# Antibunching in an optomechanical oscillator

## TL;DR

This paper theoretically investigates phonon antibunching in an optomechanical oscillator with membrane-in-the-middle geometry, showing how strong cooperativity leads to single-phonon antibunching due to effective nonlinearities.

## Contribution

It introduces a theoretical model demonstrating phonon antibunching in an optomechanical system via effective cubic nonlinearity in the weak coupling regime.

## Key findings

- Antibunching appears at high optomechanical cooperativity.
- Chaotic phonon field occurs at low cooperativity.
- Effective cubic nonlinearity enables control of phonon correlations.

## Abstract

We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode cavity field in the regime in which the cavity dissipation is a dominant source of damping, and adiabatic elimination of the cavity field leads to an effective cubic nonlinearity for the mechanics. We show analytically in the weak coupling regime that the mechan- ics displays a chaotic phonon field for small optomechanical cooperativity, whereas an antibunched single-phonon field appears for large optomechanical cooperativity. This opens the door to control of the second-order correlation function of a mechanical oscillator in the weak coupling regime.