Feedback-induced Bistability of an Optically Levitated Nanoparticle: A Fokker-Planck Treatment

TL;DR

This paper theoretically investigates feedback-induced bistability in optically levitated nanoparticles, revealing how different damping regimes affect their phase-space dynamics and demonstrating the role of stochastic processes in feedback-induced bistability.

Contribution

It introduces a generalized Fokker-Planck approach to analyze feedback-induced bistability in levitated nanoparticles across damping regimes, highlighting the role of stochastic processes.

Findings

Low damping yields single-peaked position distribution consistent with classical theory.

High damping induces a double-peaked distribution due to feedback-induced bistability.

Analytical and numerical methods confirm the bistability and phase-space dynamics.

Abstract

Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [2]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles.