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 antiphase 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. Effective unidirectional interactions lead to synchronization blockades between the undriven oscillator and the external drive as well as between both oscillators. Furthermore, we study the phase diagrams of two and three oscillators in the mean-field limit and find highly nontrivial active states.
