Nonlinear optomechanical systems with quasi-periodic and chaotic dynamics

TL;DR

This paper investigates the complex nonlinear dynamics of optomechanical systems with various photon-vibration interactions, revealing transitions from quasiperiodic to chaotic behavior and potential potential landscape transformations.

Contribution

It demonstrates how different interaction types influence the transition from quasiperiodic to chaotic dynamics in optomechanical systems with adiabatic photon field elimination.

Findings

Linear interaction leads to quasiperiodic oscillations.

Quadratic and combined interactions induce chaos.

All three interactions can produce quasi-periodic chaos.

Abstract

Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of effective potential describing the dynamics of the mechanical resonator from single-well to double-well is demonstrated. The dynamics of the mechanical resonator is considered in the presence of (i) only linear interaction, (ii) only quadratic interaction, (iii) both linear and quadratic interactions, and (iv) all three interactions, while other parameters of the optomechanical system, the modulation optical field, and the initial conditions remain fixed. Quasiperiodic oscillations of the mechanical resonator in the case (i) are replaced by chaotic ones when the cases (ii) or (iii) are realized. It is interesting that in the presence of all three interactions, the chaotic behavior of the mechanical oscillator becomes quasi-periodic. However, increasing the power of the modulation field again leads to chaos.