Passive synchronization in optomechanical resonators coupled through an optical field

Synchronization in coupled optomechanical resonators has drawn a lot of concerns. In an experimental setup where two distant mechanical resonators interact with a common optical cavity field, synchronization between mechanical resonators has been reported [Phys. Rev. Lett. 111 (2013) 213902, ibid 124 (2020) 213902]. In this work, we numerically investigate the dynamical behaviors in such an experimental setup. We find synchronous dynamics as well as asynchronous dynamics such as chaotic behaviors. However, the synchronization between two mechanical resonators is not a collective dynamics but a passive one. In these synchronous states, one resonator is slaved by the other and the dominant resonator behaves like the one in a single optomechanical oscillator. There are two types of passive synchronous states depending on which resonator is the dominant one. These two types of synchronous states always coexist and which synchronous state is realized depends on initial conditions, which suggests that there is something elusive in the experimental setup to achieve synchronization collectively.