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The spontaneous breaking of time translation symmetry in periodically drivenFloquet systems can lead to a discrete time crystal. Here we study theoccurrence of such dynamical phase in a driven-dissipative optomechanicalsystem with two membranes in the middle. We find that, under certianconditions, the system can be mapped to an open Dicke model and realizes asuperradianttype phase transition. Furthermore, applying a suitableperiodically modulated drive, the system dynamics exhibits a robust subharmonicoscillation persistent in the thermodynamic limit.

Discrete time crystal in an open optomechanical system