Δ = 1 . 02 ω$_{m}$ and we choose the source cavity to be nearly mode matched to the opto- mechanical cavity γ = 0 . 9. Before the single photon source is turned on, we assume that the opto-mechanical system has reached a steady state, which then become the initial conditions when the source is turned on; i.e. we need to find the steady state solutions of Eq(9) with γ = 0. The steady state solution for the opto-mechanical covariance matrix is given by KC$_{∞}$ + C T $_{∞}$K T = 0. A great deal of experimental effort is going into schemes to enable the mechanical motion of the mirror to be cooled to its ground state, and we first consider this case. Practically, this will occur due to optical cooling via the red-detuned pump beam if we assume that the rate of heating due to the interaction of the mechanical resonator with its environment is small . We therefore set ¯ n = 0 and µ = 0 . 001 in the equations of motion. Furthermore, we choose the single-photon linewidth γ = 0 . 9. Figure 2 shows the time-dependence of the mean cavity photon number for various cou- pling strengths g < κ, Δ. For g << Δ we simply recover the statistics of the cavity decay as no significant opto-mechanical coupling takes place. Increasing g such that κ < g < Δ we observe revivals in the detection probability, which arise because the single-photon excitation is exchanged coherently between the opto-mechanical cavity and the mechanical resonator. This can be seen directly in Figure 3 where we plot the simultaneous evolution of both the intra cavity mean photon number and the mean phonon number in the mechanical resonator for the case of g = 1 . 5. It might be noted that the photon number and phonon number oscillations are not π out of phase in the first phase of the evolution as one might expect if the cavity was started with exactly one photon at t = 0. For short times, this is due to the dynamics of the single photon source excitation of the cavity, on top of the photon-phonon interactions: the dynamics in Eq.8 depends explicitly on the correlations between the source and the optomechanical cavity, 〈 ac † + a $^{†}$c 〉 . At later times, the mean cavity photon num- ber does not peak at the same time as the minimum in mean mechanical phonon number because the decay rate of the cavity is very much greater than the mechanical decay rate. For g > κ, Δ, see Figure 4, the oscillations persist but additional frequencies appear due to normal mode splitting and there is an excitation of the dressed opto-mechanical system, analogous to heating. As discussed above we expect the dynamics for an initial Fock state in the source cavity to differ from that for an initial coherent state with the same mean photon number. This 8