  Synchronization has great impacts in various fields such as self-clocking,
communication, neural networks, etc. Here we present a mechanism of
synchronization for two mechanical modes in two coupled optomechanical
resonators by introducing the so-called PT-symmetric structure. It is shown
that the degree of synchronization between the two far-off-resonant mechanical
modes can be increased by decreasing the coupling strength between the two
optomechanical resonators. Additionally, when we consider the stochastic noises
in the optomechanical resonators, we find that more noises can enhance the
degree of synchronization of the system under particular parameter regime. Our
results open up the new dimension of research for PT-symmetric systems and
synchronization.
