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In this paper a Gaussian impurity moving through an equilibrium Bose-Einsteincondensate at T = 0 is studied. The problem can be described by aGross-Pitaevskii equation, which is solved perturbatively. The analysis is donefor 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)]. TheBogoliubov equation solutions for the condensate perturbed by a finite impurityare calculated in the co-moving frame, which are formally equivalent up to adimension dependent form factor for general dimensions. From those solutionsthe total energy of the perturbed system is determined as a function of thewidth and the amplitude of the moving Gaussian impurity and its velocity.Finally we derive the drag force the Gaussian impurity approximatelyexperiences as it moves through the superfluid, which proofs the existence of asuperfluid phase for finite extensions of the impurities below the speed ofsound and that the force increases monotonically with velocity until itdecreases again.

Gaussian impurity moving through a Bose-Einstein superfluid