Geometric potential for a Bose-Einstein condensate on a curved surface

Abstract

We compute the ground state of a Bose-Einstein condensate confined on a curved surface and unravel the effects of curvatures. Starting with a general formulation for any smooth surface, we apply it to a prolate ellipsoid, which is inspired by recent bubble trap experiments. Using only elementary tools, we perform a perturbative approach to the Gross-Pitaevskii equation and a general Ansatz, followed by a dimensional reduction. We derive an effective two-dimensional equation that includes a curvature-dependent geometric potential. We compute the ground state using Thomas-Fermi approximation and, for an isotropic confinement, we find that the highest accumulation of atoms happens on the regions with the greatest difference between the principal curvatures. For a prolate ellipsoid, this accumulation happens on the equator, which is contrary to previous findings that describe accumulation on the poles of a bubble trap. Finally, we explain the reasons for this difference: the higher accumulation of atoms on the poles happens due to anisotropies in the confinement, while the higher accumulation on the equator happens exclusively due to the geometric properties of the surface.

Discussion section was added. 22 pages and 4 figures in the main text. 32 pages and 5 figures in total

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Ultracold atoms confined in rf-induced two-dimensional trapping potentials
• Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials
• Electronic materials with nanoscale curved geometries
• One-dimensional description of a Bose-Einstein condensate in a rotating closed-loop waveguide
• Ground state of weakly repulsive soft-core bosons on a sphere
• Stability of a Bose condensed mixture on a bubble trap
• Scattering theory and equation of state of a spherical two-dimensional Bose gas
• Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength
• Bose-Einstein condensate in an elliptical waveguide
• Quantum Vortices in Curved Geometries
• Bose-Einstein condensation on axially-symmetric surfaces