c |1> a b coherent source single photon source A B FIG. 1: Scheme of the setup. A single-sided opto-mechanical cavity of frequency ω$_{c}$ (right; depicted as Fabry-Perot cavity with a moving end mirror) is driven by both a single-photon pulse and by a continuous-wave (CW) coherent pump source. The single photons are emitted from a cavity (left) at resonance with the opto-mechanical cavity, while the CW pump source is detuned from ω$_{c}$ . The pump beam produces a strong coherent field inside the cavity that enhances the coupling between the added single photons and the mechanical resonator analogous to optical three-wave mixing. An optical circulator (A) allows one to separate the photons emitted from the steady state coherent field inside the cavity from the added photons produced by the opto-mechanical interaction. The circulator may be realized by a coherent state displacer or by using an additional optical cavity as spectral separator, in which the driving field is transmitted while the added single photons are reflected. The latter are then detected on a photodetector (B). which are then detected on a photodetector (B) G is small compared to the cavity linewidth κ . However, a larger effective interaction is obtained by driving the cavity with a strong coherent laser field. In this case the amplitudes of both the cavity field and the mechanical motion will be displaced by their steady state amplitudes α$_{0}$ and β$_{0}$ , respectively. One can then linearize the radiation pressure force in the shifted reference frame to get [12] where g = Gα$_{0}$ (we have fixed the phase for the coherent drive to make this a real variable) is the effective coupling strength, Δ = ω$_{c}$ − ω$_{L}$ + 2 g is the effective cavity detuning, and a, a † and b, b † are the annihilation and creation operators for the displaced cavity field and for the motion of the mirror mechanical resonator, respectively. In the absence of damping the Heisenberg equations of motion are linear and may be solved by the method of normal 4 H = ℏ Δ a $^{†}$a + ℏ ω$_{m}$b $^{†}$b + ℏ g ( a + a $^{†}$)( b + b $^{†}$) (3)