  In this paper, results of quantum calculations are presented for feedback
cooling of an optically trapped nanoparticle in the laser-shot-noise-dominant
regime. We numerically investigate the system using both parametric and force
feedback cooling schemes. For the same measurement efficiency, the cooling
limit from the force feedback is lower than that from the parametric feedback.
We also develop a set of semi-classical equations for feedback cooling that
accurately match the quantum results. It is demonstrated, by rescaling the
semi-classical equations, that the cooling dynamics is uniquely determined by
the parameter set: the feedback strength, the measurement efficiency and the
change of occupation number over one oscillation period due to the shot noise.
The minimum occupation number is determined by the measurement efficiency and
the change of occupation number over one period.

Quantum Physics