Single-photon transport and mechanical NOON state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.