Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates

TL;DR

This paper introduces a simple analytical ansatz inspired by non-linear optics to approximate the ground-state density profile of trapped Bose-Einstein condensates, bridging noninteracting and strongly interacting regimes effectively.

Contribution

It applies a non-linear optics-inspired variational ansatz to solve the Gross-Pitaevskii equation across various interaction strengths, providing a unified analytical approach.

Findings

Accurately models density profiles in different interaction regimes

Matches well with analytical and numerical solutions

Works for both symmetric and anisotropic traps

Abstract

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.