Kerr-like nonlinearities in an optomechanical system with an asymmetric anharmonic mechanical resonator

TL;DR

This paper investigates Kerr-like nonlinearities in an asymmetric optomechanical system, revealing bistability, entanglement dynamics, and potential control mechanisms for such systems using perturbation theory.

Contribution

It introduces a theoretical framework for analyzing Kerr-like nonlinearities in asymmetric optomechanical systems with cubic and quartic nonlinearities.

Findings

Demonstrates bistable behavior controlled by cross-Kerr interaction.

Shows entanglement dynamics with Yurke-Stoler-like states.

Provides insights for controlling optomechanical systems with asymmetric oscillations.

Abstract

In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, an optomechanical system with an asymmetric anharmonic mechanical resonator is studied. The cross-Kerr interaction and the Kerr-like self-interaction of photons and vibration quanta arise in the Hamiltonian. These interactions are induced by both cubic and quartic nonlinearities of oscillations of the mechanical resonator and the cavity-resonator interaction that is linear in mechanical displacements. We demonstrate a bistable behavior of the number of vibration quanta and find that this behavior is controlled by the cross-Kerr interaction. It is shown that, without driving and dissipation, the constructed superposition Yurke-Stoler-like states of the cavity (or the mechanical resonator) disentangle at certain times the entangled modes of the system. The obtained results offer new possibilities for control of optomechanical systems with asymmetric mechanical oscillations.