# Characterization of Non-linearities through Mechanical Squeezing in Levitated Optomechanics

## TL;DR

This paper presents a method to quantify non-linearities in optically levitated nanoparticles by phase space squeezing and comparison with simulations, specifically estimating the Duffing non-linearity in the trapping potential.

## Contribution

It introduces a novel technique combining phase space squeezing and numerical matching to measure non-linearities in levitated optomechanical systems.

## Key findings

- Successfully estimates Duffing non-linearity strength.
- Demonstrates phase space squeezing as a diagnostic tool.
- Provides a new approach for characterizing trapping potentials.

## Abstract

We demonstrate a technique to estimate the strength of non-linearities present in the trapping potential of an optically levitated nanoparticle. By applying a brief pulsed reduction in trapping laser power of the system such as to squeeze the phase space distribution and then matching the time evolution of the shape of the phase space distribution to that of numerical simulations, one can estimate the strength of the non-linearity present in the system. We apply this technique to estimate the strength of the Duffing non-linearity present in the optical trapping potential.