Dicke time crystals in driven-dissipative quantum many-body systems*

Recent experimental progress has opened up an opportunity to explore nonequilibrium phenomena in AMO systems, which can exhibit interesting behavior absent in equilibrium, with time crystals---phases of quantum matter that spontaneously break time translational symmetry---as an example. In particular, the paradigmatic Dicke model, which describes an ensemble of atoms collectively coupled to a leaky cavity mode, has recently been shown to host time-crystalline-like behavior of the collective spin in the presence of periodic driving [1]. Here, we investigate the situation where the mean-field solvability of the conventional Dicke model is explicitly broken by the addition of short-range interactions between the atoms. In this context, the interplay between driving, dissipation and interactions yields a rich set of dynamical responses including long-lived and metastable Dicke time crystals. Interestingly, when the additional short-range interactions are ferromagnetic, we observe time crystalline behavior at non-perturbative values of the interaction strength, suggesting the possible existence of stable order in a driven-dissipative quantum many-body system. [1] Z. Gong, R. Hamazaki, and M. Ueda, Phys. Rev. Lett. 120, 040404 (2018)