Fate of coupled discrete time crystals in a Dicke lattice dimer

Abstract

We simulate the dynamics of coupled discrete time crystals (DTCs) within the two-site open Dicke lattice model. We find that when two DTCs are coupled together, the amplitudes of their oscillation will either increase or decrease depending on the photon dissipation rate κ, the tunneling rate J between nearest-neighbouring sites, and whether the DTCs are initially in-phase or out-of-phase. We also show that by quenching J, it is possible to 'flip' the DTC, switching its phase to the other degenerate symmetry broken state. We examine the properties of this switching behavior and determine the combinations of J and the quench duration τ_q that enable the switching dynamics. We also investigate the robustness of the switching dynamics in the presence of quantum noise.