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

TL;DR

This paper investigates the robustness of synchronization between two nanomechanical resonators coupled via a shared optical cavity, revealing that phase locking persists despite thermal noise and phase diffusion effects.

Contribution

It introduces a stochastic Langevin equation approach to analyze long-term dynamics and demonstrates the robustness of phase synchronization under thermal noise conditions.

Findings

Synchronization persists despite thermal noise

Phase difference remains locked even with phase diffusion

Thermal noise induces non-Gaussian dynamical properties

Abstract

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 multi-stable 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, their phase difference is locked, and such a phase correlation remains strong in the presence of thermal noise.