Optimal trap shape for a Bose gas with attractive interactions

TL;DR

This paper derives simple analytical formulas to determine the optimal trap shape that maximizes the number of condensed atoms in a Bose gas with attractive interactions at zero temperature.

Contribution

It provides the first straightforward analytical expressions for the optimal trap shape in Bose-Einstein condensates with attractive interactions.

Findings

Analytical formulas for optimal trap shapes are derived.

Maximal condensate atom number depends on trap geometry.

Results facilitate experimental design for Bose gases with attractive interactions.

Abstract

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.