Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps

TL;DR

This paper investigates the conditions under which the ground state of an attractively-interacting Bose-Einstein condensate in anisotropic traps resembles a bright matter-wave soliton, using variational and numerical methods to assess soliton-like behavior.

Contribution

It provides a systematic analysis of the regimes where the condensate's ground state is well-approximated by a bright soliton, highlighting the limitations imposed by trap anisotropy.

Findings

Soliton-like ground states are limited to specific trap anisotropies.

Analytic variational solutions closely match numerical results in certain regimes.

Experimental realization of soliton-like states requires challenging trap configurations.

Abstract

We consider the ground state of an attractively-interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground state takes the form of a bright soliton solution of the nonlinear Schroedinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation we systematically and quantitatively assess how soliton-like this ground state is, over a wide range of trap and interaction strengths. Our analysis reveals that the regime in which the ground state is highly soliton-like is significantly restricted, and occurs only for experimentally challenging trap anisotropies. This result, and our broader identification of regimes in which the ground state is well-approximated by our simple analytic variational solution, are relevant to a range of potential experiments involving attractively-interacting Bose-Einstein condensates.