Quantum Synchronization of Perturbed Oscillating Coherences

Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the system to satisfy specific symmetry constraints. We investigate the response of spin systems that possess such oscillating modes to generic, weak perturbations. We argue that even when these perturbations break the symmetry and lead to a single steady state, the correlations in the resulting state exhibit signatures of synchronization. Our results therefore connect the dynamical notion (based on persistent oscillations) and the steady-state notion (based on phase correlations)  of synchronization, which so far have been regarded as distinct phenomena. Furthermore, we demonstrate that in a spin-1 model the resulting steady-state synchronization exhibits the unexpected phase difference of multiples of π/3. Our work suggests robustness of synchronization and points toward a potential unifying framework of quantum synchronization.