Single-photon nonlinearities in two-mode optomechanics

TL;DR

This paper provides a theoretical analysis of two-mode optomechanical systems demonstrating nonclassical photon correlations and long-lived phonon states, advancing understanding of quantum effects in multimode optomechanics.

Contribution

It offers a detailed theoretical framework for multimode optomechanics, highlighting nonclassical correlations and phonon state preparation, which are novel insights into quantum regimes.

Findings

Nonclassical photon correlations occur when coupling exceeds cavity decay rate

Signatures of one- and two-photon resonances are identified

Long-lived correlations indicate heralded single phonon state preparation

Abstract

We present a detailed theoretical analysis of a weakly driven multimode optomechanical system, in which two optical modes are strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculate one- and two-time intensity correlations of the two optical fields and compare them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arise when the optomechanical coupling $g$ exceeds the cavity decay rate $\kappa$, and we discuss signatures of one- and two-photon resonances as well as quantum interference. We also find a long-lived correlation that decays slowly with the mechanical decay rate $\gamma$, reflecting the heralded preparation of a single phonon state after detection of a photon. Our results provide insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.