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

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