Discrete time crystal in an open optomechanical system

This is the authors' abstract. We don't add key points for this paper.

The spontaneous breaking of time translation symmetry in periodically driven Floquet systems can lead to a discrete time crystal. Here we study the occurrence of such dynamical phase in a driven-dissipative optomechanical system with two membranes in the middle. We find that, under certain conditions, the system can be mapped to an open Dicke model and realizes a superradiant-type phase transition. Furthermore, applying a suitable periodically modulated drive, the system dynamics exhibits a robust subharmonic oscillation persistent in the thermodynamic limit.