Brownian motion of a matter-wave bright soliton: realizing a quantum pollen grain

TL;DR

This paper models the Brownian motion of a matter-wave bright soliton in a thermal cloud using an open quantum systems approach, deriving a Langevin equation and confirming it with simulations, thus providing a new way to observe energy-damping interactions.

Contribution

It introduces a collective equation of motion for a matter-wave soliton interacting with a thermal cloud, highlighting energy transfer without particle exchange, and confirms the model with numerical simulations.

Findings

Derivation of a Langevin equation for soliton motion as an Ornstein-Uhlenbeck process.

Confirmation of the model through stochastic Gross-Pitaevskii equation simulations.

Proposal for experimental observation of energy-damping reservoir interactions.

Abstract

Taking an open quantum systems approach, we derive a collective equation of motion for the dynamics of a matter-wave bright soliton moving through a thermal cloud of a distinct atomic species. The reservoir interaction involves energy transfer without particle transfer between the soliton and thermal cloud, thus damping the soliton motion without altering its stability against collapse. We derive a Langevin equation for the soliton centre of mass velocity in the form of an Ornstein-Uhlenbeck process with analytical drift and diffusion coefficients. This collective motion is confirmed by simulations of the full stochastic projected Gross-Pitaevskii equation for the matter-wave field. The system offers a pathway for experimentally observing the elusive energy-damping reservoir interaction, and a clear realization of collective Brownian motion for a mesoscopic superfluid droplet.