Stationary and time dependent correlations in polariton condensates

TL;DR

This paper analytically studies the correlations in polariton condensates using the truncated Wigner method, providing results that align well with experiments and exploring the method's validity limits.

Contribution

It offers an analytical solution for the Wigner function in polariton condensates and compares it with numerical and experimental results, highlighting noise effects and time-dependent correlations.

Findings

Second order correlations match experimental data

Explicit expressions for linewidth and relaxation rate derived

Validity limits of the truncated Wigner method discussed

Abstract

The statistics of the condensed polaritons is described in terms of the Wigner function. In the framework of the truncated Wigner method, the Wigner function obeys a Fokker- Planck equation, which is solved analytically. The second order correlations in the stationary state are in excellent agreement with those obtained from the numerical solution of the master equation and show a qualitative and, well above threshold, also quantitative agreement with recent experiments. Furthermore, the contributions of the different noise effects that influence the polariton ground state statistics are explicitly defined. Exploiting the equivalence between Fokker-Planck and Langevin descriptions of stochastic processes, the time dependent correlations of the polaritons close to the stationary state are derived. Explicit expressions for the linewidth and for the relaxation rate of the polariton intensity are obtained, whose values are of the same order of magnitude of the experimental data. Finally, the limit of validity of the truncated Wigner method in the present model is discussed.