Limit-cycle bifurcations in driven-dissipative quantum systems

Driven-dissipative quantum systems often exhibit competition between coherent and dissipative driving processes and interactions. In particular, introducing correlated single-particle decay balanced by coherent hopping interactions can realize nonreciprocal and, for particular parameter tunings, uni-directional interactions. The resulting steady-states of the dynamics characterize the phase of the system and are of special interest when the steady-states are non-equilibrium. Systems with nonreciprocal interactions can exhibit phase transitions from static to dynamical phases characterized by limit-cycles, at the mean-field level, for example in the nonreciprocal Dicke model. Additionally, limit-cycle states can exhibit bifurcations of their own. In this talk, we study a two-mode bosonic model in which a system with a discrete parity symmetry nonreciprocally drives a quantum limit-cycle. We explore the correspondence between the classical and quantum limits, highlighting the introduction of noise to the system. We conclude with potential applications to experimentally realizable systems.