Nonlinear dynamics of weakly dissipative optomechanical systems

TL;DR

This paper explores the rich classical nonlinear dynamics, including chaos and bifurcations, in weakly dissipative optomechanical systems, a regime less studied compared to strongly dissipative systems, revealing new dynamical behaviors.

Contribution

It extends analysis methods to weakly dissipative regimes and uncovers novel dynamical phenomena such as chaos at lower driving strengths.

Findings

Weak dissipation enhances sensitivity to initial conditions.

Chaos can occur at lower driving strengths in weakly dissipative systems.

Identifies bifurcations and routes to chaos specific to this regime.

Abstract

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the "Generalized Alignment Index" method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the Neimark-Sacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos.