content_image/358530.jpg content_image/358535.jpg
<img src='content_image/358530.jpg'>

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] 

<img src='content_image/358535.jpg'>

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 

