Dynamics of a pseudo-2D Bose–Einstein condensate in an optical toroidal shell trap

Two dimensional quantum gases in curved geometries are of great interest and may be realizated using Bose–Einstein condensates (BECs) in microgravity. Here we investigate the dynamics of a pseudo-2D BEC confined to the surface of a torus. In our simulations, we consider ⁸⁷Rb atoms held in an optical dipole trap formed by Laguerre-Gaussian beams and an RF or MW field. The usual second-order contribution of the fields to the effective Hamiltonian is carefully canceled, which leads the third-order contribution to dominate and allows us to realize a potential in the shape of a toroidal shell. Using the Gross–Pitaevskii equation, we study how the local curvature of the trap, periodic boundary conditions, and nontrivial topology affect the evolution of vortices in the BEC. Finally, we discuss how this technique could also be used to realize a BEC confined to the surface of a trefoil knot.