  We investigate the quantum synchronization phenomena of two mechanical
oscillators of different frequencies in two optomechanical systems under
periodically modulating cavity detunings or driving amplitudes, which can
interact mutually through an optical fiber or a phonon tunneling. The cavities
are filled with Kerr-type nonlinear medium. It is found that, no matter which
the coupling and periodically modulation we choose, both of the quantum
synchronization of nonlinear optomechanical system are more appealing than the
linear optomechanical system. It is easier to observe greatly enhanced quantum
synchronization with Kerr nonlinearity. In addition, the different influences
on the quantum synchronization between the two coupling ways and the two
modulating ways are compared and discussed.
