Two-membrane cavity optomechanics: non-linear dynamics

TL;DR

This paper investigates the complex non-linear behavior of a two-membrane cavity optomechanical system, demonstrating enhanced displacement detection and synchronization phenomena through combined experimental, numerical, and analytical methods.

Contribution

It provides a comprehensive analytical model for non-linear dynamics in a multimode optomechanical cavity with two membranes, including displacement detection beyond the linear limit.

Findings

Displacement detection surpasses the cavity linewidth limit.

Synchronization effects induce small oscillations at the excited mode's frequency.

Excellent agreement between experiments, simulations, and analytical predictions.

Abstract

We study the non-linear dynamics of a multimode optomechanical system constituted of a driven high-finesse Fabry-P\'erot cavity containing two vibrating dielectric membranes. The analytical study allows to derive a full and consistent description of the displacement detection by a probe beam in the non-linear regime, enabling the faithful detection of membrane displacements well above the usual sensing limit corresponding to the cavity linewidth. In the weak driving regime where the system is in a pre-synchronized situation, the unexcited oscillator has a small, synchronized component at the frequency of the excited one; both large and small amplitude resonator motions are transduced in a nontrivial way by the non-linear response of the optical probe beam. We find perfect agreement between the experimental results, the numerical simulations, and an analytical approach based on slowly-varying amplitude equations.