Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength

Abstract

Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

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Cited by in corpus (9)

• Low-dimensional quantum gases in curved geometries
• Supersolid phases of bosonic particles in a bubble trap
• Bose-Einstein condensate in an elliptical waveguide
• Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry
• Superfluid properties of bright solitons in a ring
• Expansion of a quantum gas in a shell trap
• Dispersion Managed Elliptical Atomtronics for Interferometry
• Geometric potential for a Bose-Einstein condensate on a curved surface
• Controlled acoustic-driven vortex transport in coupled superfluid rings