Bosonic superfluid on ellipsoidal surface

¹ School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China - Beijing 100872, China
² Beijing Academy of Quantum Information Sciences - Beijing 100193, China
³ MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Opto-electronic Devices, School of Physics, Xi'an Jiaotong University - Xi'an 710049, China
⁴ Hefei National Laboratory - Hefei, 230088, China
⁵ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences Beijing, 100190, China

Received: 23 February 2025
Accepted: 16 May 2025

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.