Quantum mechanical study of a generic quadratically coupled optomechanical system

TL;DR

This paper provides a comprehensive quantum mechanical analysis of a quadratic-coupling optomechanical system, including analytical and numerical results, to explore its potential for advanced quantum measurements and state manipulation.

Contribution

It offers the first detailed quantum analysis of a generic quadratic-coupling optomechanical Hamiltonian, including dressed states, spectrum, and entanglement, with dissipation effects.

Findings

Analytical expressions for dressed states and spectrum.

Numerical results on phonon statistics and entanglement.

Potential applications in quantum state transfer and entanglement generation.

Abstract

Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for non-demolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wavefunction engineering, and entanglement generation.