Parametric state switching and transitions between discrete time crystals in the open Dicke model

Abstract

We show that the discrete time crystals (DTCs) in the periodically driven open Dicke model are accompanied by two degenerate parametric states corresponding to the possible phase shifts that the order parameter can acquire in its subharmonic response to the drive. We can induce the DTCs to switch from one state to another by ramping the phase of the periodic drive for a certain duration. We demonstrate that this parametric state switching is guaranteed to occur regardless of the initial state if the ramp duration is greater than the driving period, thus making the phase ramp protocol a robust method for dynamic control of the DTC phase.