Quantum feedback cooling of a trapped nanoparticle by using a low-pass filter

TL;DR

This paper introduces a low-pass-filter feedback control method for cooling a trapped nanoparticle, demonstrating it can surpass traditional methods in reaching the quantum ground state by reducing phonon occupation.

Contribution

The paper proposes a novel LPF feedback control scheme that outperforms existing ground-state cooling techniques for levitated nanoparticles.

Findings

LPF control achieves lower phonon occupation than traditional methods.

At 90% detection efficiency, LPF reduces phonon number to about one third of cold damping.

LPF control has a decisive advantage in reaching the quantum ground state.

Abstract

We propose a low-pass-filter (LPF) feedback control for cooling a trapped particle with a low-pass filter, which utilizes a shift of the potential caused by the feedback operation. By incorporating this shift in the energy cost function, we show that the LPF control can achieve the minimum phonon occupation number that is lower than cold damping with a band-pass filter, that with delayed feedback, and linear--quadratic--Gaussian (LQG) control, the last two of which are the standard methods of ground-state cooling of a levitated nanoparticle. For the detection efficiency of $90\%$, the achievable phonon occupation number with the LPF control is about one third, two fifths and one half of that of cold damping with a band-pass filter, that with delayed feedback, and LQG control, respectively. Thus our method has a decisive advantage to reach the absolute ground state.