Adiabatic approximation and fluctuations in exciton-polariton condensates

TL;DR

This paper examines the validity of the adiabatic approximation in exciton-polariton condensates, comparing models and analyzing how its breakdown affects fluctuations and correlations.

Contribution

It identifies three key conditions for the adiabatic approximation's validity and explores the effects of its failure on fluctuation properties in exciton-polariton models.

Findings

Adiabatic approximation validity depends on three independent conditions.

Breakdown of the approximation causes discrepancies in correlation lengths.

Beyond-Bogoliubov treatment is necessary for accurate phase and number fluctuation analysis.

Abstract

We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation that allows to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of the adiabatic approximation can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation.