  We theoretically analyse the cooling dynamics of a high-Q mode of a
mechanical resonator, when the structure is also an optical cavity and is
coupled with a NV center. The NV center is driven by a laser and interacts with
the cavity photon field and with the strain field of the mechanical oscillator,
while radiation pressure couples mechanical resonator and cavity field.
Starting from the full master equation we derive the rate equation for the
mechanical resonator's motion, whose coefficients depend on the system
parameters and on the noise sources. We then determine the cooling regime, the
cooling rate, the asymptotic temperatures, and the spectrum of resonance
fluorescence for experimentally relevant parameter regimes. For these
parameters, we consider an electronic transition, whose linewidth allows one to
perform sideband cooling, and show that the addition of an optical cavity in
general does not improve the cooling efficiency. We further show that pure
dephasing of the NV center's electronic transitions can lead to an improvement
of the cooling efficiency.
