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

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, it was argued theoretically that in two dimensions the KPZ regime may be hindered by the presence of vortices, and a nonequilibrium Berezinskii-Kosterlitz-Thouless behavior was reported close to the condensation threshold. We demonstrate here that, when a discretized two-dimensional (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.