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Single-photon Nonlinearities in Two-mode Optomechanics
We presented a detailed theoretical analysis of a weakly driven, multimode optomechanical system, in which two optical modes were strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculated one- and two-time intensity correlations of the two optical fields and compared them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arose when the optomechanical coupling g exceeded the cavity decay rate κ, and we discussed signatures of one- and two-photon resonances as well as quantum interference. We also found a long-lived correlation that decayed slowly with the mechanical decay rate γ, which reflected the heralded preparation of a single-phonon state after detection of a photon. Our results provided insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.