Bosonic superfluid on ellipsoidal surface

Abstract We consider a bosonic gas confined on an ellipsoid surface with different aspect ratio and study the single-particle and many-body properties in a unified theoretical framework. By tuning the ellipsoid from a prolate shape to a sphere, and then to an oblate shape, the change of geometric shape affects the metric, inner product and orthogonal relation of the surface. As a result, the single-particle spectrum of an ellipsoid deviates from that of a flat space or a perfect sphere. Specifically, some single-particle degeneracy is partially lifted due to the corrections related to the magnetic quantum number, and the spectrum exhibits level crossing when changing from a prolate ellipsoid to an oblate ellipsoid. We also investigate the superfluid density of a bosonic gas with contact interaction, and find that the superfluid fraction on prolate ellipsoids is higher than that on oblate ones.