# Optimal control for feedback cooling in cavityless levitated optomechanics

## TL;DR

This paper applies optimal control theory to enhance feedback cooling in cavityless levitated optomechanics, demonstrating improved cooling rates and lower temperatures through a novel tracking scheme for feedback implementation.

## Contribution

It introduces an optimal feedback strategy for cavityless levitated optomechanics and a tracking scheme to improve cooling efficiency over traditional methods.

## Key findings

- Optimal feedback achieves faster cooling rates.
- Tracking scheme enables higher feedback strength.
- Lower center-of-mass temperatures are attainable.

## Abstract

We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a tracking scheme that takes into account the modulation of the laser intensity. We show that such a tracking implementation allows us to increase the feedback strength, leading to faster cooling rates and lower center-of-mass temperatures.