# Synchronization of an optomechanical system to an external drive

## TL;DR

This paper investigates how optomechanical systems can synchronize their mechanical oscillations to external drives, analyzing classical and quantum regimes, and deriving a microscopic Adler equation for synchronization dynamics.

## Contribution

It introduces a microscopic Adler equation for optomechanical synchronization and demonstrates quantum regime synchronization, advancing understanding of quantum synchronization phenomena.

## Key findings

- Synchronization occurs in both classical and quantum regimes.
- Derived a microscopic Adler equation for optomechanical systems.
- Synchronization is achievable with optical or mechanical external drives.

## Abstract

Optomechanical systems driven by an effective blue detuned laser can exhibit self-sustained oscillations of the mechanical oscillator. These self-oscillations are a prerequisite for the observation of synchronization. Here, we study the synchronization of the mechanical oscillations to an external reference drive. We study two cases of reference drives: (1) An additional laser applied to the optical cavity; (2) A mechanical drive applied directly to the mechanical oscillator. Starting from a master equation description, we derive a microscopic Adler equation for both cases, valid in the classical regime in which the quantum shot noise of the mechanical self-oscillator does not play a role. Furthermore, we numerically show that, in both cases, synchronization arises also in the quantum regime. The optomechanical system is therefore a good candidate for the study of quantum synchronization.