Non-Hermitian coupled-mode theory for incoherently pumped exciton-polariton condensates

TL;DR

This paper develops a non-Hermitian coupled-mode theory for incoherently pumped exciton-polariton condensates, enabling faster and more insightful simulations of condensate formation under arbitrary pumping profiles.

Contribution

It introduces a modal framework based on eigenmodes of the non-Hermitian generator, simplifying the analysis of polariton condensation dynamics.

Findings

Modal description agrees with full gGPE simulations

Provides significant speedup in computational simulations

Valid across diverse dynamical regimes

Abstract

The generalized Gross-Pitaevskii equation (gGPE) is an effective phenomenological description for the dynamics of incoherently pumped exciton-polariton condensates. However, a brute force numerical simulation of the gGPE provides little physical insight into condensate formation under arbitrary pumping configurations, and is demanding in terms of computational resources. We introduce in this paper a modal description of polariton condensation under incoherent pumping of arbitrary spatial profile, based on eigenmodes of the non-Hermitian generator of the linearized dynamics. A pump-dependent basis is then introduced to formulate a temporal coupled-mode theory that captures condensate dynamics in the presence of all nonlinear interactions. Simulations using a single set of modes for a given pumping and trapping configuration agree very well with a full integration of the gGPE in diverse dynamical regimes, supporting the validity of this modal description, while also providing a speedup in simulation times.