Phase locking and frequency entrainment in driven generalized quantum Rayleigh-van der Pol oscillators

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. This work considers the master equation for the driven generalized Rayleigh-van der Pol oscillator. A key feature of the class of master equations considered is that it includes dissipators with broken rotational symmetry. This implies that the Wigner distribution of the quantum mechanical limit cycle state in the absence of the drive is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics, including the emergence of quasi-stationary states, is investigated. To characterize the synchronization, phase locking and frequency entrainment are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes.