Path integrals and nonlinear optical tweezers

TL;DR

This paper employs path integral methods to compute perturbative corrections in nonlinear optical tweezers, revealing frequency shifts due to nonlinearities and proposing an experimental approach to measure trap parameters.

Contribution

It introduces a path integral framework to analyze nonlinear optical tweezers and connects theoretical predictions with experimental parameter estimation.

Findings

Nonlinearities cause shifts in the characteristic frequency.

Theoretical results agree with numerical simulations.

Method enables experimental access to trap parameters.

Abstract

We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading order nonlinearities manifest as shifts in the characteristic frequency of the system. The results are compared to numerical simulations. The present calculations enable a direct experimental method to access the nonlinear optical trap parameters by analyzing position data, similarly to standard harmonic tweezers.