Thermally induced passage and current of particles in a highly unstable optical potential

TL;DR

This paper investigates the stochastic dynamics of particles in highly unstable nonlinear optical potentials, revealing temperature effects on first-passage times, proposing measurable indicators of nonlinearity, and analyzing steady-state distributions with potential experimental applications.

Contribution

It introduces a novel passage-time fraction as a non-invasive measure of nonlinearity and explores the temperature independence of the signal-to-noise ratio upper bound in unstable potentials.

Findings

Temperature shortens mean first-passage times.

Passage-time fraction is a parameter-independent witness of nonlinearity.

Steady-state probability distribution shifts against current direction with increasing temperature.

Abstract

We discuss the statistics of first-passage times of a Brownian particle moving in a highly unstable nonlinear potential proportional to an odd power of position. We observe temperature-induced shortening of the mean first-passage time and its dependence on the power of nonlinearity. We propose a passage-time fraction as both a simple and experimentally detectable witness of the nonlinearity. It is advantageously independent of all other parameters of the experiment and observable for a small number of trajectories. To better characterize the stochastic passage in the unstable potential, we introduce an analogy of the signal-to-noise ratio for the statistical distribution of the first-passage times. Interestingly, the upper bound for the signal-to-noise ratio is temperature independent in the unstable potential. Finally, we describe the nonequilibrium steady state of the particle cyclically passing through unstable odd nonlinearity. The maximum of the steady-state probability distribution shifts against the directions of the current and this counterintuitive effect increases with temperature. All these thermally induced effects are very promising targets for experimental tests of highly nonlinear stochastic dynamics of particles placed into optical potential landscapes of shaped optical tweezers.