Quantum calculation of feedback cooling a laser levitated nanoparticle in the shot-noise-dominant regime

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.