Noise and ergodic properties of Brownian motion in an optical tweezer: looking at the crossover between Wiener and Ornstein-Uhlenbeck processes

TL;DR

This study investigates the noise characteristics and ergodic behavior of Brownian motion in optical traps, bridging the gap between Wiener and Ornstein-Uhlenbeck processes through experimental, analytical, and simulation comparisons.

Contribution

It provides a comprehensive analysis of noise and ergodic properties across spectral regimes, introducing a tailored ergodicity test and deriving key observables for trapped diffusion.

Findings

Identification of spectral signatures distinguishing Wiener and Ornstein-Uhlenbeck regimes

Analytical derivation of noise and ergodic observables in low and high-frequency regimes

Experimental validation of theoretical predictions with good agreement

Abstract

We characterize throughout the spectral range of an optical trap the nature of the noise at play and the ergodic properties of the corresponding Brownian motion of an overdamped trapped single microsphere, comparing experimental, analytical and simulated data. We carefully analyze noise and ergodic properties $(i)$ using the Allan variance for characterizing the noise and $(ii)$ exploiting a test of ergodicity tailored for experiments done over finite times. We derive these two observables in the low-frequency Ornstein-Uhlenbeck trapped-diffusion regime and study analytically their evolution towards the high-frequency Wiener free-diffusion regime, in a very good agreement with simulated and experimental results. This leads to reveal noise and ergodic spectral signatures associated with the distinctive features of both regimes.