Cooling and squeezing via quadratic optomechanical coupling

TL;DR

This paper investigates quadratic optomechanical coupling, deriving a master equation for two-phonon cooling, revealing non-thermal steady states, and demonstrating mechanical squeezing with potential experimental applications.

Contribution

It introduces a new theoretical framework for quadratic coupling in optomechanics, enabling two-phonon cooling and mechanical squeezing analysis.

Findings

Steady-state phonon distribution is non-thermal (Gaussian).

Mean phonon number remains finite even under strong cooling.

Mechanical squeezing can be achieved via dual-beam driving.

Abstract

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.