Critical numbers of attractive Bose-condensed atoms in asymmetric traps

TL;DR

This paper investigates the stability limits of Bose-Einstein condensates with attractive interactions in various asymmetric three-dimensional harmonic traps using numerical solutions of the Gross-Pitaevskii equation.

Contribution

It provides a comprehensive numerical analysis of the critical atom number for stability in asymmetric traps, including reductions to lower dimensions and deformed geometries.

Findings

Critical atom numbers depend on trap asymmetry and dimensionality.

Stability limits are characterized for cylindrical and deformed traps.

Numerical solutions offer precise stability thresholds for experimental setups.

Abstract

The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the novel possibility to probe the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.