Superlattice switching from parametric instabilities in a driven-dissipative BEC in a cavity

We numerically obtain the full time-evolution of a parametrically-driven dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram. Beyond the normal and superradiant phases, a third nonequilibrium phase emerges as a manybody parametric resonance. This dynamical normal phase switches between two symmetry-broken superradiant configurations. The switching implies a breakdown of the system's mapping to the Dicke model. Unlike the other phases, the dynamical normal phase shows features of nonintegrability and thermalization.