Single-photon nonlinearities in two-mode optomechanics

TLDR

The study theoretically analyzes a weakly driven multimode optomechanical system where two optical modes couple strongly to a single mechanical mode through three‑wave mixing. The authors model this system and compute one‑ and two‑time intensity correlations of the coupled optical fields, benchmarking them against atom‑cavity analogues. Nonclassical photon correlations arise when the optomechanical coupling exceeds the cavity decay rate, revealing one‑ and two‑photon resonances, quantum interference, and a long‑lived correlation that decays with the mechanical rate, indicating heralded single‑phonon preparation and offering insights for quantum information processing with photons and phonons.

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 $\ensuremath{\kappa}$, 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 $\ensuremath{\gamma}$, 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.