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We study synchronization of a room temperature optomechanical system formedby two resonators coupled via radiation pressure to the same driven opticalcavity mode. By using stochastic Langevin equations and effectiveslowly-varying amplitude equations, we explore the long-time dynamics of thesystem. We see that thermal noise can induce significant non-Gaussian dynamicalproperties, including the coexistence of multi-stable synchronized limit cyclesand phase diffusion. Synchronization in this optomechanical system is veryrobust with respect to thermal noise: in fact, even though each oscillatorphase progressively diffuses over the whole limit cycle, their phase differenceis locked, and such a phase correlation remains strong in the presence ofthermal noise.

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