Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids.

We study nonequilibrium polariton superfluids in the optical-parametric-oscillator regime by using a Gross-Pitaevskii equation with pumping and decay. We identify a regime above the optical-parametric-oscillator threshold, where the system undergoes spontaneous symmetry breaking and is unstable towards vortex formation without any rotating drive. Stable vortex solutions differ from metastable ones; the latter can persist but can be triggered only externally. Both spontaneous and triggered vortices are characterized by a generalized healing length, specified by the optical-parametric-oscillator parameters only.