Single-photon nonlinearities in two-mode optomechanics
  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. 
P. K\'om\'ar, S. D. Bennett, K. Stannigel, S. J. M. Habraken, P. Rabl,   P. Zoller, and M. D. Lukin
quant-ph cond-mat.mes-hall