Parametric Feedback Cooling of Rigid Body Nanodumbbells in Levitated Optomechanics

TL;DR

This paper presents a theoretical study on parametric feedback cooling of a levitated nanodumbbell, highlighting how asymmetry in the potential enables full cooling of rotational modes, advancing toward the librational quantum regime.

Contribution

It introduces a simplified model considering nanoparticle spin and demonstrates how asymmetry in the potential enables complete cooling of all rotational degrees of freedom.

Findings

Standard feedback cooling extracts energy from two rotational modes.

Asymmetry in the potential allows full librational cooling.

Cooling rate depends non-linearly on potential asymmetry.

Abstract

We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered non-negligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession about the laser polarization axis together with spin about the nanoparticle's symmetry axis. Cooling the remaining mode requires an asymmetry in the two librational frequencies associated with motion about the polarization axis as well as information about the two frequencies of rotation about the polarization axis. Introducing an asymmetric potential allows full cooling of the librational coordinates if the frequencies of both are used in the feedback modulation and is an avenue for entering the librational quantum regime. The asymmetry in the potential needs to be large enough for practical cooling times as the cooling rate of the system depends non-linearly on the degree of asymmetry, a condition that is easily achieved experimentally.