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Optically coupled optomechanical oscillators has turned out to be a versatileexperimental resource for exploring optomechanical synchronizations andcorrelations. In this work, we investigate the phenomena of quantumsynchronization and quantum correlations in two optically coupledoptomechanical oscillators with two different topologies. In one case theoscillators are coupled with optical photons in a reversible manner, termed asbidirectional coupling, while in the other photons are allowed to enter to theother oscillator but not allowed to exchanged back in the opposite direction,termed as unidirectional coupling. Our results shows that irrespective of theseconfigurations, when synchronization builds up, the two oscillators also becomequantum mechanically correlated with a finite degree of Gaussian quantumdiscord. However, we find that depending on these topologies, bothsynchronization and quantum discord behave in a very distinctive manner. Forinstance, in bidirectionally coupled optomechanical oscillators, we find bothquantum synchronization and discord exhibit a tongue like pattern which is thequantum analogue of an Arnold tongue. Whereas, in the unidirectionally coupledoscillators, we observe a novel blockade like behavior for quantum phasesynchronization, also known as the quantum synchronization blockade, whilequantum discord being failed to map such an anomalous behavior.

Quantum synchronization and correlation in bidirectionally and unidirectionally coupled optomechanical oscillators