Bose-Einstein condensate in a harmonic trap decorated with Dirac delta functions

TL;DR

This paper investigates Bose-Einstein condensation in a harmonic trap with a Dirac delta function modeled dimple potential, providing explicit analytical and numerical insights into the effects on condensate properties.

Contribution

It introduces a simplified model using a Dirac delta function to analyze Bose-Einstein condensation in a harmonic trap, enabling explicit calculations of key properties.

Findings

The relative depth of the dimple potential influences condensate formation.

Enhanced condensate formation occurs at higher temperatures with a deep dimple.

Analytical solutions are obtained for noninteracting gases in the model.

Abstract

We study Bose-Einstein condensation in a harmonic trap with a dimple potential. We specifically consider the case of a tight and deep dimple potential which is modelled by a Dirac delta function. This allows for simpler, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrodinger equation is used instead of the Gross-Pitaevski equation. Calculating the atomic density, chemical potential, critical temperature and condensate fraction, the role of the relative depth of the dimple potential with respect to the harmonic trap in large condensate formation at enhanced temperatures is clearly revealed.