Noise robustness of synchronization of two nanomechanical resonators coupled to the same cavity field

We study synchronization of a room-temperature optomechanical system formed by two resonators coupled via radiation pressure to the same driven optical cavity mode. By using stochastic Langevin equations and effective slowly varying amplitude equations, we explore the long-time dynamics of the system. We see that thermal noise can induce significant non-Gaussian dynamical properties, including the coexistence of multistable synchronized limit cycles and phase diffusion. Synchronization in this optomechanical system is very robust with respect to thermal noise: in fact, even though each oscillator phase progressively diffuses over the whole limit cycle, its phase difference is locked, and such a phase correlation remains strong in the presence of thermal noise.