Synchronization of many nano-mechanical resonators coupled via a common cavity field

TL;DR

This paper investigates how groups of nano-mechanical resonators synchronize via a common cavity field, revealing conditions for synchronization, multi-stability, and desynchronization in coupled nano-mechanical systems.

Contribution

It introduces a novel analysis of nano-mechanical resonator synchronization using amplitude equations, highlighting the effects of dissimilarities on collective behavior.

Findings

Resonators synchronize to form a single coupled mode.

Multi-stability occurs in the synchronized state.

Dissimilar oscillators can lose synchronization and oscillate out of phase.

Abstract

Using amplitude equations, we show that groups of identical nano-mechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behaviour which, when analyzed using amplitude equations, can be shown to exhibit multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.