Bose-Einstein Condensate in a Linear Trap With a Dimple Potential

TL;DR

This paper investigates Bose-Einstein condensation in a linear trap with a dimple potential modeled by a Dirac delta function, providing analytical and numerical insights into condensate properties and the effects of the dimple's depth.

Contribution

It introduces a simplified model using the Schrödinger equation to analyze noninteracting gases in a linear trap with a dimple potential, including analytical methods for key quantities.

Findings

Dimple potential depth significantly influences condensate formation.

Analytical expressions for density, chemical potential, and critical temperature are derived.

Comparison with harmonic trap models highlights unique features of linear traps.

Abstract

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac \del function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the \Sch is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D was investigated.