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Optically levitated nanoparticles have recently emerged as versatileplatforms for investigating macroscopic quantum mechanics and enablingultrasensitive metrology. In this article we theoretically consider two dampingregimes of an optically levitated nanoparticle cooled by cavityless parametricfeedback. Our treatment is based on a generalized Fokker-Planck equationderived from the quantum master equation presented recently and shown to agreevery well with experiment [1]. For low damping, we find that the resultingWigner function yields the single-peaked oscillator position distribution andrecovers the appropriate energy distribution derived earlier using a classicaltheory and verified experimentally [2]. For high damping, in contrast, wepredict a double-peaked position distribution, which we trace to an underlyingbistability induced by feedback. Unlike in cavity-based optomechanics,stochastic processes play a major role in determining the bistable behavior. Tosupport our conclusions, we present analytical expressions as well as numericalsimulations using the truncated Wigner function approach. Our work opens up theprospect of developing bistability-based devices, characterization ofphase-space dynamics, and investigation of the quantum-classical transitionusing levitated nanoparticles.

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