Stationary density matrix of a pumped polariton system

TL;DR

This paper numerically derives the stationary density matrix of a pumped polariton system, showing it is nearly diagonal and well-described by a distorted grand canonical Gibbs distribution, highlighting the system's thermal-like behavior.

Contribution

The study provides a numerical method to obtain the stationary density matrix of a pumped polariton system and demonstrates its approximate diagonal form and thermal distribution.

Findings

Stationary density matrix is nearly diagonal in energy basis.

Occupations fit a weakly distorted grand canonical Gibbs distribution.

Coherences between eigenstates are negligible compared to occupations.

Abstract

The density matrix, \rho, of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are three orders of magnitude smaller than the occupations, meaning that the stationary density matrix is approximately diagonal in the energy representation. A weakly distorted grand canonical Gibbs distribution fits well the occupations.