# Research

## Ultrafast dynamics in semiconductor structures

The main research field of the group 'Quantum Theory of Condensed Matter' is ultrafast dynamics in semiconductor structures. On the one hand, this field is rich in fundamental questions and, on the other hand, has a high potential in terms of possible applications due to the enormous technological importance of semiconductor materials. The now available structurability on a nanometre length scale opens up a wealth of possibilities for the targeted and controlled construction of complex coupled systems. Furthermore, structured semiconductors can be considered prototypical model systems for complex many-body systems with pronounced quantum properties. One of the fundamental challenges for theory is the description of processes on ultrashort time scales, as many traditional approaches reach their limits here. For example, the interaction of charge carriers in a semiconductor is treated as a collision within the framework of the Boltzmann equation, i.e. as an event that takes place at a certain timeand at a certain place and has neither a temporal nor a spatial evolution. By using ultrashort laser pulses, it is now possible to spatiotemporally resolve interaction processes in semiconductors. In order to adequately capture the physics of interaction processes of finite duration and spatial extension, a description on the quantum kinetic level is required that takes into account the spatiotemporal memory effects relevant here. Furthermore, interactions that exist over a longer period of time can lead to fixed correlations between the particles involved. The consideration of many-particle correlations and coherences, including their spin dependencies and quantum statistical properties, is of central importance, both to gain a deeper understanding of ultrafast dynamics and with regard to possible applications in the field of innovative technologies.

## Dynamics in semiconductor quantum dots and quantum dot resonator structures

The possible realisation of basic functions of a quantum computer using optically excited quantum dots is currently a very active field of research. The work of our theory group started on this topic aims at developing a microscopic understanding of the decoherence found in quantum dots, which is a major obstacle for a successful realisation of quantum logic. Here, we focus on investigations of the coupled dynamics of electronic and phononic excitations. Our results show that the so-called pure dephasing in quantum dots represents an essential decoherence mechanism. These are electron-phonon interaction processes that do not lead to a change in the electronic occupations. This is remarkable, since in higher-dimensional systems such processes are of secondary importance. Furthermore, our results show that pure-dephasing processes can be manipulated with coherent control methods due to their non-Markovian nature and that decoherence can be reduced by using appropriate pulse sequences.

In addition to questions of decoherence, we have investigated other aspects of coupled electron-phonon dynamics. For example, we have succeeded in formulating a dynamics of generating functions for phonon-assisted density matrices that allows us to analytically describe the time evolution of the formation of acoustic polarons after ultrashort laser excitation. It could be shown that during polaron formation in quantum dots, energy is released that is transported away from the quantum dot in the form of a pulsed phonon wave packet.

Currently, the coupling of quantum dots to resonators that couple a few photon modes to the quantum dot is of particular interest. Such systems can be used as sources of many non-classical photon states, such as single photon sources, sources of entangled photon pairs, and for the generation of Schrödinger cat states or higher Fock states. It could be shown that the phonon influence on parameters important for applications, such as the degree of entanglement or the purity of the single-photon states, is not always destructive. The finding that a phonon-assisted preparation of exciton and biexciton states does not lead to a loss of quality in subsequently emitted photons is also important for applications, e.g. it could be shown that with such a preparation spatially separated simultaneously excited quantum dots can emit photons with high mutual coherence, which is of crucial importance for the scalability of corresponding applications.

To treat laser-driven quantum dot resonator systems coupled to phonons, we have developed a path integral approach that is able to describe numerically these genuine interacting many-body systems without any approximation the model. The so far most efficient algorithm for evaluating the sum over the paths could be accelerated by up to 20 orders of magnitude for these systems by a reformulation in our group. Only through this new development calculations for systems with higher photon numbers have become possible.

## Spin dynamics in magnetic semiconductor structures

This project deals with the non-thermal coherent dynamics of optically excited magnetic semiconductors. In particular, we are interested in the possibilities of coherent optical control of magnetisation on ultra-short time scales. We have dealt with both strongly localised and extended magnetic nanostructures. The first category includes a system consisting of an optically excited quantum dot with an embedded single Mn atom. It has been shown that the spin of the Mn atom can be selectively brought into any of its six quantum states by a suitable sequence of laser excitations, although there is no direct coupling to the laser field. Complete remagnetisation is possible on a time scale of a few 10 picoseconds. As a prototype of extended magnetic structures, we have analysed the spin dynamics in diluted magnetic semiconductor quantum films. Although these systems have been studied for a long time, it was clarified only through our analysis why Markovian spin relaxation rates do not lead to satisfactory agreement with experiments. Quantum kinetic effects are of crucial importance here. Among other things, it was shown that non-magnetic impurity scattering has a very large influence on the spin dynamics, although the associated Markovian rate disappears.

## Short time dynamics of BCS Systems

Modell simulations show that extternal actions can bring BCS systems (e.g. classical superconductors or some ultra cold alkaline gases) into states far from equilibrium that cannot be described as a time-dependent occupation of quasi-particles. A non-adiabatic regime is predicted where coherences between quasi-particle states are built up. A ponounced indicator for reaching the non-adiabatic regime is the occurrence of temporal oscillaions of the BCS order parameter.

This project aims on the one hand at a deeper understanding of the characteristic short time effects in BCS systems and on the other hand we would like to reveal how the unusual dynamics properties of the non-adiabatic regime are reflected in experimentally accessable signals. Our simulations demonstrate that the oscillations of the order parameter can *not* be seen as line shifts in usual pump-probe experiments. When, hoever, the excitation consists of a pair of phase-locked pulses, then the oscillations should be detectable as line shifts depending on the control delay.