## Masterarbeit "Polaritonische Effekte in der Exciton-Photon Basis"

Bose-Einstein condensates (BECs) establish a new and fascinating state of matter, but have up to now mainly been realized at extremely low temperatures. Only recently it has been demonstrated that in semiconductor nanostructures embedded in external cavities electron-hole pairs, so-called excitons, and photons form new bosonic quasi particles, which may condensate even at room temperature. This whole process is only poorly understood as major difficulties arise in obtaining a joint description of the light propagating in the cavity and the excited semiconductor material. There are models with varying degrees of sophistication which are starting from a basis of electrons, holes and photons [4, 3, 1]. These models can deliver ab-initio descriptions of light-matter interaction in semiconductors, but if higher-order correlations of electrons and holes are to be taken into account, spatially resolved simulations are no longer feasible. Recently, a formulation in the basis of excitons and photons has been proposed [5]. Since in this model the excitonic states are already known, correlations up to the level of exciton-exciton interaction can be taken into account. At the same time, the classical light wave and the material excitations are still treated independently, so that a spatially resolved semiclassical description is possible.

We offer a master or diploma thesis exploring the potential of this approach. Possible goals include:

- Formulation of spatially resolved equations of motion based on the Hamiltonian in [5]
- Implementation of a purely local approximation to exciton-exciton interaction in a simulation software
- Inclusion of exciton-phonon interaction
- Simulation of polaritonic condensation effects [2] (in arbitrary resonator geometries)

**Weiterführende Literatur**

- [1] Robert Buschlinger, Michael Lorke, and Ulf Peschel. Light-matter interaction and lasing in semiconductor nanowires: A combined finite-difference time-domain and semiconductor bloch equation approach. Phys. Rev. B, 91:045203, Jan 2015.
- [2] Iacopo Carusotto and Cristiano Ciuti. Quantum fluids of light. Rev. Mod. Phys., 85:299-366, Feb 2013.
- [3] W.W. Chow and S.W. Koch. Semiconductor-Laser Fundamentals: Physics of the Gain Materials. Springer, 1999.
- [4] H. Haug and S.W. Koch. Quantum Theory of the Optical and Electronic Properties of Semiconductors (4th Edition). World Scientific, 2004.
- [5] G. Rochat, C. Ciuti, V. Savona, C. Piermarocchi, A. Quattropani, and P. Schwendimann. Excitonic bloch equations for a two-dimensional system of interacting excitons. Phys. Rev. B, 61:13856-13862, May 2000.