Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions

We elucidate the role that the dissipation in a bosonic channel plays in the prevalence and stability of time crystals (TCs) in a periodically driven spin-boson system described by the Dicke model. Here, the bosons are represented by photons, and they mediate the infinite-range interactions between the spin systems. For strong dissipation, we study the dynamics using an effective atom-only description and the closed Lipkin-MeshkovGlick model. By mapping out the phase diagrams for varying dissipation strengths, ranging from zero to infinitely strong, we demonstrate that the area in the phase diagram, where a TC exists, grows with the dissipation strength but only up to an optimal point, beyond which most of the TCs become unstable. We find TCs in both closedsystem and dissipative regimes, but dissipative TCs are shown to be more robust against random noise in the drive and are only weakly affected by the choice of initial state. We present the finite-sized behavior and the scaling of the lifetime of the TCs with respect to the number of spins and the interaction strength within a fully quantum mechanical description.

Automated summary

We investigate the impact of dissipation in a bosonic channel on the prevalence and stability of time crystals (TCs) in a periodically driven spin-boson system described by the Dicke model. By mapping out the phase diagrams for varying dissipation strengths, we find that the region where a TC exists expands with increasing dissipation strength but only up to a certain point, beyond which most TCs become unstable. We demonstrate that dissipative TCs are more robust against random noise in the drive and are only weakly affected by the choice of initial state.