Kardar-Parisi-Zhang universality in the phase distributions of one-dimensional exciton-polaritons

Abstract

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.

Unstable and stable regimes of polariton condensation

“…Using a lattice to invert the sign of the polariton mass allows to suppress this instability and prepare extended condensates with high spatial and temporal coherence. This method opens exciting possibilities in view of investigating novel driven-dissipative phenomena [36][37][38][39][40][41][42][43] with bosonic condensates in a controlled platform.…”

“…In that case, the confinement-induced kinetic energy and, possibly, the outwards flow due to the overall density profile competes with attractive interactions so that stable condensates can be achieved even for negative g eff . But this method imposes small condensate sizes, which limits the capacity of polaritons to serve as a platform for simulating novel drivendissipative phenomena [36][37][38][39][40][41][42][43]. A promising alternative are the large condensates recently demonstrated in cavities with long lifetimes and reduced wedge [61].…”

“…In contrast to all these works, here we demonstrate how the dynamical instability of condensates under CW pumping with a large spot (≈ 90 µm) can be tamed by introducing a periodic potential. When condensation occurs into negative mass states, stable condensates of arbitrarily large size (only limited by the available total pump power) can be obtained while maintaining a coupling to an excitonic reservoir of the standard form (2), for which rich KPZ driven-dissipative phase transitions are expected [38,39,[41][42][43]. In the experiments described below, polaritons are excited non-resonantly with a CW monomode laser tuned to 740 nm.…”

“…When the cavities are spatially patterned into lattices so that condensation occurs in negative mass states, the modulational instability is suppressed and all previous signatures of instability disappear: the condensates reach a stable steady-state with high homogeneity and coherence. This method for suppressing instabilities opens avenues for studying the rich phenomenology of driven-dissipative condensates [36][37][38][39][40][41][42][43], such as Kardar-Parisi-Zhang (KPZ) universal scalings, in a controlled environment. The presented results are relevant to a wide range of photonic plateforms sustaining Bose-Einstein-like transitions, such as vertically emitting laser diodes [44], photon condensates [45] and plasmonic structures embedded in cavities [46].…”

Topological Defects in Anisotropic Driven Open Systems

“…Due to this non-linear term, the vortex interaction is exponentially screened at large distances -thus, the ordered phase ceases to exist. This finding is particularly relevant, since the cKPZ equation is the long-wavelength description of a vast variety of systems, ranging from "polar active smectics" or "moving stripes" [11], to driven-dissipative condensates such as exciton-polaritons [3,[8][9][10][12][13][14][15][16][17][18][19], synchronization in arrays of limit-cycle oscillators [20], and limit-cycle phases that emerge from a Hopf bifurcation [21][22][23][24][25] such phases have attracted a lot of attention recently and could be coined dissipative time crystals [26].…”