Abstract
We investigate an optomechanical system which realizes the Jaynes-Cummings (JC) model known in cavity QED. Such a system consists of a single photon and an optomechanical cavity with two optical cavity modes and one mechanical mode. Under the resonance condition when the mechanical frequency is close to the frequency difference between the optical modes, the photon and phonons can be strongly coupled. We present an analytic solution of single-photon scattering and show that the spectrum of the scattered photon exhibits excitation-number-dependent Rabi splitting of the JC model. In addition, we examine the response of the mechanical mode to a sequence of single photons, with one photon in the cavity at a time. We show that sequential photon scattering can efficiently excite the mechanical mode and generate sub-Poisson phonon statistics.
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