Quantum synchronization blockade induced by nonreciprocal coupling

Abstract: Recently, the synchronization of coupled quantum oscillators has attracted a great deal of interest. Synchronization requires driven constituents, and in such systems, the coupling can be designed to be nonreciprocal. Nonreciprocally-coupled oscillators exhibit a rich variety of behavior including active traveling-wave type states. In this work, we study the interplay of three competing synchronization mechanisms in a setup of two nonreciprocally-coupled quantum van der Pol oscillators. One of the oscillators is driven externally which induces phase locking. A dissipative interaction leads to anti-phase locking, whereas a coherent interaction nurtures bistable phase locking and active states. We approximate the phase diagram of the quantum case by evaluating the synchronization measure of a perturbation expansion of the steady state. Furthermore, we study the phase diagrams of two and three oscillators in the mean-field limit and find highly nontrivial active states.