Quantum nonlinear dynamics of optomechanical systems in the strong coupling regime

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.

arXiv comment5 pages, 4 figures

References in corpus (18)

• Cavity Optomechanics
• Laser cooling of a nanomechanical oscillator into its quantum ground state
• Sideband Cooling Micromechanical Motion to the Quantum Ground State
• Observation of strong coupling between a micromechanical resonator and an optical cavity field
• Circuit cavity electromechanics in the strong coupling regime
• The photon blockade effect in optomechanical systems
• Single-photon Optomechanics
• Preparation of Nonclassical States in Cavities with a Moving Mirror
• Ponderomotive Control of Quantum Macroscopic Coherence
• The optomechanical instability in the quantum regime
• Signatures of nonlinear cavity optomechanics in the weak coupling regime
• Nonlinear interaction effects in a strongly driven optomechanical cavity
• Quantum Signatures of the Optomechanical Instability
• Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime
• Amplitude Noise Squeezing in Cavity-Driven Oscillations of a Mechanical Resonator
• Strong optomechanical interactions in a sliced photonic crystal nanobeam
• Nonclassical mechanical states in an optomechanical micromaser analogue
• Real photons from vacuum fluctuations in optomechanics: the role of polariton interactions

Cited by in corpus (5)

• Phase-Controlled Phonon Laser
• Nonlinear Sideband Cooling to a Cat State of Motion
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model
• Unraveling nonclassicality in the optomechanical instability
• Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators