One dimensional Bose-Einstein condensate under the effect of the extended uncertainty principle

TL;DR

This paper investigates how the extended uncertainty principle (EUP) influences a one-dimensional Bose-Einstein condensate, analyzing stability and density using analytical, variational, and numerical methods under different potentials.

Contribution

It provides the first analytical and numerical analysis of EUP effects on 1D BECs, including stability and density modifications under various potentials.

Findings

EUP affects free dark soliton solutions within specific deformation ranges.

EUP is applicable to BECs in harmonic potentials for certain parameters.

EUP does not influence free bright soliton solutions.

Abstract

In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose-Einstein condensate (BEC) described by the deformed one-dimensional Gross-Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter $\alpha$, while it is not valid for the free bright soliton solution.