Analytical Investigation of Focusing Bose-Einstein condensates

TL;DR

This paper provides an analytical study of how Bose-Einstein condensates focus when propagating under different conditions, using a scaling solution approach to understand the dynamics influenced by interparticle interactions.

Contribution

It introduces an analytical method based on a scaling solution to examine focusing dynamics of Bose-Einstein condensates, incorporating interparticle interactions and comparing with numerical solutions.

Findings

Analytical expressions for focusing profiles and densities.

Influence of optical potential parameters on focusing quality.

Validation of analytical results with numerical simulations.

Abstract

The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use a scaling solution method comprising a time-dependent scaling function to analytically examine the dynamics of a falling Bose-Einstein condensate in different regimes of propagation including the expansion and compression zones. Our model is based on the Gross-Pitaevskii equation which involves the interparticle interactions between atoms, and consequently their influence on the focused structures. We investigate the focused profile characteristic factors such as the resolution and peak density for various cases of the focusing optical potential parameters as well as the factors associated with the moving cloud. Our results are compared with numerical solutions of the Gross-Pitaevskii equation.