Kardar-Parisi-Zhang universality in optically induced lattices of exciton-polariton condensates

We investigate space-time coherence in one-dimensional lattices of exciton-polariton condensates formed by fully reconfigurable nonresonant optical pumping. Starting from a driven-dissipative Gross-Pitaevskii equation with deterministic reservoir kinetics and stochastic condensate noise, we derive a discrete complex-field model that incorporates coherent tunneling, reservoir-mediated dissipative coupling, and gain-saturation nonlinearity. The combination of these mechanisms, playing a crucial role in synchronization of driven-dissipative polariton condensate lattices, provides a multidimensional parameter space, allowing controllable switching between Kardar-Parisi-Zhang (KPZ) and Edward-Wilkinson (EW) dynamics. Adiabatic elimination of fast density fluctuations reveals a wedge-shaped region in the complex hopping plane where the coarse-grained phase dynamics reduces to the KPZ equation. By computing high-resolution phase diagrams of the temporal and spatial scaling exponents we pinpoint the boundaries separating the KPZ domain from the EW regime. Large-scale graphics processing unit (GPU) simulations of chains containing up to $N=2000$ condensates confirm these predictions: inside the wedge the exponents converge to ${\ensuremath{\beta}}_{N}=\mathbf{0}.\mathbf{329}(3)\ensuremath{\approx}1/3$ and ${\ensuremath{\chi}}_{N}=\mathbf{0}.\mathbf{504}(4)\ensuremath{\approx}1/2$, whereas outside it the dynamics moves away from KPZ and ultimately flow toward the EW fixed point, although finite system size and finite observation time may yield intermediate effective exponents.