Exact analytical solution for density matrix of a non-equilibrium polariton Bose-Einstein condensate

TL;DR

This paper provides an exact analytical quantum description of a non-equilibrium polariton Bose-Einstein condensate, revealing quantum correlations, distribution properties, and temperature behavior near the condensation threshold.

Contribution

It introduces an analytical solution for the full polariton density matrix considering quantum correlations in non-equilibrium conditions.

Findings

Density matrix includes quantum correlations between all polariton states.

Cross-correlations peak at the condensation threshold.

Polariton population follows Bose-Einstein distribution with near-zero chemical potential above threshold.

Abstract

In this letter, we give an analytical quantum description of a non-equilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a non-equilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the non-equilibrium nature of polariton systems, we show the average population of polariton states exhibits the Bose-Einstein distribution with an almost zero effective chemical potential above the condensation threshold similar to an equilibrium BEC. We demonstrate that above threshold the effective temperature of polariton condensate drops below the reservoir temperature.