Shell-shaped Bose—Einstein condensates in toroidal optical traps

Bose—Einstein condensates (BECs) confined in curved, two-dimensional geometries exhibit unique properties that are absent in their flat counterparts due to their periodic boundary conditions and nonzero local curvature. In this work, we consider a shell-shaped ⁸⁷Rb BEC confined to the surface of an anisotropic torus and discuss how this system could be realized in a microgravity environment with an optical trap. Using the Gross-Pitaevskii equation, we obtain the interaction energy of vortex pairs and study the dynamics a rotating BEC. Additionally, we introduce an optical lattice potential and show how the energy band structure varies by tuning the anisotropy and spatial curvature of the trap, which modify the vector potential felt by the atoms.