We consider a single-mode optical cavity of length L , frequency ω$_{c}$ and linewidth κ , with a moving end mirror that is modeled as a simple mechanical resonator with mass m and resonant frequency ω$_{m}$ . We also assume operation in the resolved-sideband regime, i.e. κ < ω$_{m}$ . The cavity is strongly driven with a coherent pump field at frequency ω$_{L}$ . We describe the interaction through a linearized treatment that is expanded around the steady state field amplitude in the cavity, which would arise in the absence of the opto-mechanical interaction. In addition to the coherent driving field, the cavity is also driven by a single- photon source. This is intended to be a sequence of pulses with one and only one photon per pulse, however it will suffice to consider only a single pulse for the purposes of the calculation presented here. To model the single-photon source we include a source cavity of frequency ω$_{s}$ and of decay rate γ , which at t = 0 is prepared in a single photon state (Figure 1). The coupling between the source cavity and the opto-mechanical cavity is irreversible and can be described using the cascaded systems approach [13, 14]. In this way we obtain a source that produces a single-photon pulse with a Lorentzian line shape. In the following, the single-photon source cavity is on resonance with the opto-mechanical cavity. The additional coherent laser driving field of frequency ω$_{L}$ enhances the opto-mechanical radiation pressure coupling. This field is spectrally detuned from the cavity resonance by multiples of the mechanical resonance frequency so that motional side bands can be addressed. Our objective is to demonstrate coherent exchange of the added single-photon optical excitation with the vibrational exci- tation of the mechanical mirror. To this end we compute the dynamics of the mean added photon number in the cavity, n$_{a}$ , which then determines the single-photon detection rate at detector A as κn$_{a}$ where the cavity damping rate is κ . We will find that for strong coupling this detection probability oscillates due to the coherent exchange of the single photon with the mechanical phonon number. The interaction between the cavity field of the source and the mechanical motion of the end mirror is via the standard radiation pressure coupling[15, 16] with the coupling rate where m is the effective mass of the moving mirror. For current opto-mechanical systems 3 H$_{rp}$ = ℏ Ga $^{†}$a ( b + b $^{†}$) (1) G = ω$_{c}$ L √ ℏ mω$_{m}$ (2)