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In this paper, we study the synchronization of dissipative quantum harmonicoscillators in the framework of quantum open system via the Active-PassiveDecomposition (APD) configuration. We show that two or more quantum systems maybe synchronized when the quantum systems of interest are embedded indissipative environments and influenced by a common classical system. Such aclassical system is typically termed as a controller, which (1) can drivequantum systems to cross different regimes (e.g., from periodic to chaoticmotions) and (2) constructs the so-called Active-Passive Decompositionconfiguration such that all the quantum objects under consideration may besynchronized. The main findings of this paper is that we demonstrate that thecomplete synchronizations measured by the standard quantum deviation may beachieved for both stable regimes (quantum limit circles) and unstable regimes(quantum chaotic motions). As an example, we numerically show in anoptomechanical setup that the complete synchronization can be realized inquantum mechanical resonators.

Quantum synchronization via Active-Passive-Decomposition configuration: An open quantum system study