# Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control

## TL;DR

This paper demonstrates an optimal feedback control method using Coulomb forces and machine learning to efficiently cool a levitated nanoparticle's motion, achieving rapid and low-temperature cooling suitable for advanced sensing applications.

## Contribution

It introduces a novel optimal control protocol with machine learning optimization for Coulomb-based feedback cooling of levitated nanoparticles, surpassing traditional optical methods.

## Key findings

- Achieved a minimum temperature of 5 mK at ultra-high vacuum conditions.
- Cooling transients are 10 to 600 times faster than cold damping.
- Method is adaptable for 3D cooling and high-repetition-rate experiments.

## Abstract

We use an optimal control protocol to cool one mode of the center of mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center of mass temperature of 5 mK at $3\times 10^{-7}$ mbar and transients 10 to 600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.