On Translational Superfluidity and the Landau Criterion for Trapped Bose gases in the Gross-Pitaevski Limit

TL;DR

This paper compares two criteria for superfluidity in trapped Bose gases, revealing that the Landau criterion may not apply in the Gross-Pitaevskii limit, affecting how superfluidity is identified.

Contribution

It demonstrates that the Landau criterion's applicability is limited for trapped Bose gases in the Gross-Pitaevskii limit, emphasizing the relevance of the two-fluid criterion for translational superfluidity.

Findings

Two-fluid criterion predicts translational superfluidity.

Landau criterion may not hold in the GP limit for trapped gases.

Large compressibility indicates the relevance of the two-fluid criterion.

Abstract

The two-fluid and Landau criteria for superfluidity are compared for trapped Bose gases. While the two-fluid criterion predicts translational superfluidity, it is suggested, on the basis of the homogeneous Gross-Pitaevski limit, that a necessary part of Landau's criterion, adequate for non-translationally invariant systems, d oes not hold for trapped Bose gases in the GP limit. As a consequence, if the compressibility is detected to be very large (infinite by experimental standards) the two-fluid criterion is seen to be the relevant one in case the system is a tranlational superfluid, while the Landau criterion is the relevant one if translational superfluidity is absent.