# Self-organized synchronization of mechanically coupled resonators based on optomechanics gain-loss balance

## TL;DR

This paper demonstrates how optomechanical gain-loss engineering in coupled resonators induces self-organized synchronization, revealing rich collective dynamics and potential applications in phonon-based technologies.

## Contribution

It introduces a method to achieve synchronization in coupled mechanical resonators via optomechanical gain-loss balance, including the effects of quadratic coupling.

## Key findings

- Synchronization depends on mechanical coupling and optomechanical parameters.
- Quadratic coupling enhances in-phase synchronization.
- Remotely induced phonon synchronization enables new technological applications.

## Abstract

We investigate collective nonlinear dynamics in a blue-detuned optomechanical cavity that is mechanically coupled to an undriven mechanical resonator. By controlling the strength of the driving field, we engineer a mechanical gain that balances the losses of the undriven resonator. This gain-loss balance corresponds to the threshold where both coupled mechanical resonators enter simultaneously into self-sustained limit cycle oscillations regime. Rich sets of collective dynamics such as in-phase and out-of-phase synchronizations therefore emerge, depending on the mechanical coupling rate, the optically induced mechanical gain and spring effect, and the frequency mismatch between the resonators. Moreover, we introduce the quadratic coupling that induces enhancement of the in-phase synchronization. This work shows how phonon transport can remotely induce synchronization in coupled mechanical resonator array and opens up new avenues for metrology, communication, phonon-processing, and novel memories concepts.