Analyzing quantum synchronization through Bohmian trajectories

We analyze quantum effects involved in continuous variable synchronization between two self-sustaining resonators in the framework of Bohmian mechanics. Bohmian trajectories provide visual descriptions of significant nonclassical dynamics, which allow us to characterize the level of quantum synchronization more intuitively compared with only utilizing some designed synchronization measures. It is found that in the quantum limit, the Bohmian trajectories will deviate from their corresponding semiclassical limit cycle behavior after they are distorted by the quantum potential. We explore the roles of zero-point fluctuation, superposition, and nonlocal correlation in synchronization dynamics, corresponding to the oscillators in a coherent state, superposition state, and entanglement state, respectively. We also explore the influence of squeezed Hamiltonian on spontaneous synchronization.