Quantum nonlinear dynamics of optomechanical systems in the strong coupling regime

TL;DR

This paper investigates the quantum nonlinear dynamics of optomechanical systems in the strong coupling regime, revealing self-sustained oscillations, spectral features, and nonclassical phonon states beyond linear models.

Contribution

It provides a novel analytical approach to analyze quantum nonlinear effects in optomechanics in the multi-photon strong coupling regime, including nonlinear oscillations and phonon state engineering.

Findings

Mechanical resonator exhibits self-sustained oscillations beyond linear instability predictions.

Additional peaks in the cavity power spectral density due to frequency mixing.

Creation of sub-Poissonian phonon states under red detuning, even with strong driving.

Abstract

With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multi-photon strong coupling regime retaining nonlinear terms. This is achieved by performing a Schrieffer-Wolff transformation on the Hamiltonian including driving terms. The approach is valid away from the red- and blue-sideband drive. We show that the mechanical resonator displays self-sustained oscillations in regimes where the linearized model predicts instabilities, and that the amplitude of these oscillations is limited by the nonlinear terms. Related oscillations of the photon number are present due to frequency mixing of the shifted mechanical and cavity frequencies. This leads to additional peaks in the cavity's power spectral density. Furthermore, we show that it is possible to create phonon states with sub-Poissonian statistics when the system is red-detuned. This result is valid even with strong driving and with initial coherent states.