Quantum synchronization of indirectly coupled oscillators in a Kerr resonator optomechanical system

We investigate the quantum synchronization of two indirectly coupled mechanical oscillators with different frequencies in the Kerr resonator optomechanical system, where the two driving fields are modulated. Our findings indicate that Kerr nonlinearity facilitates quantum synchronization, while quadratic coupling tends to suppress it. When both nonlinearities are present, quadratic coupling enhances synchronization in the presence of weak Kerr nonlinearity, whereas strong Kerr nonlinearity causes it to suppress synchronization. These results imply the existence of an optimal parameter regime for maximizing quantum synchronization. Moreover, under the joint influence of Kerr nonlinearity and quadratic coupling, perfect synchronization can be achieved under specific parameters. Our results provide insight into the manipulation of quantum synchronization utilizing nonlinearities in cavity optomechanical systems.