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.
We investigate synchronization and entanglement in two coupled cavity optomechanical systems. The classical synchronization, quantum synchronization and entanglement of the two cavity fields and the two mechanical oscillators are analysed, respectively. Our results show that the two cavity resonators are synchronization without entanglement, while the two mechanical oscillators are entangled with quantum-phase synchronization. We conclude that the quantum synchronization and entanglement have no affirmatory relationship although they are both signature of correlation.
Quantum synchronization and its connection with other quantum correlations have attracted considerable attention. Here we present a theoretical scheme to simultaneously represent and significantly enhance the level of quantum synchronization and entanglement between two indirectly coupled mechanical membranes, which are coupled to a common optical field within a cavity. By applying a two-tone driving laser with weighted amplitudes and specific frequencies, both synchronization gauged by Mari's criterion and entanglement estimated by logarithmic negativity can be greatly enhanced. We then clarify the relationship between quantum synchronization and entanglement in detail. Numerical simulation results show that the influence of the coupling asymmetry
G2/G1 on quantum complete synchronization behaves similarly to that on the purity while the influence of the coupling asymmetry
G2/G1 on quantum phase synchronization is more similar to that on quantum entanglement. Besides, we demonstrate that although quantum synchronization and quantum entanglement are not directly related, both of them are sensitive to the squeezing parameter and the cooling effect. Furthermore, it is also shown that detuning the frequencies of two mechanical oscillators can actually help quantum synchronization and entanglement, which is somewhat similar to the case of quantum synchronization blockade.