Quantum synchronization in an asymmetric coupled optomechanical system

In this work, we investigate the quantum synchronization and phi synchronization of two mechanical oscillators of different frequencies in two optomechanical systems with asymmetric coupling interaction. The whole system can be modulated by cavity detuning or driving amplitudes. Under certain parameters, quantum phi synchronization can be enhanced by asymmetric coupling in optomechanical systems, and the phase difference phi has an inversion. Moreover, we show that with the introduction of Kerr nonlinear medium, nonlinearity is dominated in achieving synchronization within asymmetric coupled cavities and phi can be corrected. Apart from achieving quantum synchronization, quantum anti-synchronization can be observed depending on the asymmetric coupling and the asymmetric external driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations in asymmetric coupled optomechanical systems.