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

TL;DR

This paper presents quantum calculations for feedback cooling of a laser-trapped nanoparticle in a shot-noise-dominant regime, comparing parametric and force feedback schemes and developing semi-classical models.

Contribution

It introduces a semi-classical model that accurately reproduces quantum feedback cooling results and analyzes the influence of measurement efficiency and shot noise on cooling limits.

Findings

Force feedback achieves lower cooling limits than parametric feedback at the same measurement efficiency.

The semi-classical equations can be rescaled to match quantum results, simplifying analysis.

Cooling dynamics depend primarily on feedback strength, measurement efficiency, and occupation number change per oscillation.

Abstract

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.