Theory of bifurcation amplifiers utilizing the nonlinear dynamical response of an optically damped mechanical oscillator

TL;DR

This paper explores the nonlinear response and multistability of an optomechanical system with a driven mechanical oscillator and optical damping, proposing its use as a bifurcation amplifier for sensitive signal detection.

Contribution

It introduces a theoretical framework for dynamical multistability in optomechanical systems and demonstrates their potential as bifurcation amplifiers for detecting small signals.

Findings

System exhibits dynamical multistability above a critical cooperativity.

Thermal and quantum noise induce switching between stable states.

Related setups can achieve similar effects with less mechanical oscillation.

Abstract

We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard optomechanical damping to the dynamical attractors known from the theory of optomechanical self-sustained oscillations. We also investigate the effect of thermal and quantum noise and estimate the noise-induced switching rate between the stable states of the system. We then consider applications of this system and primarily focus on how it can be used as bifurcation amplifiers for the detection of small mechanical or optical signals. Finally, we show that in a related but more complicated setup featuring resonant optomechanical interactions, the same effects can be realized with a relaxed requirement on the size of the mechanical oscillations.