Spontaneous vortex arrays in a parametrically driven polariton condensate

We study theoretically a condensate of microcavity polaritons, driven resonantly in the optical parametric oscillator regime. Using a driven-dissipative generalized Gross-Pitaevskii equation, we model a finite system populated by a novel and experimentally viable pump with circular symmetry and radial currents. The resulting nonequilibrium superfluid is unstable to spontaneous symmetry-breaking and undergoes the formation of vortex arrays, which arise in the absence of any external field, potential, or rotation. The vortex arrays have nonzero net angular momentum and can rotate in one of two degenerate but chirally distinct states. This new phenomenon exists in a regime readily accessible to experiments, and we discuss possible experimental signatures of such an array.