Quantum synchronization and quantum φ synchronization in a coupled optomechanical system with Kerr nonlinearity

In this work, we study the quantum synchronization and quantum 0 synchronization of two mechanical oscillators in a coupled optomechanical system. The oscillators are coupled to an optical cavity filled with a Kerr nonlinear medium and subjected to periodic modulation of the cavity detunings and driving amplitudes by a common driving field. Our results show that the quantum synchronization and quantum 0 synchronization in nonlinear systems exhibit more favorable behaviors than in linear systems. In addition, we have investigated the performances of two synchronization measurements to various parameters by analyzing the sensitivity of 0. Accordingly, perfect synchronization can be achieved under specific parameters by periodically modulating the cavity and driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations.