# $\mathcal{PT}-$symmetry and chaos control via dissipative optomechanical coupling

## TL;DR

This paper explores how dissipative optomechanical coupling influences PT-symmetry and chaos, demonstrating control over complex dynamics and low-threshold phase transitions in a coupled system.

## Contribution

It introduces a novel approach to control chaos and phase transitions in dissipative PT-symmetric optomechanical systems using dissipative coupling.

## Key findings

- EP occurs at low threshold driving strength due to dissipative coupling.
- Dissipative coupling induces strong mechanical resonator interaction.
- Switching dissipative coupling restores regular dynamics from chaos.

## Abstract

We study a dissipative, mechanically coupled optomechanical system that accommodates gain and loss. The gain (loss) is engineered by driven a purely dispersive optomechanical cavity with a blue-detuned (red-detuned) electromagnetic field. By taking into account the dissipative coupling, the Exceptional Point (EP), which is the $\mathcal{PT}-$symmetry phase transition, occurs at low threshold driving strength compared to the purely dispersive system. In the linear regime, the $\mathcal{PT}-$symmetry is unbroken and the dissipative coupling induces strong coupling between the mechanical resonators, leading to an increase in energy exchange. For sufficiently strong driving, the system enters into a nonlinear regime where the $\mathcal{PT}-$symmetry is broken. In this regime, the mechanical resonators exhibit chaotic beats like-behaviour in the purely dispersive system. By switching on the dissipative coupling, the complex dynamics is switched off, restoring regular dynamics to the system. This work suggests ways to probe quantum phenomena in dissipative $\mathcal{PT}-$symmetric systems at low-threshold driving strength. It also provides a new way to control complex dynamics in optomechanics and related fields.