Kardar-Parisi-Zhang universality in discrete two-dimensional driven-dissipative exciton polariton condensates

TL;DR

This paper demonstrates that discrete two-dimensional driven-dissipative exciton polariton condensates exhibit universal KPZ behavior, with numerical simulations confirming KPZ scaling laws and non-Gaussian phase fluctuation distributions.

Contribution

It shows that universal KPZ properties can emerge in 2D polariton systems when discretized, challenging previous notions about vortex hindrance in the KPZ regime.

Findings

First-order correlation functions follow KPZ scaling laws.

Phase fluctuation distributions are non-Gaussian, consistent with KPZ.

Numerical results match KPZ theoretical predictions.

Abstract

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the phase dynamics can be mapped to the stochastic Kardar-Parisi-Zhang (KPZ) equation. However, in two dimensions (2D), it was theoretically argued that the KPZ regime may be hindered by the presence of vortices, and a non-equilibrium BKT behavior was reported close to condensation threshold. We demonstrate here that, when a discretized 2D polariton system is considered, universal KPZ properties can emerge. We support our analysis by extensive numerical simulations of the discrete stochastic generalized Gross-Pitaevskii equation. We show that the first-order correlation function of the condensate exhibits stretched exponential behaviors in space and time with critical exponents characteristic of the 2D KPZ universality class, and find that the related scaling function accurately matches the KPZ theoretical one, stemming from functional Renormalization Group. We also obtain the distribution of the phase fluctuations and find that it is non-Gaussian, as expected for a KPZ stochastic process.