## Abstract

The subject of the research project is the theory of semiconductor nanostructures in the regime of strong light-matter coupling, with the goal to develop the theoretical models, to elucidate conceptual questions and to propose technological applications.
In semiconductor microcavities, strong light-matter coupling results in the so-called polariton quasi-particles that are a coherent superposition of quantum well exciton and microcavity photon. Thanks to their composite nature, these bosonic quasi-particles combine significant interactions with good quantum coherence. These favorable properties have led to the first observation of Bose-Einstein condensation (BEC) in the solid state. The research on polariton BEC has developed in a lively subject of fundamental research, on the crossroad between of semiconductor physics, quantum optics and quantum gases and enjoys fruitful collaboration between theorists and experimentalists. Besides their interest from the fundamental physics side, microcavities in the strong coupling regime have high potential for technological applications, such as ultralow threshold lasing, generation of entangled photon pairs, miniaturized nonlinear optical devices and ultrafast optical memories.
The two elements that make polaritons different from other realizations of quantum degenerate bose gases are the finite polariton life time and their interactions with the solid state environment. These pose great challenges for their theoretical description. Due to the finite polariton life time, the polariton gas does not reach thermodynamic equilibrium. As a consequence, the steady state cannot be found by minimizing a free energy. Instead, the kinetics has to be modeled. The nonequilibrium character also raises conceptual questions related to the meaning of superfluidity, because standard treatments rely on thermodynamic arguments.
We plan to attack the polariton quantum kinetics with methods based on quasi-probability distributions developed in quantum optics. These distributions can be sampled with stochastic classical fields, using Monte Carlo techniques. I have developed effective models of this type before, but these exploratory studies contained quite drastic approximations. It is the aim of the present research project to go beyond these simplifications and to develop a full model for the kinetics of a quantum degenerate polariton gas that interacts with its solid state environment.
Applications of the theoretical model will include among others a quantitative study of the long range spatial coherence, density fluctuations, the dynamics of the formation of coherence, the shape of the condensate state and its coherence in the presence of periodic or disordered potentials and the polarization state of polariton condensates. In addition, we will consider the application of the developed formalisms to study different physical systems. One promising example is a nanocavity with an embedded quantum dot, where recently the controversial observation of lasing in the strong coupling regime was reported.
In addition, we will seek to make conceptual progress in the domain of polariton superfluidity. Our model will contain all the ingredients to make a microscopic calculation of the superfluid fraction. Such a calculation is important, because of the two dimensional nature of the polariton fluid: from the analogy with the two-dimensional bose gas at thermodynamic equilibrium, it is expected that the transition from the incoherent to coherent state is of the Berezinskii-Kosterlitz-Thouless type, characterized by a jump in the superfluid fraction.
Finally, the directions of technological applications that we think of are based on the polarization dynamics, that was recently exploited to construct an ultrafast all optical spin memory.

## Researcher(s)

## Research team(s)