Superfluidity in Dilute Trapped Bose Gases

TL;DR

This paper rigorously proves that dilute trapped Bose gases with repulsive interactions exhibit complete superfluidity in the dilute limit, confirming theoretical predictions with a mathematically rigorous approach in a realistic continuum model.

Contribution

It provides the first rigorous verification of superfluidity in an experimentally realistic continuum model of dilute trapped Bose gases.

Findings

Gas with repulsive interactions is 100% superfluid in the dilute limit

Superfluidity is verified through response to imposed velocity fields

Gross-Pitaevskii equation accurately describes the system in this limit

Abstract

A commonly used theoretical definition of superfluidity in the ground state of a Bose gas is based on the response of the system to an imposed velocity field or, equivalently, to twisted boundary conditions in a box. We are able to carry out this program in the case of a dilute interacting Bose gas in a trap. We prove that a gas with repulsive interactions is 100% superfluid in the dilute limit in which the Gross-Pitaevskii equation is exact. This is the first example in an experimentally realistic continuum model in which superfluidity is rigorously verified.