Complex dynamics of nano-mechanical membrane in cavity optomechanics

TL;DR

This paper investigates the complex, chaotic dynamics of a nano-mechanical membrane in an optomechanical cavity, modeling it as a kicked harmonic oscillator and analyzing stability and phase space structures.

Contribution

It introduces a mathematical model using a stochastic web map to describe the membrane's dynamics and explores conditions leading to chaos in the system.

Findings

The web map is area-preserving and exhibits q-fold symmetry.

Chaotic behavior occurs under specific parameter control.

Stability analyzed via Lyapunov exponents and survival probability.

Abstract

Theoretical analysis of a suspended nanomechanical membrane subject to an optical driving field in an optomechanical cavity is presented, which is confirmed through numerical simulations. In the presence of an optical field between its mirrors, the high-finesse optomechanical resonator acts as an oscillator driven by a radiation pressure force. The periodic nature of the radiation pressure force makes the nano-mechanical membrane in the optomechanical system as a kicked harmonic oscillator. Mathematically the physical system displays a stochastic web map that helps to understand several properties of the kicked membrane in classical phase space. We find that our web map is area preserving and displays quasiperiodic symmetrical structures in phase space which we express as $q$-fold symmetry. It is shown that under appropriate control of certain parameters, namely the frequency ratio and the kicking strength, the dynamics of kicked membrane exhibits chaotic dynamics. We provide the stability analysis by means of Lyapunov exponent and survival probability.