0 2 4 6 8 10 12 14 16 18 20 0.45 0.5 0.55 0.6 0.65 0.7 0.75 g =2.0 t n$_{a}$ FIG. 4: The mean photon number in the opto-mechanical cavity versus time: ¯ n = 0 , γ = 0 . 9 , κ = 1 . 0 , µ = 0 . 001 , ω$_{m}$ = 4 . 4 , Δ = 1 . 02 ω$_{m}$, ω$_{m}$ = 4 . 4 with g = 2 . 0. 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 α 2 = 5 α $^{2}$ = - 5 n=5 t n$_{a}$ FIG. 5: The mean photon number in the opto-mechanical cavity versus time, contrasting the case of an initial Fock state source and an initial coherent state source. In all cases g = 1 . 5. The mechanical resonator is at zero temperature, ¯ n = 0, and the opto-mechanical cavity starts with no photons. The source cavity is prepared in a Fock state n = 5 (solid line) or a coherent state with amplitude √$_{5 ( dashed-dot) and}$ √$_{5}$$_{i}$ (dashed) single photon further helps to reduce noise in the experiment by a gated detection scheme. 11