# Optimal Position Detection of a Dipolar Scatterer in a Focused Field

## TL;DR

This paper presents a theoretical analysis of detecting a dipolar scatterer's position in a focused optical field, proposing an optimal measurement scheme that achieves Heisenberg-limited precision and enables feedback cooling in levitated optomechanics.

## Contribution

It introduces a new optimal measurement approach for three-dimensional position detection of dipolar scatterers at the quantum limit.

## Key findings

- Achieves Heisenberg-limited position resolution in three dimensions.
- Demonstrates feedback cooling of a levitated particle below one phonon.
- Shows backscattering detection suffices for quantum-level control.

## Abstract

We theoretically analyze the problem of detecting the position of a classical dipolar scatterer in a strongly focused optical field. We suggest an optimal measurement scheme and show that it resolves the scatterer's position in three dimensions at the Heisenberg limit of the imprecision-backaction product. We apply our formalism to levitated-optomechanics experiments and show that backscattering detection provides sufficient information to feedback-cool the particle's motion along the optical axis to a phonon occupancy below unity under realistic experimental conditions.