnetooptical spectra of the diluted magnetic semiconductor InMnSb show only one strong and broad resonance. Contrary to what one expects, particularly in narrow gap materials with large g factors and small effective masses, the shape and position of this resonance do not change with the applied magnetic field. It is found, however, that the amplitude depends linearly on the magnetization of the samples. In this paper we describe how these observations can be understood by means of a k · p theory incorporating the exchange interaction of free carriers with localized electrons in the Mn ions.

M. Vogel, A. Vagov, V.M. Axt, A. Seilmeier and T. Kuhn,
 Spinsensitive intersubbanddynamics of optically generated carriers in semiconductor quantum wells
Abstract:
A theoretical analysis of the intersubband dynamics in undoped quantum wells is presented where spinoriented carriers are initially generated by circularly polarized interband excitations. Subsequent resonant intersubband excitations induce Rabi rotations between the subbands resulting in a fast periodic modulation of the spin orientation in each subband. It is investigated whether pure spin modulations can be performed where the charge density of the subbands is kept constant when initially equal occupations of the two lowest conduction subbands with opposite spin orientations have been prepared. While this is the expected behavior for a threeband model of noninteracting particles it turns out that when the Coulomb interaction is taken into account the spin modulations are typically accompanied by corresponding modulations of the subband occupations. It is demonstrated that under realistic conditions it should nevertheless be feasible to realize a pure spin rotation in a given subband provided the intersubband excitations are sufficiently short or the carrier density is sufficiently low. Successive spin rotations are shown to decrease the degree of spin polarization even when spinrelaxation processes are neglected.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 20, Issue 16, Nanomagnetism and Spintronics (Oct 2009)

A. Vagov, H. Schomerus and V.V. Zalipaev,
 Asymptoticboundarylayer method for unstable trajectories: Semiclassical expansions for individual scar wave functions
Abstract:
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wavefunction asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

T. Kuhn, D.E. Reiter and V.M. Axt ,
 Optical control of the spin state in a semimagnetic quantum dot
Abstract:
In a Mn doped quantum dot the spin state of the Mn atom can be controlled via a well chosen sequence of laser pulses, which create or annihilate excitons in the quantum dot. The change of the state consists of a flip of the Mn spin accompanied by a simultaneous spin flip of an electron or light hole induced by the exchange interaction between Mn spin and electron or hole spin. All flipping processes can be interpreted in terms of exchangeinduced Rabi oscillations. The period and amplitude of the oscillations are determined by the coupling strength of the exchange interactions, which also strongly influences the energy splitting between the involved states. External magnetic fields can be used to tune the energies of the exciton states and thereby minimize the energy splitting between the states involved in the spin flip process. Thus the switching dynamics can be optimized by applying a magnetic field.

T. Papenkort, T. Kuhn and V.M. Axt ,
 Ultrafast coherent dynamics in optically driven BCS systems
Abstract:
We present simulations of the nonlinear ultrafast dynamics of a BCS superconductor. Pumpprobe measurements and a coherent control technique are employed to gain insight into the excitation dynamics of the superconductor. In pumpprobe spectra the energy gap of the superconductor is visible as an area of low absorption followed by a sharp peak. Excitation with a short laser pulse lowers the gap and thereby shifts the peak. However, the numerical calculations reveal the emergence of a nonadiabatic regime on short time scales: A sufficiently short pump pulse causes a fast oscillation of the modulus of the BCS order parameter. Although this parameter can usually be identified with the energy gap, its oscillation remains hidden in pumpprobe spectra, i.e., the gap observed in the spectra is independent of the delay time. Instead the gap in the spectra corresponds to the mean value of the oscillation. By making use of a coherent control technique involving a second pump pulse, this oscillation may be made visible in probe spectra. This is because the reaction of the BCS system to the second pump pulse depends strongly on its instantaneous state at the time of the impact of this pulse. In particular the gap observed in the spectra after the second pump pulse for varying pumppump delay times mimics the oscillation of the order parameter after the first pump pulse.

D.E. Reiter, V.M. Axt and T. Kuhn,
 Spin control by ultra short laser pulses in a Mn doped quantum dot
Abstract:
Optically induced spin flip processes in quantum dots doped with a single Mn atom are discussed. On the femtosecond time scale the exciton can be controlled by ultra short laser pulses. Via the exchange interaction the Mn spin can flip on a picosecond time scale by transferring its angular momentum to the exciton. For a heavy hole system this flipping process can be described in terms of exchangeinduced Rabi oscillations between the bright and dark exciton state accompanied by a flip of the Mn spin. Because of the energy splitting between bright and dark excitons the Rabi oscillations are offresonant and a series of laser pulses is required to achieve a complete flip. When a light hole exciton is resonantly excited in addition to the heavy hole exciton we show that a flip of the Mn spin by two can be achieved by a series of light pulses while the exciton system returns to its initial state.

M. Vogel, A. Vagov, V.M. Axt, A. Seilmeier and T. Kuhn,
 Intersubbanddynamics of spin polarized carriers
Abstract:
The intersubband (ISB) dynamics of spin orientated carriers generated in undoped quantum wells by circularly polarized interband excitations is analyzed theoretically. It is shown that short THz pulses in resonance with the lowest conduction ISB transition can be used to switch the spin orientation in a given subband without changing the total subband occupation. For longer ISB pulses a periodic modulation of the spin orientation is found. However, when the Coulomb interaction is taken into account the total subband density is typically also modulated which differs from expectations based on calculations in a three band model of noninteracting particles. The dependence on the ratio of the subband masses is discussed as well as the observability of these effects in pumpprobe type measurements.

D.E. Reiter, S. Sauer, J. Huneke, T. Papenkort, T. Kuhn, A. Vagov
and V.M. Axt,
 Generation of squeezed phonon states by optical excitation of a quantum dot
Abstract:
A theoretical analysis of the fluctuation properties of optical phonons generated by the optical excitation of a quantum dot is presented. In particular we study whether squeezed states may be generated where either the fluctuations of the displacement or of the momentum fall below the vacuum level. The calculations are based on a generating functions formalism which provides analytical results for the case of excitation by ultrashort optical pulses. While after a single pulse excitation no squeezing occurs we find that after an excitation with two phaselocked pulses phonon states can be created where the uncertainties of displacement or momentum temporarily fall below their vacuum values.

T. Papenkort, T. Kuhn and V.M. Axt,
 Nonequilibrium dynamics and coherent control of BCS superconductors driven by ultrashort THz pulses
Abstract:
The nonequilibrium dynamics of BCS superconductors after excitation with short THz pulses slightly above the superconducting gap is studied theoretically. Calculated pumpprobe spectra show how the gap is influenced by this optical excitation. For ultrashort pump pulses a nonadiabatic regime emerges, in which the BCS order parameter exhibits oscillations. These oscillations do not show up in pumpprobe spectra. However they may be made visible by using a coherent control type excitation with two phaselocked pump pulses.

D.E. Reiter, T. Kuhn, V.M. Axt and P. Machnikowski,
 Dynamics of a single Mn spin in a quantum dot: The role of magnetic fields in Faraday and Voigt geometry
Abstract:
A theoretical analysis of the optically driven spin dynamics of a single Mn atom in a quantum dot in the presence of magnetic fields in different geometries is presented. When a magnetic field in Faraday configuration is applied, the Mn spin can be flipped from its initial state into each of its six spin eigenstates via optical excitation and manipulation of excitons. In the case of a magnetic field in Voigt configuration, the presence of an exciton leads to a precession of the Mn spin around the combination of external and exchangeinduced magnetic field. By using optical pulses this precession can be switched on and off.

J. Huneke, T. Kuhn, V.M. Axt and P. Machnikowski,
 Impact of traveling phonon wave packets on the optical response of quantum dots
Abstract:
The influence of phonon wave packets created by the optical excitation of a quantum dot (QD) structure on fourwavemixing (FWM) signals is analyzed theoretically. Two different structures are compared: a single QD in a halfspace geometry located close to the surface, where the emitted phonon wave packet after reflection at the surface reenters the QD and a pair of QDs in an infinite medium, where the phonon wave packet created in one QD travels across the other QD. Although the strain fields are very similar pronounced differences in the FWM polarizations are found. In the single QD system we observe clear signatures of the reflected wave packet in the FWM signal at positive delay times, which can also be observed in the timeintegrated FWM signal from an inhomogeneously broadened ensemble of such QDs. In the two QD case no signatures of the traveling wave packet are seen in the signal at positive delays and, consequently, in the ensemble signal. However, they are clearly seen in the FWM signal at negative delay times.

K. Roszak, P. Machnikowski, V. M. Axt and T. Kuhn,
 Exciton spin decay in quantum dots: single and double phonon assisted transitions
Abstract:
We study phonon assisted transitions leading to exciton spin decay in quantum dots. We concentrate on couplings specific to the hole (BirPikus Hamiltonian) and the exciton as a whole (shortrange exchange interaction). A system strongly confined in a selfassembled quantum dot is considered. We discuss singlephonon assisted processes arising from the interplay of these interactions and show the dominating role of transverse phonons. We have also found a new twophonon assisted transition, connected with the interplay of different parts of the BirPikus Hamiltonian in the presence of the singlettriplet splitting.
2008

A. Vagov, M.D. Croitoru, V.M. Axt, T. Kuhn and F. Peeters,
 Real time path integrals in studies of quantum dots dynamics: Nonmonotonous decay rate and reappearance of Rabi rotations
Abstract:
The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using the path integral method. We explore the cases of long pulses, strong dotphonon and dotlaser coupling and high temperatures, which up to now have been inaccessible. We find that the decay rate of the Rabi oscillations is a nonmonotonic function of the laser field leading to the decay and reappearance of the Rabi oscillations in the field dependence of the dot exciton population.

J. Huneke, A. Krügel, T. Kuhn, A. Vagov and V. M. Axt,
 Impact of strain waves traveling across a quantum dot on the optical response of the dot: Distinction between strain waves of different origin
Abstract:
The influence of strain waves traveling across a semiconductor quantum dot on the optical spectra of the lowest quantum dot transition is analyzed. Pure dephasing interactions between electronic and phononic degrees of freedom in quantum dot systems are considered, which represent the most important type of electronphonon interaction in strongly confined quantum dots. For the case of excitation by ultrafast laser pulses, a generating function formalism provides analytical results, which are exact within the framework of the model. Two situations are compared: (i) a phonon wave packet is generated by the optical excitation of a singlequantum dot near a surface, which after reflection at the surface reenters the quantum dot and (ii) a phonon wave packet is generated by the excitation of a nearby second dot and then travels across the quantum dot. Although the displacement fields passing the dot are almost identical in these two situations, we find that the real time responses as well as the corresponding spectra exhibit qualitative differences and thus allow for a discrimination of phonon wave packets from different origins.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 7, Issue 9, Condensed Matter Physics (Sep 2008)

T. Papenkort, T. Kuhn and V.M. Axt,
 Coherent control of the gap dynamics of BCS superconductors in the nonadiabatic regime
Abstract:
By exciting a BCS superconductor with ultrashort pulses in the frequency range of the superconducting gap a nonadiabatic regime can be reached. In this regime the modulus of the order parameter oscillates in time. Although its average value can be identified with the gap in the absorption spectrum, the oscillation itself remains invisible in pumpprobe spectra. In this Brief Report we demonstrate that by employing a coherent controltype scheme of excitation by two phaselocked pump pulses this oscillation can be unveiled in the probe spectrum. We find that the reaction of the superconductor to a second pump pulse depends strongly on its instantaneous state at the time of the impact of the second pulse. Based on numerical calculations performed on the meanfield level it is shown that by varying the delay time between the two pump pulses the transient oscillation of the order parameter can be transformed into an oscillation of its longtime value, which shows up in the absorption spectrum of a subsequent weak probe pulse as an oscillation of the gap when plotted as a function of the delay time.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 7, Issue 11, Condensed Matter Physics (Nov 2008)

T. Kuhn, D. Reiter and V.M. Axt,
 Coherent control of carrier capture and wave front dynamics in homogeneously excited quantum wiredot systems
Abstract:
We study the coherent control of capture and transport processes in a quantum wirequantum dotsystem which is homogeneously excited by ultrafast laser pulses. Due to the carrier capture into the quantum dot a spatial profile of the carrier density in the wire region builds up exhibiting wave fronts moving away from the dot. In the presence of a dot with two or more bound levels wave fronts resulting from the capture into different states can clearly be distinguished. By using a pair of phase locked pulses the capture rates into different levels but also the spatiotemporal dynamics in the wire region can be coherently controlled.

K. Roszak, P. Machnikowski, V.M. Axt and T. Kuhn ,
 One and two phonon assisted transitions between exciton spin states in a quantum dot
Abstract:
Exciton spin decay is studied in a selfassembled InAs/GaAs quantum dot. The spin relaxation results from an interplay of two factors: the BirPikus Hamiltonian and the shortrange exchange interaction, leading to one and two phonon assisted transitions. We establish a hierarchy between the resulting transition rates and show the dominating role of transverse phonons for all the transitions.
2007

A. Vagov, M.D. Croitoru, V.M. Axt, T. Kuhn and F.M. Peeters,
 Nonmonotonic field dependence of damping and reappearance of Rabi oscillations in quantum dots
Abstract:
The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using a numerical path integral method. We explore the cases of long pulses, strong dotphonon and dotlaser coupling, and high temperatures, which, up to now, have been inaccessible. We find that the phononinduced damping of Rabi rotations is a nonmonotonic function of the laser field that is increasing at low fields and decreasing at high fields. This results in a reappearance of Rabi rotations at high fields. This phenomenon is of a general nature which occurs for all temperatures and carrierphonon coupling strengths.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 15, Issue 23, Optical Properties and Quantum Optics (Jun 2007)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 6, Issue 7, Condensed Matter Physics (Jul 2007)

P. Machnikowski, V.M. Axt and T. Kuhn,
 Quantum information encoding in dressed qubits
Abstract:
It is shown that quantum information stored in a twolevel system coupled to a superOhmic bosonic bath is coherently distributed between the system and the environment. A different twolevel subsystem, including a proper coherent state of the environment, satisfies all control, reset, and measurement conditions required for a qubit, including twoqubit conditional gates. Such a dressed qubit is decoupled from the remaining environmental degrees of freedom but its control imposes specific adiabaticity conditions. The dressed qubit is the actual physical medium in which quantum information is encoded whenever control operations are slower than the environment dynamics.
ausgewählt für: Virt. J. Quantum Inf., Vol. 7, Issue 6, Error Correction (Jun 2007)
sowie auch für: Virt. J. Nan. Sci. & Tech., Vol. 15, Issue 22, Quantum Coherence Computing and Information Storage (Jun 2007)

T. Papenkort, V.M. Axt and T. Kuhn,
 Coherent dynamics and pumpprobe spectra of BCS superconductors
Abstract:
The density matrix formalism is employed to calculate pumpprobe spectra of BCS superconductors in the coherent regime. Two dynamical regimes, one adiabatic and one nonadiabatic, can be clearly distinguished. In the adiabatic regime, the modulus of the BCS order parameter can be identified with half the gap in the probe spectra. In the nonadiabatic regime, the order parameter oscillates in real time, whereas the gap observed in the spectra reflects its temporal average. The transition between these regimes is accompanied by a qualitative change of the intensity dependence of the dynamical gap renormalization. Furthermore, a holeburning effect occurs if the spectral shape of the pump pulse is sufficiently sharp. A probe pulse preceding the pump pulse leads to spectral oscillations, and both the gap before and after the pump pulse are visible in the probe spectra.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 7, Issue 1, Condensed Matter Physics (Jan 2008)

D. Reiter, M. Glanemann, V.M. Axt and T. Kuhn,
 Spatiotemporal dynamics in optically excited quantum wiredot systems: Capture, escape, and wavefront dynamics
Abstract:
Transitions of optically excited carriers between delocalized states in a quantum wire and localized states in a quantum dot are studied on a quantum kinetic level. These transitions are mediated by the emission or absorption of longitudinal optical phonons. Three different excitation scenarios are considered: The capture of a traveling wave packet results in occupations of the bound states and, under suitable conditions, in coherent superpositions. Both occupations and coherences decay due to thermal escape processes resulting from the absorption of phonons. A spatially homogeneous excitation in the quantum wire below the threshold for optical phonon emission leads to capture processes associated with the buildup of a wave front in the carrier density between regions which are already influenced by the capture and regions where this influence is not yet present. A selective excitation of the quantum dot exciton is at elevated temperatures followed by thermal escape processes with a subsequent spreading of the carriers in the quantum wire. We find that for a physically meaningful description of the spatiotemporal dynamics a consistent treatment of both diagonal and offdiagonal density matrix elements is essential in all three scenarios.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 15, Issue 22, Optical Properties and Quantum Optics (Jun 2007)

K. Roszak, V.M. Axt, T. Kuhn and P. Machnikowski,
 Exciton spin decay in quantum dots to bright and dark states
Abstract:
We study the phonon influence on the spin of an exciton confined in a quantum dot. A process causing the transition of an initial bright heavy hole exciton spin state to dark states is identified. For a set of parameters typical for InAs/GaAs selfassembled quantum dots the corresponding decay times are over two orders of magnitude faster than for the previously studied transition between bright states and are comparable to exciton lifetimes already at temperatures of several tens of Kelvins.
Erratum: Phys. Rev. B 77, 249905(E) (2008)
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 16, Issue 24, Optical Properties and Quantum Optics (Dec 2007)

A. Krügel, A. Vagov, V.M. Axt and T. Kuhn
 Monitoring the buildup of the quantum dot polaron: Pumpprobe and fourwave mixing spectra from excitons and biexcitons in semiconductor quantum dots
Abstract:
Pumpprobe (PP) and fourwave mixing (FWM) signals from a single quantum dot are presented which are based on a fourlevel quantum dot model, accounting for the fine structure splitting as well as for the biexciton binding and phononinduced pure dephasing. We have derived closed form analytical expressions for the PP and FWM polarization components in the time domain after excitation with a pair of ultrafast laser pulses. The solutions are exact within this model. We discuss the dependence of the signals on the polarization of the exciting pulses. We show that for PP spectra after excitation with collinearly polarized pulses and for FWM spectra after cocircular excitation changes in the line shape are entirely due to the polaron formation leading to a fixed shape when this process is completed. For PP spectra after cocircular excitation and FWM spectra after collinear excitation in general periodic modulations of the shape are superimposed which persist even on long time scales and reflect quantum beats due to the fine structure splitting or the biexciton binding energy.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 16, Issue 21, Optical Properties and Quantum Optics (Nov 2007)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 6, Issue 12, Condensed Matter Physics (Dec 2007)

A. Krügel, V.M. Axt, T. Kuhn and A. Vagov,
 Combined influence of Coulomb, exchange and phonon couplings on the line shape of quantum dot spectra
Abstract:
We study single quantum dot (QD) four wave mixing (FWM) and pump probe (PP) spectra calculated numerically from the exact analytical solution for a four level QD model with pure dephasing. Due to Coulomb and exchange interaction the spectra exhibit a fine structure splitting of the exciton and biexciton lines. The combination of the different interaction contributions leads to new features such as biexciton contribution in PP spectra after cocircular excitation.

D. Reiter, V.M. Axt and T. Kuhn,
 Spatiotemporal dynamics of charge carriers in quantum dotwire systems following delocalized optical excitations
Abstract:
The density matrix formalism for quantum kinetics is used to model the Spatiotemporal dynamics of the carrier density after a spatially homogeneous excitation in a coupled semiconductor quantum wiredot system. The carrier capture leads to a wave front dynamics in the carrier distribution in the quantum wire region and the formation of a plateau between the fronts. The dynamics are analyzed using different excitation energies.
2006

D. Reiter, M. Glanemann, V.M. Axt and T. Kuhn,
 Controlling the capture dynamics of traveling wave packets into a quantum dot
Abstract:
An analysis of the control of capture processes from a traveling wave packet in a semiconductor quantum wire into localized states of a quantum dot is presented. On ultrafast time scales this capture in general leads to occupations of the discrete states as well as to coherences among these states. We show that both occupations and coherences can be efficiently controlled by excitation with a pair of spatially localized laser pulses which are spatially, temporally, or spectrally displaced with respect to each other. The coherences between discrete dot states are controlled by spatially nonoverlapping pulses by varying either their spatial or their temporal displacement. For spatially overlapping pulses an effective pulse shaping occurs which modifies both occupations and coherences. By using twocolor laser pulses the dot states can be selectively addressed which may result in particularly pronounced coherences.
Erratum: Phys. Rev. B 73, 209901(E) (2006)
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 13, Issue 13, Optical Properties and Quantum Optics (Apr 2006)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 5, Issue 4, Condensed Matter Physics (Apr 2006)

A. Krügel, V.M. Axt and T. Kuhn,
 Back action of nonequilibrium phonons on the optically induced dynamics in semiconductor quantum dots
Abstract:
The dynamics in a GaAstype quantum dot induced by excitation with Gaussian laser pulses of arbitrary duration are calculated in the density matrix formalism using the correlation expansion. In particular the backaction of nonequilibrium phonons, i.e., the coherent phonon amplitude and the nonequilibrium phonon occupation, on the electronic twolevel system are studied. We find that especially for long pulses and low temperatures nonequilibrium phonons play an important role and cannot be neglected.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 13, Issue 2, Optical Properties and Quantum Optics (Jan 2006)

S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V.M. Axt, T. Kuhn and A. Zrenner
 Twophoton Rabi oscillations in a single In_{x}Ga_{1x}As/GaAs quantum dot
Abstract:
We report on Rabi oscillations of the biexciton in a single InxGa1–xAs/GaAs quantum dot, induced via a coherent twophoton process. In contrast to singleexciton Rabi oscillations the measured population oscillation is not purely sinusoidal in excitation pulse area. The experimental results are well reproduced by a theoretical calculation that relies only on the pulse shape and biexciton binding energy. Dephasing times of the biexciton are similar to those of the single exciton under the applied measurement conditions reaching up to 220 ps.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 13, Issue 11, Optical Properties and Quantum Optics (Mar 2006)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 5, Issue 4, Photonics (Apr 2006)

T. Voss, I. Rückmann, and J. Gutowski, V.M. Axt and T. Kuhn,
 Coherent control of the exciton and excitonbiexciton transitions in the generation of nonlinear wavemixing signals in a semiconductor quantum well
Abstract:
By use of an optical coherentcontrol technique we demonstrate and analyze the control of transitions involved in the generation of fourwavemixing signals in a semiconductor quantum well for the two different fourwavemixing directions and for different sequences of the excitation pulses. Results are presented for frequency as well as for timeresolved signals. A doubling of the coherent switching frequency is found which occurs if the laser pulses performing the control process contribute quadratically to the wavemixing signal. A direct comparison between experiment and microscopic theory reveals how the coherentcontrol process acts on the coherent polarization of the excitonbiexciton system in all different configurations. An additional interpretation of the experimental results based on a simplified fewlevel model is able to provide an intuitive understanding of the relevant processes which govern the coherent control of the excitonic and biexcitonic wavemixing polarizations.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 5, Issue 4, Photonics (Apr 2006)

A. Vagov, M.D. Croitoru, V.M. Axt, T. Kuhn and F.M. Peeters,
 High pulse area undamping of Rabi oscillations in quantum dots coupled to phonons
Abstract:
We study the dynamics of strongly confined semiconductor quantum dots, coupled to acoustic phonons and driven by external laser pulses, by a numerical path integral method. Our method fully explores the relevant memory of the system thus accounting for all nonMarkovian features of the dynamics. The decay time and the frequency of Rabi oscillations are found to depend notably on the temperature and the applied field. The field dependence is nonmonotonic leading to an undamping of Rabi oscillations at high pulse areas.

T. Voss, I. Rückmann, J. Gutowski, V.M. Axt and T. Kuhn
 Coherent control of excitonbiexciton beats: Direction selectivity of fourwavemixing signals in experiment
Abstract:
In experiments and simulations based on a microscopic theory the optical coherent control of excitonbiexciton beats in coherent fourwavemixing signals from a semiconductor quantum well is demonstrated. It is found that a reduction of the beat amplitude for one fourwavemixing direction may at the same time coincide with a large beat amplitude for the other direction. The results can be understood by considering that at least twophoton processes are required to coherently excite biexcitonic transitions which are responsible for the occurrence of the beat structure in the fourwavemixing signals.

D. Reiter, M. Glanemann, V.M. Axt and T. Kuhn,
 Control of captureinduced coherences in wave packet transport through nanostructures
Abstract:
Two different scenarios of controlling occupations and coherences of a quantum dot are discussed. In both cases two wave packets travelling through a quantum wire are used. In the first scenario the two wave packets are generated at both sides of the dot and the coherence is controlled by transport mechanisms. In the second scenario the wave packets are generated at the same spot so that the occupations and coherence are strongly affected by the interference between the laser pulses. Additionally in the latter scenario we show the crossover from the pulse shaping induced coherent control to the control by means of transport.

A. Krügel, V.M. Axt, T. Kuhn, A. Vagov and F.M. Peeters,
 Coherent nonlinear optical response of excitons and biexcitons in quantum dots coupled to phonons
Abstract:
Four wave mixing signals from single dots and dot ensembles involving excitonic and biexcitonic transitions are discussed. The results have been obtained analytically from a four level dot model coupled to longitudinal acoustic phonons. Time integrated four wave mixing amplitudes for quantum dot ensembles exhibit polarization dependent quantum beats that have already been found in experimental data. In four wave mixing signals of single quantum dots we find that the ground state to exciton transition has two contributions. One is identical to the known solution of the two level quantum dot model and leads to symmetric spectra for longer delay times, while the other comprises phase information from the biexciton and results in asymmetric spectra.

P. Machnikowski, V.M. Axt, T. Kuhn and L. Jacak,
 Exploiting the nonMarkovian nature of carrierphonon dynamics: Multipulse control of decoherence in quantum dots
Abstract:
We show that pure dephasing of an exciton in a quantum dot may be reduced by performing the optical excitation with a series of ultrafast pulses. Dephasing may considerably decrease already for a few pulses. In terms of the resulting coherence vs. control time, a multipulse approach is often more efficient than using smooth (Gaussian) pulses. These results show that a significant reduction of dephasing is achievable even with relatively limited experimental resources.

T. Kuhn, B. Krummheuer and V.M. Axt
 Influence of surfaces on the pure dephasing of quantum dots
Abstract:
An analysis of the influence of confined acoustic phonons on the pure dephasing of a single quantum dot located in a half space or a freestanding slab is given. We find that the proximity to a surface leaves distinct traces in the polarization and the absorption spectrum which can be traced back to the interaction of the dot with surface phonons and a reflected phonon wave packet.

D. Reiter, V. M. Axt, and T. Kuhn ,
 CaptureInduced Quantum Dot Coherences Controlled by Traveling Wave Packets of Different Spatial Extension
Abstract:
The injection of two wave packets with different spatial extensions is used to control the coherences, which build up when traveling wave packets are captured into a quantum dot.
2005

V.M. Axt, A. Vagov, B. Krummheuer, T. Kuhn, P. Machnikowski, J. Krasnyj and L. Jacak,
Semiconductor Macroatoms, pp.221248 (2005)

M. Glanemann, V.M. Axt and T. Kuhn,
 Transport of a wave packet through nanostructures: Quantum kinetics of carrier capture processes
Abstract:
Capture processes of an electronic wave packet traveling in a quantum wire into localized states of an embedded quantum dot by means of phonon emission are studied in a quantum kinetic approach. It turns out that due to the ultrashort length and time scales involved the capture processes exhibit a variety of quantum kinetic features which cannot be described by a simple semiclassical capture rate. We find in general a nonmonotonic rise of the occupation of bound states even at low temperatures where no phonon absorption is possible. This is related to the finite collision duration and the presence of coherent superpositions between initial and final states in the scattering process giving rise to phonon Rabi oscillations between free and trapped states. In the case of more than one bound state in the dot typically a linear combination of these bound states is populated, which leads to a nontrivial dynamics of the trapped carrier density. For potential profiles with large reflection probability it turns out that also the transmission and reflection behavior is modified by the capture process. Finally the theory is applied to a twoband model including optical excitation and excitonic effects. For the scenarios studied in the paper these phenomena lead to some quantitative modifications but they do not change the characteristic quantum features of the capture dynamics.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 12, Issue 5, Optical Properties and Quantum Optics (Aug 2005)

B. Krummheuer, V.M. Axt, T. Kuhn, I. D'Amico and F. Rossi,
 Pure dephasing and phonon dynamics in GaAs and GaNbased quantum dot structures: Interplay between material parameters and geometry
Abstract:
The pure dephasing of excitons in quantum dot structures due to their interaction with acoustic phonons as well as the spatiotemporal dynamics of the created nonequilibrium phonon population is studied theoretically. The theory is applied to GaAs as well as GaNbased heterostructures. A detailed analysis of the interplay between different material parameters, different quantum dot geometries, and different electric fields is presented. The optical polarization induced by an ultrashort laser pulse exhibits a characteristic nonexponential behavior: it decays on a pico or subpicosecond time scale to a value that strongly depends on temperature, structure, and material parameters and is then retained until, on a typically much longer time scale, it finally decays because of electronhole recombination or transitions to other states. We find that, in general, the remnant optical polarization is much higher in the GaAsbased structures than in the GaNbased structure mainly because of the strongly enhanced piezoelectric coupling in GaN quantum dots. The optical excitation also leads to the buildup of a phonon population consisting of a polaron part that remains localized in the region of the quantum dot and a traveling part that leaves the dot region at the speed of sound. This traveling part exhibits characteristic anisotropies reflecting both the anisotropy of the quantum dot structure and of the coupling matrix elements.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 12, Issue 2, Optical Properties and Quantum Optics (Jul 2005)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 4, Issue 7, Condensed Matter Physics (Jul 2005)

V.M. Axt, P. Machnikowski and T. Kuhn,
 Reducing decoherence of the confined exciton state in a quantum dot by pulsesequence control
Abstract:
We study the phononinduced dephasing of the exciton state in a quantum dot excited by a sequence of ultrashort pulses. We show that the multiplepulse control leads to a considerable improvement of the coherence of the optically excited state. For a fixed control time window, the optimized pulsed control often leads to a higher degree of coherence than the control by a smooth, single Gaussian pulse. The reduction of dephasing is considerable already for 2–3 pulses.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 11, Issue 15, Optical Properties and Quantum Optics (Apr 2005)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 4, Issue 5, Condensed Matter Physics (May 2005)

V.M. Axt,T. Kuhn, A. Vagov and F.M. Peeters,
 Phononinduced pure dephasing in excitonbiexciton quantum dot systems driven by ultrafast laser pulse sequences
Abstract:
A semiconductor quantum dot model accounting for single exciton as well as biexciton states coupled to phonons and laser light is investigated in the limit of strong electronic confinement. For an arbitrary sequence of excitations with ultrafast pulses analytical solutions are obtained for all densitymatrix elements. The results are nonperturbative with respect to both the carrierphonon and the carrierlight coupling. Numerical results for a single pulse excitation are presented illustrating spectral features of our solution as well as pulse area and temperature dependences.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 12, Issue 12, Optical Properties and Quantum Optics (Sep 2005)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 4, Issue 10, Condensed Matter Physics (Oct 2005)

A. Krügel, V.M. Axt, T. Kuhn, P. Machnikowski and A. Vagov,
 The role of acoustic phonons for Rabi oscillations in semiconductor quantum dots
Abstract:
The damping of Rabi oscillations in quantum dots as well as the renormalization of the carrierlight coupling, due to the interaction with longitudinal acoustic phonons are studied as a function of temperature and laser pulse parameters. Numerical results are obtained by using a correlation expansion within the density matrix theory. The observed features like a nonmonotonous dependence of the damping on the pulse duration are characteristic for the strongly nonMarkovian nature of the phonon coupling in these systems. The results can be well interpreted on the level of a perturbation expansion in the carrierphonon interaction.

B. Krummheuer, V.M. Axt and T. Kuhn,
 Coupled polarization and acousticphonon dynamics after optical excitation of quantum dots near surfaces
Abstract:
An analysis of the pure dephasing of a single quantum dot embedded in a halfspace or a freestanding slab due to the interaction of the carriers with confined acoustic phonons is presented. We discuss the time dependence of the polarization and the relative volume change based on exact expressions which hold for ultrafast excitation. We find that the proximity of the quantum dot to a surface leaves distinct traces in the polarization and in the case of the halfspace leads to an additional decay. In the case of the slab the polarization shows a pronounced periodic structure depending on the width of the slab.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 13, Issue 2, Optical Properties and Quantum Optics (Jan 2006)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 5, Issue 1, Condensed Matter Physics (Jan 2006)

V.M. Axt, T. Kuhn, A. Vagov, P. Borri, W. Langbein and U. Woggon,
 Observation of an unusual temperature dependence of the initial decoherence time in quatum dots
Abstract:
We report on fourwavemixing experiments in selfassembled InAs/GaAs quantum dots and compare with a theory that accounts for the puredephasing induced by acoustic phonons. The measurements demonstrate an unusual nonmonotonous temperature dependence of the initial decoherence time in full agreement with previous theoretical predictions made on the basis of a model that concentrates on the lowest electronic states. For samples exhibiting strong electronic confinement this model even yields a good quantitative agreement with the experiments while for less confined samples there are some systematic deviations although many qualitative features are still well reproduced by the model.

V.M. Axt,
 Unusual properties and control of the initial decoherence in quantum dots
Abstract:
Pure dephasing is a genuine quantum kinetic process resulting in a nonexponential decay of optical signals with an unusual nonmonotonous temperature dependence of the decay time. The coherent controllability of the initial decoherence is demonstrated.

H. Lohmeyer, V.M. Axt and T. Kuhn,
 Electronphonon quantum kinetics beyond the secondorder Born approximation
Abstract:
For a oneband model of a quantum wire coupled to LOphonons we present results for the dynamics of the coupled electronphonon system calculated with quantum kinetic equations obtained in the density matrix approach. Using a correlation expansion for the truncation of the infinite hierarchy of equations of motion we go beyond the usual secondorder Born approximation by taking into account twoparticle correlations and twofold phononassisted density matrices. The different approximation levels are compared among each other and with an exact solution for a simplified case.

V.M. Axt, J. Wühr and T. Kuhn,
 Mixing of discrete and continuum excitations induced by nonperturbative Coulombcorrelations
Abstract:
Taking into account all types of twopair coherences we have calculated fourwavemixing (FWM) spectra emitted from a quantum wire for excitation conditions where excitons and free electronhole pairs are simultaneously excited. The spectra exhibit a mixing of discrete and continuous emissions which is shown to indicate nonperturbative Coulomb correlations. The line shapes are found to depend sensitively on the central frequency, the strength of the interaction as well as on the delay between the pulses.

T. Voss, H.G. Breunig, I. Rückmann, J. Gutowski, V.M. Axt and T. Kuhn,
 Coherent control of the excitonbiexciton system demonstrated in fourwavemixing experiments
Abstract:
Systematic measurements and microscopic simulations were performed to study the optical coherent control of the excitonbiexciton systems in a ZnSe quantum well. Our results show that the spectral components in the fourwave mixing signal at the exciton and the excitonbiexciton transition, respectively, can be separately controlled in the coherent regime. This separate control also results in different beat structures on the realtime transients of the nonlinear wavemixing polarization. With respect to all important features experiment and simulation are in excellent agreement.
2004

V.M. Axt and T. Kuhn,
 Femtosecond spectroscopy in semiconductors: a key to coherences, correlations and quantum kinetics
Abstract:
The application of femtosecond spectroscopy to the study of ultrafast dynamics in semiconductor materials and nanostructures is reviewed with particular emphasis on the physics that can be learned from it. Excitation with ultrashort optical pulses in general results in the creation of coherent superpositions and correlated manyparticle states. The review comprises a discussion of the dynamics of this correlated manybody system during and after pulsed excitation as well as its analysis by means of refined measurements and advanced theories. After an introduction of basic concepts—such as coherence, correlation and quantum kinetics—a brief overview of the most important experimental techniques and theoretical approaches is given. The remainder of this paper is devoted to specific results selected in order to highlight how femtosecond spectroscopy gives access to the physics of coherences, correlations and quantum kinetics involving charge, spin and lattice degrees of freedom.
First examples deal with the dynamics of basic laserinduced coherences that can be observed, e.g. in quantum beat spectroscopy, in coherent control measurements or in experiments using fewcycle pulses. The phenomena discussed here are basic in the sense that they can be understood to a large extent on the meanfield level of the theory. Nevertheless, already on this level it is found that semiconductors behave substantially differently from atomic systems. Subsequent sections report on the occurrence of coherences and correlations beyond the meanfield level that are mediated either by carrier–phonon or carrier–carrier interactions. The corresponding analysis gives deep insight into fundamental issues such as the energy–time uncertainty, pure dephasing in quantum dot structures, the role of twopair or even higher correlations and the buildup of screening. Finally results are presented concerning the ultrafast dynamics of resonantly coupled excitations, where a combination of different interaction mechanisms is involved in forming new types of correlations. Examples are coupled plasmon–phonon and Bloch–phonon oscillations.
The results reviewed in this paper clearly reveal the central role of manyparticle correlations and coherences for the ultrafast dynamics of dense semiconductor systems. Both the presence of strong correlation effects and the formation of coherences in a genuine manyparticle system have important implications for the controllability of optical signals from this class of materials, which is of utmost importance for applications in presentday and future optoelectronic devices.

V.M. Axt, T. Kuhn, B. Haase, U. Neukirch and J. Gutowski,
 Estimating the Memory Time Induced by ExcitonExciton Scattering
Abstract:
It is shown that lower bounds for the effective memory time induced by twopair correlations can be estimated by monitoring changes of the shape of excitonic fourwavemixing spectra. Experimentally we demonstrate a memory time of at least 540 fs for a ZnSe single quantum well. Microscopic calculations reveal that this lower bound is not sharp. Interactions retarded by more than 800 fs are shown to influence the dynamics, reflecting the presence of a long time tail in the memory kernel.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 10, Issue 13, Optical Properties and Quantum Optics (Sep 2004)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 3, Issue 10, Condensed Matter Physics (Oct 2004)

A. Vagov, V.M. Axt, T. Kuhn, W. Langbein, P. Borri and U.Woggon,
 Nonmonotonous temperature dependence of the initial decoherence in quantum dots
Abstract:
We have analyzed the initial decoherence of strongly confined semiconductor quantum dots by performing fourwavemixing experiments and comparing with theory. The measurements are in quantitative agreement with analytical results accounting for the pure dephasing induced by acoustic phonons. The experiments confirm the recent prediction of an unusual nonmonotonous temperature dependence of the initial decoherence time.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 10, Issue 21, Optical Properties and Quantum Optics (Nov 2004)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 3, Issue 12, Condensed Matter Physics (Dec 2004)

J. Wühr, V.M. Axt and T. Kuhn,
 Nonperturbative Coulomb correlations generated by simultaneous excitation of excitonic and bandtoband continuum transitions
Abstract:
We investigate theoretically the nonlinear optical response of a semiconductor for excitation conditions where simultaneously all kinds of correlated twopair transitions contribute to the dynamics. This includes transitions to biexcitons, excitonexciton scattering states, two free electronhole pairs as well as twopair states involving an exciton and a free electronhole pair. For certain excitation conditions twopair correlations give rise to a complex line shape of fourwavemixing spectra with an emission spread over the whole range between the exciton line and the bandedge. Even a strong suppression of the signal at the exciton line can be achieved while the emission is still concentrated between the exciton and the bandedge. The dependence of these features on the excitation conditions and on the strength of the Coulomb interaction is discussed. Comparing a nonperturbative treatment of the Coulomb interaction with the Born approximation and the meanfield theory clearly reveals the importance of nonperturbative Coulomb correlations even for excitations involving the continuum of free electronhole pairs.

V.M. Axt,
 Coherent manipulation of biexcitonic transitions and other twopair correlations
Abstract:
Twopair correlations are shown to induce dependences of the nonlinear optical response of semiconductors that can be used for a coherent manipulation of the resulting emission. Influences of biexcitonic transitions as well as transitions to twopair scattering states are discussed within a microscopic density matrix approach. It is shown that the coherent control of biexciton beats is selective with respect to the propagation direction of the emitted signal, in contrast to the control of beats where all beat partners are generated by single photon processes. Furthermore, it is demonstrated that memory structures induced by exciton–exciton scattering states enable coherent manipulations of the excitonic line shape that allow us to estimate lower bounds for the corresponding memory time from experimentally accessible data.

B. Krummheuer, A. Vagov, T. Kuhn, M. Glanemann, V.M. Axt, I. D'Amico and F. Rossi,
 Ultrafast carrier and phonon dynamics in GaAs and GaN quantum dots
Abstract:
We analyse the electronic and phononic dynamics in GaAs and GaN quantum dot structures due to their interaction with acoustic phonons. We compare results for two specific quantum dot heterostructures which have been proposed as hardware building blocks for a quantum computer in recent quantum computation/information schemes. In particular, we are interested in the loss of coherence after excitation with an ultrashort laser pulse and in the dynamics of phonons which are created as a consequence of the optical excitation process. Our results are nonperturbative with respect to both carrier–phonon and carrier–light interaction and therefore include multiphonon processes of arbitrary order. We find that, due to different quantum dot sizes, involved electric fields and material parameters, the decoherence is stronger in the GaN dots. The interplay of these effects also strongly determines the details of the created phonon occupation, which splits into two parts: one remains in the vicinity of the dot and forms a stable polaron and another leaves the dot as a phononic wave packet travelling with the velocity of sound. Due to the dot geometry and the carrier–phonon coupling matrix elements this phonon emission is strongly anisotropic.

M. Glanemann, V.M. Axt and T. Kuhn,
 Thermal escape and capture processes in quantum wiredot structures
Abstract:
We study the dynamics of an electronic wave packet in a quantum wire with an embedded quantum dot interacting with an LOphonon bath at room temperature. Two different cases are studied: in the first scenario (escape scenario), we determine the probability for the electrons to leave the dot by absorption of an LOphonon. In the second scenario (capture and escape scenario), we study the capture process from the delocalized states of the wire into the localized states of the dot accompanied by reemission into the delocalized states. These scenarios are analysed by using a quantum kinetic theory for the electron LOphonon interaction. The thermal escape scenario shows a continuous flow of density directed with equal probabilities to both sides from the dot accompanied by small oscillations in the density of bound carriers. For the capture and escape scenario, we find an interplay between thermal escape and a coherent escape process, the latter being present even at zero temperature. In the coherent escape, a part of the captured density reescapes and forms additional travelling wave packets following the original wave packet.
2003

T. Wolterink, V. M. Axt and T. Kuhn,
 Role of exchange interaction in Coulomb quantum kinetics
Abstract:
In a quantumkinetic approach based on densitymatrix formulation we study the role of exchange interaction for ultrafast carrier relaxation. We find that the exchange contributions to scattering and screening tend to compensate each other. With very short times, however, due to the retarded buildup of the screening the exchange contribution to scattering prevails resulting in a reduced relaxation.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 7, Issue 12, Optical Properties and Quantum Optics (Mar 2003)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 2, Issue 3, Condensed Matter Physics (Mar 2003)

A. Vagov, V. M. Axt and T. Kuhn,
 Impact of pure dephasing on the nonlinear optical response of single quantum dots and dot ensembles
Abstract:
The nonlinear optical response to ultrafast laser pulses of semiconductor quantum dots coupled to acoustic phonons is discussed on the basis of closedform analytical results valid for dots in the strong confinement regime. General properties of fourwavemixing (FWM) signals are derived from the analytical formulas. Numerical results are presented for twopulse FWM signals from single quantum dots and from dot ensembles in the time and the frequency domains. Interestingly, the initial decay time of the signal is found to depend nonmonotonously on temperature and delay time. In general, the phonon coupling leads to a modulated decay of the time domain optical response which is neither exponential nor Gaussian. The strength of the modulations is influenced by inhomogeneous broadening and temperature as well as by the relative localization lengths of electrons and holes. FWM spectra of single dots evolve from asymmetric functions for coinciding pulses into symmetric spectra for large delays. Nonlinear signals are compared with linear signals revealing striking similarities but also significant differences, e.g., concerning the depth of the initial drop.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 7, Issue 14, Optical Properties and Quantum Optics (Apr 2003)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 2, Issue 4, Condensed Matter Physics (Apr 2003)

M. Herbst, M. Glanemann, V. M. Axt and T. Kuhn,
 Electronphonon quantum kinetics for spatially inhomogeneous excitations
Abstract:
The dynamics of optically generated carriers interacting with longitudinal optical phonons in spatially inhomogeneous systems is analyzed on a quantum kinetic level. A microscopic densitymatrix theory is formulated accounting for arbitrary spatial inhomogeneities in the semiconductor structure and the excitation conditions. The physical origin of the various contributions entering the dynamical equations is discussed. The theory is applied to the dynamics of a wave packet optically generated locally in a quantum wire. We study quantum kinetic features due to the interaction with phonons in the expansion process both in a oneband and a twoband model as well as the generation and dynamics of coherent phonon amplitudes.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 2, Issue 6, Condensed Matter Physics (Jun 2003)

H.G. Breunig, T. Voss, I. Rückmann, J. Gutowski, V.M. Axt and T. Kuhn,
 Influence of higher Coulomb correlations on optical coherentcontrol signals from a ZnSe quantum well
Abstract:
The manipulation of the coherent optical polarization in a quantum well with a pair of phaselocked laser pulses is investigated by using wavemixing signals. The measurements are performed in four and sixwavemixing geometries with different polarization states of the excitation pulses. Even at moderate excitation densities, the signals are modulated by higher harmonics that correspond to highorder optical nonlinearities. A significant effect of higher Coulomb correlations on the coherentcontrol signals is demonstrated by comparing the experiments with calculations based on a microscopic densitymatrix theory. The theoretical approach makes use of the dynamicscontrolled truncation scheme. The corresponding numerical results are in good agreement with the experiment.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 2, Issue 8, Ultrafast Methods and Measurement Techniques (Aug 2003)

J. Wühr, V. M. Axt and T. Kuhn,
 Dynamics of twopair correlations induced by simultaneous excitation of excitonic and bandtoband continuum transitions
Abstract:
The impact of all kinds of twopair correlations (biexcitons, excitonexciton scattering states, two free electronhole pairs) on fourwavemixing (FWM) signals generated by ultrashort optical pulses that simultaneously excite excitons and free electronhole pairs is analyzed. Signatures of twopair correlations are identified by comparing the full theory with meanfield (MF) results. For systems with strong exciton binding twopair correlations suppress changes of the line width of the excitonic emission that are predicted by the MF theory when the central excitation energy is varied above the band edge. For systems with weakly bound excitons the presence of twopair correlations leads to an emission in between the exciton and the band edge with a complex line shape which strongly depends on the excitation energy.

V. M. Axt, B. Krummheuer, A. Vagov and T. Kuhn,
 Analytical results for nonlinear optical signals from quantum dots coupled to phonons
Abstract:
The impact of pure dephasing processes on the optically induced nonlinear dynamics of quantum dots is analyzed. Concentrating on small dots pure dephasing can be studied analytically in the limit of ultrafast excitation. General conclusions from the analysis of the closed form formulas include the prediction that fourwavemixing (FWM) spectra of single dots change from asymmetric to symmetric lineshapes with increasing pulse delay. Furthermore, in contrast to phenomenological dephasing models the delay dependence of the time integrated FWM amplitude P_{FWM} generated by a strongly inhomogeneously broadened ensemble deviates from the real time dependence of P_{lin}^{2}, where P_{lin} is the linear polarization emitted by a single dot. Numerical results are presented for FWM signals from dots coupled to bulk acoustic phonons. Surprisingly, the initial decay time of the signal depends nonmonotonously on the temperature. In addition, it is shown that for certain material parameters the coupling to the smooth continuum of acoustic phonons may result in pronounced oscillations.

A. Vagov, V. M. Axt and T. Kuhn,
 Nonperturbative treatment of quantum dots coupled to light and phonons
Abstract:
We present an exact solution for the dynamics of a quantum dot (QD) coupled to phonons and excited by ultrashort light pulses. The solution is nonperturbative with respect to both carrierphonon and carrierlight coupling, and accounts for an arbitrary number of pulses. Explicit expressions for the one and two pulse solutions are used to obtain the nonlinear fourwavemixing optical response by a single QD as well as by disordered QD arrays. Phonon emission by the excited QD is shown to be qualitatively different from that in the phonon assisted carrier relaxation.

T. Kuhn, M. Glanemann and V.M. Axt,
 Quantum control of capture processes into localized states of a quantum dot
Abstract:
The capture of an electronic wave packet moving in a quantum wire into localized states of a quantum dot by means of LO phonon emission is studied on a quantum kinetic level. In general, if there is more than one bound state the capture process leads to the creation of a superposition of these states resulting in an oscillating wave packet inside the dot. It is shown that these oscillations can be efficiently controlled by means of the capture of a second wave packet moving towards the dot from the other side. Depending on the phase of the oscillations at the time of arrival of the second wave packet the amplitude of the spatial oscillations is either reduced or enhanced.

T. Kuhn, M. Glanemann and V.M. Axt
 Creation of oscillating electronic wave packets in a quantum dot by capture processes
Abstract:
The creation of oscillating electronic wave packets in a quantum dot embedded in a quantum wire is studied. The packets build up due to optical phonon induced capture processes of electrons from the delocalized states of the wire into the localized states of the dot. The calculations are performed on a quantum kinetic level within the framework of the density matrix theory. Since the trapped electrons in general are found to be in coherent superpositions of the available localized dot states the wave packet exhibits oscillatory dynamics. We have analyzed the impact of the initial spatial extension of the wave packet and of the spatial and spectral properties of the quantum dot on the capture process. It turns out that the resulting electronic oscillations crucially depend on the ratio of the dot excitation time and the period corresponding to the energetic splitting of the dot levels.

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V.M. Axt,
T. Kuhn, S. Eshlaghi and A.D. Wieck,
 Ultrafast coherent spectroscopy of a single quantum dot
Abstract:
The nonlinear optical response of a single quantum dot is studied for the first time with femtosecond resolution. We find pronounced spectral oscillations in the differential reflectivity reflecting the perturbed free induction decay of the coherent polarization of a single exciton.
2002

T. Guenther, C. Lienau, T. Elsaesser, M. Glanemann, V.M. Axt, T. Kuhn, S. Eshlaghi and A.D. Wieck,
 Coherent nonlinear optical response of single quantum dots studied by ultrafast nearfield spectroscopy
Abstract:
The nonlinear response of single GaAs quantum dots is studied in femtosecond nearfield pumpprobe experiments. At negative time delays, transient reflectivity spectra show pronounced oscillatory structure around the quantum dot exciton line, providing the first evidence for a perturbed free induction decay of the excitonic polarization. Phasedisturbing Coulomb interactions between the excitonic polarization and continuum excitations dominate the optical nonlinearity on ultrafast time scales. A theoretical analysis based on the semiconductor Bloch equations accounts for this behavior.
Erratum: Phys. Rev. Lett. 89, 179901 (2002)
Reply: Phys. Rev. Lett. 90, 139702 (2003)
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 6, Issue 5, Optical Properties and Quantum Optics (Jul 2002)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 1, Issue 3, Photonics (Aug 2002)

B. Krummheuer, V. M. Axt and T. Kuhn,
 Theory of pure dephasing and the resulting absorption lineshape in semiconductor quantum dots
Abstract:
The pure dephasing of the optical polarization and the corresponding line shape of absorption spectra in small quantum dots due to the interaction of the exciton both with optical and acoustic phonons is calculated. By restricting ourselves to the exciton ground state we obtain a model which is known to be exactly solvable. We study the temperature dependence and the influence of a static electric field. The spectra exhibit strongly nonLorentzian line shapes including a sharp zerophonon line. Optical phonons lead to phonon sidebands which may acquire a finite width due to the dispersion of the phonon branch; the width increases with decreasing dot size. Acoustic phonons both due to deformation potential and piezoelectric coupling lead to a broad background in the spectra which is strongly temperature dependent. Typical features of the spectra are qualitatively well reproduced by a perturbative approach based on onephonon processes. Multiphonon processes, however, give significant contributions in particular in the case of acoustic phonons. Lateral or vertical electric fields lead to an increasing efficiency of the polar interaction mechanisms while deformation potential interaction is much less influenced.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 5, Issue 19, Optical Properties and Quantum Optics (May 2002)

A. Vagov, V. M. Axt and T. Kuhn,
 Electronphonon dynamics in optically excited quantum dots: Exact solution for multiple ultrashort laser pulses
Abstract:
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent densitymatrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wavevector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple twolevel systems. Three typical applications of the general results are worked out: (a) the influence of phonons on fourwavemixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 6, Issue 19, Optical Properties and Quantum Optics (Nov 2002)
sowie auch für: Virt. J. Ultrafast Sci., Vol. 1, Issue 6, Condensed Matter Physics (Nov 2002)

T. Voss, H. G. Breunig, I. Rückmann, J. Gutowski, V. M. Axt
and T. Kuhn,
 Biexcitonic effects in the coherent control of the excitonic polarization detected in sixwavemixing signals
Abstract:
Coherently controlled sixwavemixing experiments on a ZnSe single quantum well are performed with different polarizations of the excitation pulses to enable or disable the creation of a biexcitonic polarization. A significant contribution of the biexcitonic polarization and other twopair correlations is observed in the signal which is mainly modulated with the exciton transition frequency. A microscopic theory based on the dynamics controlled truncation scheme including sixpoint correlations is able to reproduce the experimental results.
ausgewählt für: Virt. J. Ultrafast Sci., Vol. 1, Issue 5, Condensed Matter Physics (Oct 2002)

V. M. Axt, T. Kuhn and A. Stahl,
 Coherent description of Coulomb scattering in semiconductor optics
Abstract:
Equations for the optically induced dynamics of one, two and three electronhole pairs are analyzed by using a coherent amplitude representation of the theory. The equations allow for a complete calculation of all ^{(5)} contributions to the optical response. It is discussed how a theory formulated in terms of coherent amplitudes can account for decoherence. It is shown that a Boltzmanntype Coulomb scattering dynamics is included in the coherent description as a limiting case.

K. Siantidis, V. M. Axt, J. Wühr and T. Kuhn,
 Theory of exciton formation and relaxation in quantum wires,
Abstract:
The relaxation dynamics of electronhole pairs generated by a short laser pulse near the band edge of a GaAs quantum wire is analyzed by using a microscopic density matrix approach. We account for Coulomb renormalizations of various scattering mechanisms that are of importance near the band gap. The exciton formation dynamics, photoluminescence signals, and the buildup of centerofmass kinetic energies depend crucially on the excitation energy. Exciton formation and dissociation are shown to change characteristically with temperature.

J. Wühr, V. M. Axt, K. Siantidis and T. Kuhn,
 Signatures of twopair correlations after simultaneous excitation of excitons, and free electronhole pairs in a quantum wire
Abstract:
The impact of all kinds of twopair correlations (biexcitons, excitonexciton scattering states, two free electronhole pairs) on fourwavemixing (FWM) signals generated by ultrashort optical pulses that simultaneously excite excitons and free electronhole pairs is analyzed. Calculations accounting nonperturbatively for the Coulomb interaction are compared with the Born approximation (BA) and meanfield (MF) results. Thereby signatures of twopair correlations are identified as well as qualitative differences between microscopic scattering theories and phenomenological treatments of pair relaxations.

T. Kuhn, M. Glanemann and V. M. Axt,
 Quantum kinetics of carrier capture processes into a quantum dot
Abstract:
The capture of electrons moving in a quantum wire into an embedded quantum dot due to the interaction with optical phonons is studied on a quantum kinetic level within the density matrix approach. We find even at low temperatures where only phonon emission is possible a nonmonotonic timedependence of the bound state occupations due to virtual transitions. In the case of several bound dot states the capture in general results in a coherent superposition of these states.

K. Siantidis, T. Wolterink, V. M. Axt and T. Kuhn,
 Formation of excitons from correlated electronhole pairs
Abstract:
We analyze the decoherence, exciton formation, and relaxation of electron–hole pairs in a GaAs quantum wire following a pulsed optical excitation near the band edge. Within a microscopic density matrix theory the combined dynamics of coherent and incoherent electron–hole pairs in bound as well as in scattering states is studied for excitations below, at, and above the band gap. We account for a variety of scattering mechanisms and discuss related correlationinduced renormalizations of the relaxation properties.

T. Wolterink, V. M. Axt and T. Kuhn,
 Coulomb quantum kinetics beyond RPA and Born approximation
Abstract:
The relaxation of a twodimensional electron gas due to Coulomb scattering is analyzed theoretically within the density matrix formulation. By comparing results for quantum kinetic scattering in different approximations (e.g., Born approximation, random phase approximation, Tmatrix approximation), we find substantial changes in the relaxation process due to different contributions. The influence of exchange contributions is discussed. By comparing different scattering models we can clearly identify the buildup of screening.

V.M. Axt, B. Krummheuer, A. Vagov and T. Kuhn,
 Pure dephasing in the linear and nonlinear optical response of quantum dots
Abstract:
A comprehensive analysis of the effect of pure dephasing processes on the linear as well as the nonlinear optical response of quantum dots is presented. The focus is on small dots where it is permissible to consider only the lowest energy states. It turns out that pure dephasing can be studied analytically in this limit. The analysis is based on exact closed form expressions for the linear susceptibility as well as for the nonlinear response to a sequence of delta pulses. The dependences of linear absorption spectra on statically applied fields and on the temperature for different dot sizes are discussed. Exact results are compared with calculations based on the correlation expansion. FourWaveMixing spectra are presented for different temperatures and strength of the inhomogeneous broadening. Good qualitative agreement with experiments is found.

T. Wolterink, V.M. Axt and T. Kuhn,
 Importance of exchange contributions to scattering and screening in the quantum kinetic regime
Abstract:
We study the role of exchange contributions for the ultrafast carrier relaxation in the quantum kinetic regime. The analysis is based on a density matrix approach where besides the direct contributions to Coulomb scattering and screening in the random phase approximation (RPA) also the corresponding exchange terms are included which are necessary to satisfy the correct antisymmetry of the twoparticle density matrix. At early times we find significant deviations from the commonly used RPA where these exchange contributions are neglected. At later times exchange contributions to scattering and screening tend to compensate each other and the differences between RPA and the calculations including exchange are reduced.

T. Voss, H.G. Breunig, I. Rückmann, J. Gutowski, V.M. Axt and
T. Kuhn,
 Signatures of highorder Coulomb correlations in coherently controlled four and sixwavemixing experiments on a ZnSe quantum well
Abstract:
In this paper we present experimental and theoretical investigations of coherently controlled four and sixwavemixing experiments on a ZnSe single quantum well. In the signal which is mainly modulated with the exciton transition frequency we observe strong contributions of integer harmonics of this frequency if the experiment is carried out with colinearly polarized excitation pulses. If the the polarization states are switched to a cocircular polarization state these harmonics are strongly suppressed but do not vanish completely. This polarization dependence of the harmonics suggests that biexcitons as well as twoexciton scattering states play an important role in the microscopic origin of this nonlinear behavior. A theoretical approach based on the dynamicscontrolled truncation scheme (DCT) is able to reproduce the experimental findings on a level on which sixpoint correlations are included. By selectively switching on and off parts of the full theory we clearly demonstrate that twopair correlations, in particular biexcitons, crucially determine the occurrence and intensity of the observed additional frequencies.
2001

V.M. Axt, B. Haase and U. Neukirch,,
 Influence of twopair continuum correlations following resonant excitation of excitons
Abstract:
The memory structure induced by coherent transitions to the excitonexciton scattering continuum is shown to have significant influence on spectrally resolved fourwavemixing signals even under selective excitation of 1s excitons. Comparisons between experiments and calculations that account nonperturbatively for these quantum kinetic Coulomb correlations demonstrate large compensations between meanfield contributions and transitions to the twopair continuum. Experiments with different polarizations of the laser pulses show that twopair continuum correlations are responsible for delaytime dependent shifts of the excitonic emission as well as for substantial deformations of the line shape.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 3, Issue 21, Optical Properties and Quantum Optics (May 2001)

V.M. Axt, S.R. Bolton, U. Neukirch, L.J. Sham and D.S. Chemla,
 Evidence of sixparticle Coulomb correlations in sixwavemixing signals from a semiconductor quantum well
Abstract:
Sixwavemixing signals from a ZnSe quantum well are analyzed experimentally and with a microscopic densitymatrix description using the dynamicscontrolledtruncation scheme. For each physically distinct combination of polarizations of the exciting pulses, the spectrum of sixwavemixing emission is measured as a function of time delay. The experimental results are compared with calculations performed at different levels of approximation. Although the leading order contributions to sixwavemixing signals are of fifth order in the laser field, we show that there are significant signal components that are due to at least χ^{(7)} processes. The sensitivity of sixwavemixing signals to highorder Coulomb correlations is demonstrated. Sixpoint density matrices are found to be indispensable for the interpretation of our experiments, while some details seem to indicate the involvement of even higherorder correlation functions. Furthermore, we find a remarkable dynamical decoupling of spectral signatures and the delaytime behavior after excitation with linearly polarized pulses.
ausgewählt für: Virt. J. Nan. Sci. & Tech., Vol. 3, Issue 11, Optical Properties and Quantum Optics (Mar 2001)

K. Siantidis, V. M. Axt and T. Kuhn,
Phys. Rev. B 65, 035303 (2001)

V.M. Axt and B. Haase,
 Correlated Coulomb quantum kinetics in optically excited semiconductors
Abstract:
Correlations due to biexcitons as well as to twopair scattering states are direct manifestations of Coulomb quantum kinetics. Effects resulting from the memory structure of the corresponding contributions to the optical interband polarization are analyzed taking a ZnSe singlequantum well as model system. Our calculations are based on a microscopic density matrix description using the dynamics controlled truncation scheme for closing the hierarchy of higherorder density matrices. A detailed comparison between experiment and theory allows for the identification of numerous effects directly reflecting different aspects of paircorrelations. In particular, we demonstrate various influences of the twopair scattering continuum on fourwavemixing signals. Furthermore, we show that signals with a dynamically changing polarization sensitively monitor a competition between coherent parts of the dynamics and signal components induced by incoherent exciton densities. Surprisingly, the phase of these signals is found to be almost unaffected by the presence of incoherent densities. This result can be traced back to a compensation of the influences on the phases resulting from different incoherent parts of the dynamics. Sixparticle correlations representing transitions from incoherent densities to twopair correlations turn out to be indispensable for a proper description of this effect.

S.R. Bolton, U. Neukirch, D.S. Chemla, V.M. Axt and L.J. Sham,
 Sixthorder Coulomb correlations identified in a semiconductor single quantum well
Abstract:
The nonlinear optical response in semiconductors has traditionally been treated in a mean field approximation at the 2particle level. Recent work, in particular comparisons of fourwave mixing (FWM) with microscopic theory, have demonstrated the importance of 4particle correlations. Such experiments, however, are not optimally sensitive to correlations at the 6particle level. In order to probe such sixparticle correlations, we compare the results of sixwave mixing (SWM) measurements with a detailed microscopic theory based on the dynamics controlled truncation scheme (DCT). Experiments were performed on a single 5 nm ZnSe quantum well.
2000

S.R. Bolton, U. Neukirch, L.J. Sham, D.S. Chemla and V.M. Axt,
 Demonstration of sixthorder Coulomb correlations in a semiconductor single quantum well
Abstract:
Sixwave mixing in a ZnSe quantum well is investigated and compared with microscopic theory. We demonstrate that sixthorder Coulomb correlations have a significant qualitative impact on the nonlinear optical response. Sixwave mixing is shown to be a uniquely sensitive tool for investigation of correlations beyond the fourpoint level.

V.M. Axt, G. Bartels, B. Haase, J. Meinertz, U. Neukirch and J. Gutowski,
 How correlated Coulomb quantum kinetics affects the optical phase of fourwavemixing signals
Abstract:
The optical phase of fourwavemixing (FWM) signals from a ZnSe single quantum well is analyzed experimentally and theoretically. The focus is on excitation conditions where the polarization state of the emitted light is dynamically changing rather than being fixed by selection rules, a case known to be sensitive to highorder Coulomb correlations. The phase is measured using an iterative procedure taking as input FWM signals with realtime resolution as well as frequency regime data. The results are compared with a microscopical densitymatrix description using the dynamics controlled truncation (DCT) scheme. Meanfield Coulomb interactions, Pauli blocking and transitions to biexcitons and the twopair scattering continuum are accounted for. Calculations in the coherent limit are able to reproduce the measured phases. The correlated twopair scattering continuum is shown to have a significant impact on the phase.

M. Herbst, V. M. Axt, and T. Kuhn,
 Temporally and spatially resolved electronphonon quantum kinetics
Abstract:
A quantum kinetic theory that is able to resolve interaction processes between carriers and phonons in time and in space is presented. The dynamics of spatially localized wavepackets is analyzed accounting for coherent as well as incoherent phonons. It is found that, as a consequence of the energytime uncertainty, a fast initial carrier transport takes place leading to occupations of space regions which are out of reach at early times within a semiclassical description on the level of the Boltzmann equation. The charge separation that accompanies the transport of electrons is a source of coherent phonons. The corresponding polarizations of the ionlattice show oscillations that form a spatially expanding wavefront. Adding incoherent phonons leads to a damping of these waves due to phononassisted carrier redistributions.

B. Haase, U. Neukirch, J. Gutowski, J. Nürnberger, W. Faschinger, M. Behringer, D. Hommel, V.M. Axt, G. Bartels and A. Stahl,
 Lineseshape of fourwavemixing signals: dependence on the sample geometry and excitation conditions
Abstract:
We present an analysis of the dependence of the line shape of fourwavemixing (FWM) signals on the sample geometry and the excitation conditions based on ZnSe single quantum wells with varying width and barrier composition. We analyze the geometry dependence of the biexciton binding energy and observe a strong influence of reabsorption and of the signal polarization on the spectral structures. The results exhibit excellent agreement with calculations based on a microscopic densitymatrix theory considering the biexcitonic continuum for a 2D model.

B. Haase, U. Neukirch, J. Meinertz, J. Gutowski, V.M. Axt, G. Bartels, A. Stahl, J. Nürnberger and W. Faschinger,
 Intensity dependence of signals obtained in fourwavemixing geometry: influence of higherorder contributions
Abstract:
The nonlinear optical response of a single ZnSe quantum well is investigated in fourwavemixing geometry. Contributions above third order in the driving fields are quantified by intensitydependent measurements. Comparison with a microscopic densitymatrix approach yield good agreement between experiment and theory. It is found that substantial contributions above third order are generated even at lowest excitation levels necessary in current experiments.

S.R. Bolton, U. Neukirch, D.S. Chemla, V.M. Axt and L.J. Sham,,
 Higher order exciton correlations from sixwave mixing
Abstract:
The nonlinear optical response in semiconductors has traditionally been treated in a mean field approximation at the 2particle level. Recent work, in particular comparisons of fourwave mixing (FWM) with microscopic theory, have demonstrated the importance of 4particle correlations. Such experiments, however, are not optimally sensitive to correlations at the 6particle level. In order to probe such sixparticle correlations we compare the results of sixwave mixing (SWM) measurements with a detailed microscopic theory based on the dynamics controlled truncation scheme (DCT).
1999

T. Kuhn, V.M. Axt, M. Herbst and E. Binder
 Coherent control of heavylight hole and phonon quantum beats
Abstract:
The control of quantum beats by two phaselocked optical pulses is analyzed theoretically. We compare the case of heavylight hole quantum beats as an example of a purely electronic coherenc with the case of phonon quantum beats which are a characteristic feature of electronphonon quantum kinetics. The maxima and minima of the beat amplitudes can be understood by the same arguments. For the case of phonon quantum beats an excatly solvable model is presented which allows us to analyze the role of the electronphonon coupling constant.

B. Haase, U. Neukirch, J. Gutowski, G. Bartels, A. Stahl, V.M. Axt, J. Nürnberger and W. Faschinger,
 Manifestation of excitonamplitude fluctuations in the transient polarization state of fourwavemixing signals
Abstract:
The polarization state of the diffracted beam in degenerate fourwave mixing is experimentally and theoretically investigated, resolved in the time as well as in the frequency domain. The use of thin ZnSe quantum wells having large (bi)exciton binding energies makes it possible to restrict the optical excitation by broadband 110 fs pulses to quasitwodimensional heavyhole excitons and biexcitons only. Despite these most simple experimental conditions, an extremely complex dynamics of the polarization state is observed when one circularly and one linearly polarized beam are used for excitation. The detailed behavior sensitively depends on the excitation density, showing the importance of nonlinearities of higher than third order even at exciton densities less than 0.01 times the Mott density. A comparison of the experimental data with theoretical results obtained by a microscopic densitymatrix approach yields very close agreement. It turns out that a dynamical object describing fluctuations of the exciton amplitude has to be included in the theory in addition to biexcitonic contributions and correlated parts of the excitonexciton scattering continuum.

D. Steinbach, G. Kocherscheidt, M. U. Wehner, H. Kalt, M. Wegener, K. Ohkawa, D. Hommel and V.M. Axt,
 Electronphonon quantum kinetics in the strongcoupling regime
Abstract:
The quantum kinetics of optically excited crystal electrons coupled to a bath of dispersionless phonons is studied in the regime of strong electronphonon coupling. Four wavemixing experiments on a thin film of bulk ZnSe using 13 fs blue pulses give evidence for corresponding effects that are distinctly different from those found for GaAs which has proven to be a model system for the weakcoupling regime. The experimental results on ZnSe are compared with solutions of a simple model Hamiltonian of electronphonon interaction suitable for both GaAs and ZnSe. Exact analytic solutions of this model for arbitrary electronphonon coupling strengths are compared with numerical solutions of the same model following the usual approach in terms of an infinite hierarchy of correlation functions. Virtues and limitations of the simple model Hamiltonian with respect to the experiment are discussed.

V.M. Axt, M. Herbst and T. Kuhn,
 Coherent control of phonon quantum beats,
Abstract:
The coherent control of excitons coupled to longitudinal optical phonons is analyzed in the quantum kinetic regime. Different models allowing for different levels of sophistication in the theoretical treatment are compared. Within a simple twolevel model of the exciton system analytical results relevant for shorttime excitation in the lowdensity regime are derived, which are nonperturbative with respect to the exciton–phonon interaction. For pulses of finite duration and high intensity, numerical calculations are presented realizing a nonperturbative treatment with respect to both the exciton–phonon as well as the exciton–photon coupling. It is shown that for twolevel systems, the use of high intensity pulses opens new possible control scenarios that combine the effects of phase control with Rabi oscillations. These findings are compared with quantum kinetic calculations for a twoband semiconductor model. Here we present results for one, two and three dimensions. Within this model, the coupling to the continuum of states above the band edge provides a dephasing mechanism missing in fewlevel models. It is shown that also the dephasing properties can be coherently controlled. Furthermore, it is demonstrated that the strength and controllability of phonon beats characteristically depend on the dimension of the system.

R. Otremba, S. Grosse, M. Koch, J. Feldmann, V.M. Axt, T. Kuhn, and W. Stolz,
 Excitonic wave packets observed in space and time resolved pump and probe experiments
Abstract:
We investigate the coherent time regime in space and timeresolved pump and probe experiments on a symmetrically strained InGaAs/GaAsP multiple quantum well. The spatial width of the transmission profiles shows a modulation which reflects the dynamics of an excitonic wave packet. This spatio–temporal beating originates from the combined action of various signal components which are detected simultaneously because of the collinearity of our experiment. The experimental results are in qualitative agreement with calculations obtained with a simplified model on the Hartree–Fock level.

V.M. Axt, K. Siantidis, M. Herbst, T. Kuhn, S. Grosse, M. Koch and J. Feldmann,
 Coherent and incoherent aspects of the coupled exciton phonon system
Abstract:
We present results of the optically excited dynamics in semiconductor quantum wells on short length and time scales. Nonlinear optical experiments are performed with high temporal and high spatial resolution. To interpret the experimental findings calculations are performed on different approximation levels. Two different time regimes are investigated: In the incoherent time regime we study the dynamics of heating, cooling, and the formation of excitons by measuring the temporal behavior of the lateral expansion rate of locally created electronhole pairs or excitons. A monomolecular exciton formation process is found. The experimental results in this regime are well reproduced by the Boltzmann equation for incoherent exciton densities with phenomenological scattering rates. In addition we have performed a microscopic density matrix analysis for the heating scenario where we have modeled explicitly the initial transformation of coherent excitations into incoherent exciton densities. It is found that the heating due to scattering with acoustic phonons gives reasonable agreement with the observed rates. In the coherent time regime a spatiotemporal beating is observerd. This unexpected nonmonotonic modulation of the spatial width arises from excitonic wavepackets which modulate the detected lateral profile of the optical nonlinearity in a characteristic way. It is explained by the superposition of various signal components which are detected simultaneously due to the collinearity of our experiment. This effect is illustrated by calculations using a simplified model on the HartreeFock level.

B. Nottelmann, V.M. Axt and T. Kuhn,
 Manybody effects in intersubband transitions of modulationdoped quantum wells
Abstract:
Based on the timedependent Hartree–Fock equations we study manybody effects in the absorption spectra as well as temporally and spectrally resolved fourwavemixing signals of modulationdoped quantum well structures. For sufficiently long dephasing times we find a beating behavior in the timereolved signals related to the Coulomb enhancement.

M. Herbst, T. Kuhn and V.M. Axt,
 Coherent control of carrierphonon scattering processes
Abstract:
The coherent control of LOphonon quantum beats is analyzed theoretically within the density matrix formalism. By comparing results for one, two, and threedimensional systems we find that the beat strength depends on the dimension. It is shown that both the beat amplitude and the dephasing of the interband polarization can be coherently controlled.

U. Neukirch, B. Haase, J. Gutowski,G. Bartels, A. Stahl, V.M. Axt,
J. Nürnberger and W. Faschinger,
 Transient polarization state of fourwavemixing signals: Identification of higherorder correlations
Abstract:
Recently, fourwavemixing (FWM) experiments on semiconductors have been extended by timeresolved analysis of the polarization state of the diffracted pulses. It was found that the seemingly unpolarized fraction of the signal observed in timeintegrated data is caused by averaging over a pulse having a perfect polarization state which, however, changes in time. Since in certain configurations the occurrence of a time dependent polarization is due to processes of higher than third order in the driving fields, the measurement of its intensity dependence allows for a sensitive test of theories which include higherorder correlations as is presented below. The experiments are conducted on a ZnSe/ZnMgSSe single quantum wells.

V.M. Axt, T. Kuhn, K. Siantidis, S. Grosse, M. Koch, J. Feldmann and W. Stolz,
 Spatiotemporal dynamics of optical nonlinearities in semiconductor quantum wells
Abstract:
We present results of the optically excited dynamics in semiconductor quantum wells on short length and time scales. Nonlinear optical experiments are performed with high temporal and high spatial resolution. To interpret the experimental findings calculations are performed on different approximation levels. Two different time regimes are investigated: in the incoherent time regime we study the dynamics of heating, cooling, and the formation of excitons by measuring the temporal behavior of the lateral expansion rate of locally created electronhole pairs or excitons. A monomolecular exciton formation process is found. The experimental results in this regime are well reproduced by the Boltzmann equation for incoherent exciton densities with phenomenological scattering rates. In addition we have performed a microscopic density matrix analysis for the heating scenario where we have modeled explicitly the initial transformation of coherent excitations into incoherent exciton densities. It is found that the heating due to scattering with acoustic phonons gives reasonable agreement with the observed rates. In the coherent time regime a spatiotemporal beating is observed. This unexpected nonmonotonic modulation of the spatial width arises from excitonic wavepackets which modulate the detected lateral profile of the optical nonlinearity in a characteristic way. It is explained by the superposition of various signal components which are detected simultaneously due to the collinearity of our experiment. This effect is illustrated by calculations using a simplified model on the HartreeFock level.
1998

V. M. Axt and S. Mukamel,
 Nonlinear optics of semiconductor and molecular nanostructures; a common perspective
Abstract:
A unified microscopic theoretical framework for the calculation of optical excitations in molecular and semiconductor materials is presented. The hierarchy of manybody density matrices for a pairconserving manyelectron model and the Frenkel exciton model is rigorously truncated to a given order in the radiation field. Closed equations of motion are derived for five generating functions representing the dynamics up to third order in the laser field including phonon degrees of freedom as well as all direct and exchangetype contributions to the Coulomb interaction. By eliminating the phonons perturbatively the authors obtain equations that, in the case of the manyelectron system, generalize the semiconductor Bloch equations, are particularly suited for the analysis of the interplay between coherent and incoherent dynamics including manybody correlations, and lead to thermalized exciton (rather than singleparticle) distributions at long times. A complete structural equivalence with the Frenkel exciton model of molecular materials is established.

G. Bartels, A. Stahl, V.M. Axt, B. Haase, U. Neukirch and J. Gutowski,
 Identification of higherorder electronic coherences in semiconductors by their signature in fourwavemixing signals
Abstract:
Fourwavemixing signals from excitons under linearcircular polarized excitation exhibit an elliptical polarization, depending on both the pulse delay and the spectral position. Besides the resonances corresponding to excitons and excitonbiexciton transitions, a breakup of the exciton line is found reflecting the influence of correlations on the fourpoint level. An analysis accounting for the exciton density, the bound biexciton, and the excitonexciton scattering continuum reveals that these features are not due to an antibound twoexciton state. Instead, they result from an interference of the correlated exciton continuum with the exciton density. In addition, the modeling shows that the signals ellipticity is highly sensitive to the influences of different correlations and, therefore, allows for a discrimination of their contributions.

R.A. Kaindl, S. Lutgen, M. Woerner, T. Elsaesser, B. Nottelmann, V.M. Axt, T. Kuhn, A. Hase, and H. Künzel,
 Ultrafast dephasing of coherent intersubband polarizations in a quasitwodimensional electron plasma
Abstract:
We present the first study of coherent intersubband polarizations in a pure electron plasma by femtosecond fourwave mixing in the midinfrared. Resonantly excited polarizations between consecutive conduction subbands of narrow GaInAs/AlInAs quantum wells decay within about 500 fs, much faster than intersubband relaxation of electrons. The relation between the decay rate of the signals and the dephasing rate is analyzed by solving the timedependent HartreeFock equations for the singleparticle density matrix. Electronelectron scattering is identified as the main dephasing mechanism.

V.M. Axt, K. Victor, and T. Kuhn,
 The excitonexciton continuum and its contribution to fourwave mixing signals
Abstract:
The combined influence of biexcitons and the twoexciton scattering continuum is analyzed. The analysis is based on a density matrix description of a twoband semiconductor accounting for meanfield contributions, bound biexcitons and the correlated parts of the twoexciton scattering continuum on a common footing. Consistent with the microscopic formulation, the influence of biexcitons as well as that of the twoexciton continuum is represented by a correlation kernel which is obtained from an integral equation. For a onedimensional model fourwave mixing signals are calculated solving numerically the resulting coupled nonlinear equations for excitation conditions in the vicinity of the 1s resonance. A strong compensation between the excitonexciton continuum and the meanfield contribution is found for all excitation conditions studied. Surprisingly, biexcitonic signatures turn out to be enhanced when continua are included in the description.

V.M. Axt and S. Mukamel,
 Influence of a phonon bath on electronic correlations and optical response in molecular aggregates
Abstract:
A generating function algorithm that allows the calculation of the optical response of coupled excitonphonon systems is developed. For a model of assemblies of threelevel molecules coupled via dipole interaction and interacting linearly with nuclear degrees of freedom, we derive a closed set of equations of motion for five generating functions representing the exact response to third order in the external field. These are equivalent to an infinite hierarchy of equations of motion for phononassisted variables. Starting with the equations for the generating functions, several reduction schemes are derived. By eliminating the phonon degrees of freedom in favor of selfenergies, the HakenStrobl model of relaxation is recovered as a limiting case. A set of timelocal equations is presented extending the HakenStrobl treatment by keeping the temperature dependence as well as the excitonic signatures of the phonon selfenergies. Finally, we derive equations that interpolate between the coherent and incoherent limits of exciton propagation and properly include the two exciton dynamics.

V.M. Axt and S. Mukamel,
 Realspace densitymatrix description of dynamic correlations in the optical response of manyelectron systems
Abstract:
A realspace formulation of the Quantum BogolyubovBornGreenKirkwoodYvon (QBBGKY)hierarchy is worked out in a form particularly suitable for applications to the optical response ofmanyelectron systems. Comparison is made to CoupledCluster approaches. A new hierarchy of contractionfree correlation functions is presented, that overcomes the problem of violated trace relations inherent in the truncated QBBGKYhierarchy.

S. Grosse, R. Otremba, G. von Plessen, M. Koch, J. Feldmann, V.M. Axt, T. Kuhn, R. Rettig and W. Stolz,
 Excitonic quantum beating in space and timeresolved pump and probe experiments
Abstract:
In spatially and temporally resolved pump and probe experiments we observe a spatial beating which reflects the coherent dynamics of an excitonic wave packet.

M. Koch, R. Otremba, S. Grosse, G. von Plessen, J. Feldmann,
W. Stolz, V.M. Axt and T. Kuhn,
Proceedings of ICPS24

B. Haase, U. Neukirch, J. Gutowski, G. Bartels, A. Stahl, V.M. Axt,
J. Nürnberger and W. Faschinger,
 Spectral signature of biexciton beats in fourwavemixing experiments
Abstract:
The spectral signature of biexciton beats in fourwavemixing signals of ZnSe quantum wells is investigated both experimentally and theoretically. Its complex dependence on polarization, intensity, and relative delay of the exciting pulses is consistently explained within a microscopic densitymatrix approach. Single χ^{(3)} and two cascaded χ^{(3)} processes (which are effectively of fifth order) are determined to be relevant for the signal generation at moderate excitation densities. The selection rules applying for the excitation of bound and unbound twoexciton states during these processes determine the spectral signatures of the beating.
1997

F. Wolter, P. Haring Bolivar, G. Bartels, H.G. Roskos, H. Kurz, V.M. Axt and K. Köhler,
 Coulombrenormalized intraband dynamics probed by THz emission
Abstract:
THz emission from a narrowminiband superlattice excited at its lower band edge reveals a hyperbolic bias dependence of the emission frequency. This reflects the emission from Coulombrenormalized states, namely the anticrossing between the miniband exciton and the hh_{2} and hh_{1} WannierStarkLadder states visible in the interband absorption spectra. An analysis of the intraband and interband dephasing times, respectively, reveals that the intraband dynamics remains to be Coulombrenormalized even after the dephasing of the interband coherence. This demonstrates that THz emission is dominated by longlived excitionic contributions, in contrast to predictions at a HartreeFock level. The dynamics controlled truncation (DCT) approach taking into account the dynamics of the fourpoint correlation for the intraband current density is able to account for this experimental observation.

S. Grosse, R. Arnold, G. von Plessen, M. Koch, J. Feldmann, V.M. Axt, T. Kuhn, R. Rettig and W. Stolz,
 Relaxation dynamics of electronhole pairs studied by spatiotemporal pump and probe experiments
Abstract:
The temporal evolution of the ambipolar diffusivity of optically excited electronhole pairs is investigated for a strained quantum well structure by temporally and spatially resolved pump and probe experiments. Dependent on the excitation conditions the diffusivity transients reflect the cooling and heating processes of excitons as well as the formation dynamics of excitons out of free electronhole pairs within less than 10 ps. Diffusivity transients obtained by Monte Carlo simulations of a simplified excitonic Boltzmann equation display all features of the experimental curves and support our interpretation of the lateral propagation dynamics in terms of formation, cooling and heating of excitons.

M. Herbst, V.M. Axt, T. Kuhn and J. Schilp,
 Electronphonon quantum kinetics: Relaxation in the presence of an electric field
Abstract:
The carrier generation and relaxation dynamics in a quantum wire in the presence of a constant electric field along the wire direction is studied in a quantum kinetic model based on the density matrix approach. Besides energynonconserving transitions at short times, the intracollsional field effect is included both for carrierlight and carrierphonon interaction. We show that fieldassisted generation and relaxation leads to shifts of the peaks in the distribution function of the generated carriers and of the phonon replicas due to the influence on the quantum mechanical interference process.

V.M. Axt, O. Kühn and S. Mukamel,
 Coherent versus incoherent energy transfer in light harvesting antenna complexes
Abstract:
Equations of motion for one and twoexciton amplitudes as well as exciton population variables which describe the dynamics of Frenkel excitons in optically excited aggregates are presented. Numerical calculations illustrate the interplay of coherent and incoherent transfer dynamics in a LightHarvesting Complex II (LHCII) monomer.

F. Wolter, P. Haring Bolivar, V.M. Axt, G. Bartels, H.G. Roskos, K. Kohler, A. Stahl and H. Kurz ,
QELSProceedings, OSA Technical Digest series, 139140 (1997)

V.M. Axt and G. Bartels,
QELSProceedings, OSA Technical Digest series, 3738 (1997)
1996

V.M. Axt, G. Bartels and A. Stahl,
 Intraband dynamics at the semiconductor band edge: Shortcomings of the Bloch equation method
Abstract:
The validity of the semiconductor Bloch equations (SBE) depends on the approximate decomposition of an intraband correlation function into a product of interband transition densities. We analyze the consequences of this approximation on the intraband dynamics of an optically excited semiconductor. As a special example where the SBE treatment becomes questionable we consider the THz emission of a narrow band superlattice in a static bias field. A comparison of the second order SBE solution with a rigorous second order treatment of this system helps one identify the weak points of the SBE approach and understand the physical background of its failure.

V.M. Axt, K. Victor and A. Stahl,
 Influence of a phonon bath on the hierarchy of electronic densities in an optically excited semiconductor
Abstract:
The influence of a phonon bath on the dynamics of the manybody density matrices relevant for the nonlinear optical response of semiconductors is studied. It is shown that, as in the phononfree case, only a finite set of electronic density matrices is needed to describe the optical response in a χ^{(n)} experiment. However, to obtain a closed set of equations of motion on the χ^{(n)} level additional truncation concepts have to be introduced in order to decouple the infinite hierarchy of phononassisted density matrices. Relations characteristic of intrinsic systems, that have previously been derived to reduce the number of independent dynamical variables in the phononfree case, are generalized. While in a coherent system the optical response is completely determined by transitiontype variables, under the influence of a phonon bath occupation densities can also become independent dynamical quantities. Numerical results for a simple onedimensional model are presented. Memory effects and dephasing induced by the electronphonon coupling are discussed for all χ^{(3)} relevant electronic density matrices. The pumpprobe signal for σ^{+}σ^{} excitation in the spectral region of the biexciton is analyzed. The respective contributions of two processes for the generation of biexcitons, via two photon transitions (TPT’s) or from previously generated exciton densities, to the microscopic dynamics are identified. The second process yields a χ^{(3)} signal only due to the coupling to the phonon bath and turns out to contribute considerably less than the TPT under all conditions studied in this paper.

K. Victor, V.M. Axt, G. Bartels, A. Stahl, K. Bott and P. Thomas,
 Microscopic foundation of the phenomenological fewlevel approach to coherent semiconductor optics
Abstract:
It is shown how a phenomenological fewlevel description of coherent semiconductor optics is related to microscopic densitymatrix theory. It turns out that the fewlevel dynamics is not obtained by simply projecting the microscopic dynamics onto a suitable chosen set of energy eigenstates. Therefore, a new hierarchy of microscopic densities is introduced with the property that their expansion in terms of energy eigenstates yields the level dynamics. The transformation rules between the fewlevel variables and the traditional density matrices are established. The problem of incorporating the coupling to continua into a fewlevel model is discussed. A refined fewlevel model approximating the influence of the continua by modified couplings between the levels is presented. The modified couplings turn out to be similar in structure to phenomenologically introduced refinements like local fields. The analysis makes clear that intuitively similar approximations have a different meaning when applied in the context of a fewlevel model or a truncated microscopic hierarchy.
1995

G. Bartels, V.M. Axt, K. Victor, A. Stahl, P. Leisching and K. Köhler,
 χ^{(5)}  signature in the fourwavemixing signal from a GaAs/Al_{0.3}Ga_{0.7} As superlatice
Abstract:
We analyze coherent beats with a period corresponding to the biexciton binding energy in timeintegrated fourwavemixing experiments in a GaAs/Al_{0.3}Ga_{0.7}As superlattice at high excitation densities. Theoretical and experimental evidence is presented that the beating in the decay is a fifthorder process in the electric field, and therefore χ^{(5)} contributions to the fourwavemixing signal in the 2k_{2}k_{1} direction have to be considered for a qualitative interpretation of the measured data. In order to model the experiment we use a microscopic dynamic densitymatrix theory in a realspace representation.

K. Victor, V.M. Axt and A. Stahl,
 The hierarchy of density matrices in coherent semiconductor optics
Abstract:
The hierarchy of manybody density matrices describing the nonlinear optical response of semiconductors is studied. The analysis is restricted to the coherent electronic dynamics generated by the relevant Hamiltonian. The strength of the optical excitation is used as a perturbation parameter, allowing a controlled truncation of the hierarchy and a drastic reduction of the number of independent multipoint functions describing the response to any given order. Thus the manybody effects contributing to the nth order susceptibility χ^{(n)} are described by [n+1/2] independent multipoint functions. As a consequence of the assumed coherence it turns out that all densitylike variables can be expressed in terms of transitionlike quantities. The proposed systematic treatment of Coulomb correlations is compared with the conventional randomphase approximation factorization of manybody matrices.

V.M. Axt, A. Stahl, E.J. Mayer, P. Haring Bolivar, S. Nüsse, K. Ploog and K. Köhler,
 Fourwavemixingtheory beyond the semiconductor Bloch equations
Abstract:
Fourwavemixing (FWM) experiments using a dynamical density matrix model of the semiconductor band edge are discussed. Higherorder correlation functions are retained which are neglected in the commonly used RPA treatment leading to the semiconductor Bloch equations. In order to terminate the hierarchy of the equations of motion for the higherorder density matrices systematically a truncation scheme controlled by orders in the driving field is applied. For any prescribed order n in the exciting field a closed set of equations is obtained from which the dielectric response up to order n can be calculated exactly. In addition it turns out that in a coherently driven system part of the remaining density matrices become redundant and can be eliminated. Fourwavemixing experiments are dominated by thirdorder contributions. Applying the abovedescribed results one ends up with only two functions in this case. These are the excitonic and the biexcitonic transition densities. As an application of our method the example of a GaAs single quantum well is studied. Two pulses with finite lengths are assumed such that both heavyand lighthole excitons are excited. The influence of the biexciton contribution on the polarization properties of the FWM signal is analyzed and compared with experimental results.
1994

V.M. Axt and A. Stahl,
 A dynamicscontrolled truncation scheme for the hierarchy of density matrices in semiconductor optics
Abstract:
We discuss the interaction of coherent electromagnetic fields with the semiconductor band edge in a dynamic density matrix model. Due to the influence of the Coulombinteraction the npoint density matrices are coupled in an infinite hierarchy of equations of motion. We show how this hierarchy is related to an expansion of the density matrices in terms of powers of the exciting field. We make use of the above results to set up a closed set of equations of motion involving two, fourand sixpoint correlation functions, from which all third order contributions to the polarization can be calculated exactly. Comparison of our treatment of the hierarchy with the widely used RPA decoupling on the twopoint level, gives interesting insight into the validity of the RPA. In particular we find, that a RPAlike factorization for two of the relevant densitymatrices yields a solution of their respective equations of motion to lowest order in the electric field.

V.M. Axt and A. Stahl,
 The role of the biexciton in a dynamic density matrix theory of the semiconductor band edge
Abstract:
We describe the dielectric response of the semiconductor band edge in a dynamic density matrix model. Our treatment is based on a set of χ_{3}relevant constitutive equations involving two, four and sixpoint density matrices. We demonstrate that under certain conditions all contributions to the third order susceptibility can be expressed in terms of excitonic and biexcitonic transitions. As a first application of these χ_{3}relevant equations we investigate the influence of the biexciton on the optical Stark effect in CuCl. We calculate shifts and lineshapes. Our results turn out to be in excellent agreement with experiments as well as with other theoretical predictions.
1993

K. Victor, V.M. Axt and A. Stahl,
 Excitonpolaritons in halfspace
Abstract:
A rigorous method is presented describing the coupling between an exciton polariton in a halfspace semiconductor and the external driving field. The method is based on density matrix theory. It allows to consider realistic electronhole interactions, spatial dispersion and extrinsic surface potentials. Without invoking additional boundary conditions or an artificial subdivision of the semiconductor it is shown that the influence of the surface can be isolated from the bulk behaviour. This is accomplished by a symmetric continuation of the restricted configuration space to bulk geometry inspired by the image source method in electrostatics. As a demonstration the solution is worked out for a simplified polariton model. The results are compared with other theories and with experimental reflection spectra.
1991

V.M. Axt and A. Stahl,
 A new approach to the excitonpolariton problem in halfspace geometry (ABCProblem)
Abstract:
The excitonic boundary value problem in a semiconducting halfspace is discussed on the basis of a dynamical twoband density matrix theory. A new approximate solution is presented. Reflection spectra calculated according to this method are compared with experimental data as with other theories.