Mode locking and mode competition in a nonequilibrium solid-state condensate

A trapped polariton condensate with continuous pumping and decay is analyzed using a generalized Gross-Pitaevskii model. Whereas an equilibrium condensate is characterized by a macroscopic occupation of a ground state, here the steady states take more general forms. Some are characterized by a large population in an excited state; others by large populations in several states, which may overlap spatially. In the latter case, the highly populated states synchronize to a common frequency above a critical density. At intermediate densities, they can drive condensation in other trap modes by parametric scattering. Estimates for the critical density of the synchronization transition are consistent with experiments.