# Spectral analysis and parameter estimation in levitated optomechanics

## TL;DR

This paper develops a spectral analysis framework for parameter estimation in levitated optomechanics, enhancing the precision of force measurements and thermodynamic quantity inference using maximum likelihood methods.

## Contribution

It introduces a theoretical spectrum model and an optimized apparatus for sensitive measurements, accounting for sinusoidal interferometric signals and enabling improved parameter inference.

## Key findings

- Accurate parameter estimation from spectra using maximum likelihood.
- Enhanced sensitivity along one motional degree of freedom.
- Successful extraction of thermodynamic quantities in complex regimes.

## Abstract

Optical levitation of nanoscale particles has emerged as a platform for precision measurement. Extremely low damping, together with optical interferometric position detection, makes possible exquisite force measurement and promises low-energy tests of fundamental physics. Essential to such measurement is an understanding of the confidence with which parameters can be inferred from spectra estimated from the indirect measurement provided by interferometry. We present an apparatus optimized for sensitivity along one motional degree of freedom, a theoretical model of the spectrum, and maximum likelihood estimation. The treatment accounts for the sinusoidal dependence of interferometric signal on particle position, and we use the technique to extract thermodynamic quantities in a regime where simpler treatments are confounded.