Overdamped dynamics of a Brownian particle levitated in a Paul trap

TL;DR

This paper investigates the overdamped motion of a Brownian particle in a Paul trap, providing analytical solutions, comparing with experiments, and demonstrating the spectral density's approximation to an Ornstein-Uhlenbeck process.

Contribution

It offers an exact analytical solution for the stochastic dynamics of a levitated particle in a Paul trap and validates the spectral density approximation through experiments.

Findings

Analytical expressions for standard deviation and thermalization times.

Spectral density approximates an Ornstein-Uhlenbeck process.

Calibration method for particle motion using derived spectral density.

Abstract

We study the dynamics of the center of mass of a Brownian particle levitated in a Paul trap. We focus on the overdamped regime in the context of levitodynamics, comparing theory with our numerical simulations and experimental data from a nanoparticle in a Paul trap. We provide an exact analytical solution to the stochastic equation of motion, expressions for the standard deviation of the motion, and thermalization times by using the WKB method under two different limits. Finally, we prove the power spectral density of the motion can be approximated by that of an Ornstein-Uhlenbeck process and use the found expression to calibrate the motion of a trapped particle.