Hydrodynamic spectrum of a superfluid in an elongated trap

TL;DR

This paper investigates the hydrodynamic spectrum of a superfluid in a cylindrical trap, revealing a specific dispersion relation and its implications for the superfluid's critical velocity, which is reduced compared to free space.

Contribution

It provides a detailed analysis of the phonon dispersion relation in a trapped superfluid and quantifies how the critical velocity is affected by trapping parameters.

Findings

Dispersion relation scales as √q at large q

Critical velocity is reduced by a factor related to trap frequency and chemical potential

Hydrodynamic approximation breakdown sets the actual critical velocity

Abstract

--In this article we study the hydrodynamic spectrum of a superfluid confined in a cylindrical trap. We show that the dispersion relation $\omega$(q) of the phonon branch scales like $\sqrt$ q at large q, leading to a vanishingly small superfluid critical velocity. In practice the critical velocity is set by the breakdown of the hydrodynamic approximation. For a broad class of superfluids, this entails a reduction of the critical velocity by a factor ($\omega$ $\perp$ /\"i1/2c) 1/3 with respect to the free-space prediction (here $\omega$ $\perp$ is the trapping frequency and \"i1/2c the chemical potential of the cloud).