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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., Comment: revised version, an appendix added, 14 pages, 8 figures

Revealing universal behaviors is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces, of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. This universality stems from a common underlying effective dynamics governed by the non-linear stochastic Kardar-Parisi-Zhang (KPZ) equation. Recent theoretical works suggest that this dynamics also emerges in the phase of out-of-equilibrium systems displaying macroscopic spontaneous coherence. Here, we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws, combined with a theoretical microscopic analysis that consistently reveals the other key signatures of this universality class, together with the possible resilience of KPZ dynamics to the presence of space-time vortices. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a new paradigm for exploring universal behaviors in open systems.

Exciton-polariton condensates under driven-dissipative conditions are predicted to belong to the Kardar-Parisi-Zhang (KPZ) universality class, the dynamics of the condensate phase satisfying the same equation as for classical stochastic interface growth at long distance. We show that by engineering an external confinement for one-dimensional polaritons we can access two different universality sub-classes, which are associated to the flat or curved geometry for the interface. Our results for the condensate phase distribution and correlations match with great accuracy with the exact theoretical results for KPZ: the Tracy-Widom distributions (GOE and GUE) for the one-point statistics, and covariance of Airy processes (Airy1 and Airy2) for the two-point statistics. This study promotes the exciton-polariton system as a compelling platform to investigate KPZ universal properties., Comment: 16 pages, 14 figures. Updated Fig. 2 and added Fig. 5 and Fig. 6, minor review done

We investigate the universal behavior of the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise. The presence of time correlations in the microscopic noise breaks the statistical tilt symmetry, or Galilean invariance, of the original KPZ equation with delta-correlated noise (denoted SR-KPZ). Thus it is not clear whether the KPZ universality class is preserved in this case. Conflicting results exist in the literature, some advocating that it is destroyed even in the limit of infinitesimal temporal correlations, while others find that it persists up to a critical range of such correlations. Using non-perturbative and functional renormalization group techniques, we study the influence of two types of temporal correlators of the noise: a short-range one with a typical time-scale $\tau$, and a power-law one with a varying exponent $\theta$. We show that for the short-range noise with any finite $\tau$, the symmetries (the Galilean symmetry, and the time-reversal one in $1+1$ dimension) are dynamically restored at large scales, such that the long-distance and long-time properties are governed by the SR-KPZ fixed point. In the presence of a power-law noise, we find that the SR-KPZ fixed point is still stable for $\theta$ below a critical value $\theta_{\textrm{th}}$, in accordance with previous renormalization group results, while a long-range fixed point controls the critical scaling for $\theta>\theta_{\textrm{th}}$, and we evaluate the $\theta$-dependent critical exponents at this long-range fixed point, in both $1+1$ and $2+1$ dimensions. While the results in $1+1$ dimension can be compared with previous studies, no other prediction was available in $2+1$ dimension. We finally report in $1+1$ dimension the emergence of anomalous scaling in the long-range phase., Comment: 20 pages, 11 figures, a section added

Exciton-polaritons under driven-dissipative conditions exhibit a condensation transition which belongs to a different universality class than equilibrium Bose-Einstein condensates. By numerically solving the generalized Gross-Pitaevskii equation with realistic experimental parameters, we show that one-dimensional exciton-polaritons display fine features of Kardar-Parisi-Zhang (KPZ) dynamics. Beyond the scaling exponents, we show that their phase distribution follows the Tracy-Widom form predicted for KPZ growing interfaces. We moreover evidence a crossover to the stationary Baik-Rains statistics. We finally show that these features are unaffected on a certain timescale by the presence of a smooth disorder often present in experimental setups., Comment: 4 pages, 4 figures