Abstract
We explore the phenomenon of quantum phase synchronization in two optomechanical oscillators, coupled either bidirectionally or unidirectionally to each other. We first show that irrespective of the configuration of the optomechanical oscillators, synchronization can be achieved, with a finite degree of quantum correlation. However, while looking at the variation of the synchronization against the frequency detuning of the two oscillators, we observe a profound effect of the directionality of the optical coupling. For instance, we find that when the two optomechanical cavities exchange photons bidirectionally, synchronization traces the classic Arnold tongue. Whereas, for the unidirectional configuration, synchronization exhibits a novel blockade-like behavior where finite detuning favors synchronization. We also observe a strong connection between synchronization blockade and synchronization phase transition.
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