Bose-Einstein condensates and the thin-shell limit in anisotropic bubble traps

TL;DR

This paper investigates the physics of anisotropic bubble traps in Bose-Einstein condensates, focusing on the thin-shell limit and deriving an effective 2D Hamiltonian relevant to current experiments.

Contribution

It establishes how physical parameters influence the manifold geometry in anisotropic bubble traps and derives an effective 2D Hamiltonian in the thin-shell limit.

Findings

Conditions for non-collapsing thin-shell limit identified

Effective 2D Hamiltonian derived for bubble trap systems

Perturbative solutions provided for specific cases

Abstract

Within the many different models that appeared with the use of cold atoms to design BECs the bubble trap shaped potential has been of great interest. For the anisotropic bubble trap physics in the thin-shell limit the relationship between the physical parameters and the resulting manifold geometry is yet to be fully understood. In this paper, we work towards this goal showing how the parameters of the system must be manipulated in order to allow for a non-collapsing thin-shell limit. In such a limit, a dimensional compactification takes place thus leading to an effective 2D Hamiltonian which relates to up-to-date bubble trap experiments. At last, our Hamiltonian is pertubatively solved for some particular cases as applications of our theory.