Symmetry-breaking oscillations in membrane optomechanics

TL;DR

This paper investigates the classical dynamics of a symmetric membrane in an optomechanical cavity, revealing symmetry-breaking bifurcations, self-sustained oscillations, and routes to chaos driven by laser detuning and intensity variations.

Contribution

It provides a detailed analysis of symmetry-breaking bifurcations and oscillations in membrane optomechanics, including the route to chaos, with a comprehensive theoretical framework.

Findings

Observation of supercritical and subcritical pitchfork bifurcations

Identification of hysteresis in fixed point patterns

Description of route to chaos in membrane dynamics

Abstract

We study the classical dynamics of a membrane inside a cavity in the situation where this optomechanical system possesses a reflection symmetry. Symmetry breaking occurs through supercritical and subcritical pitchfork bifurcations of the static fixed point solutions. Both bifurcations can be observed through variation of the laser-cavity detuning, which gives rise to a boomerang-like fixed point pattern with hysteresis. The symmetry-breaking fixed points evolve into self-sustained oscillations when the laser intensity is increased. In addition to the analysis of the accompanying Hopf bifurcations we describe these oscillations at finite amplitudes with an ansatz that fully accounts for the frequency shift relative to the natural membrane frequency. We complete our study by following the route to chaos for the membrane dynamics.