Gaussian impurity moving through a Bose-Einstein superfluid

TL;DR

This paper investigates the behavior of a Gaussian impurity moving through a Bose-Einstein condensate at zero temperature, analyzing the system's energy, perturbations, and drag force across different dimensions to understand superfluid properties.

Contribution

It generalizes previous work by solving the Gross-Pitaevskii equation perturbatively for 2D and 3D systems, deriving the impurity's energy and drag force in a superfluid context.

Findings

Superfluid phase persists below the speed of sound for finite impurity sizes.

Drag force increases monotonically with velocity up to a point.

Analytical solutions for perturbations in different dimensions are provided.

Abstract

In this paper a Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions and generalises the work by [G.E. Astrakharchik and L.P. Pitaevskii, Phys. Rev. A 70, 013608 (2004)]. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame, which are formally equivalent up to a dimension dependent form factor for general dimensions. From those solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. Finally we derive the drag force the Gaussian impurity approximately experiences as it moves through the superfluid, which proofs the existence of a superfluid phase for finite extensions of the impurities below the speed of sound and that the force increases monotonically with velocity until it decreases again.