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

Billam, T.P.; Wrathmall, S.A.; Gardiner, S.A.

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 Schrödinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation, we systematically and quantitatively assess how solitonlike 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 solitonlike 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.

Citation

Billam, T., Wrathmall, S., & Gardiner, S. (2012). Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps. Physical Review A, 85(1), Article 013627. https://doi.org/10.1103/physreva.85.013627

• Journal Article Type: Article
• Publication Date: Jan 19, 2012
• Deposit Date: Jan 26, 2012
• Publicly Available Date: Feb 12, 2014
• Journal: Physical Review A
• Print ISSN: 1050-2947
• Electronic ISSN: 1094-1622
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Issue: 1
• Article Number: 013627
• DOI: https://doi.org/10.1103/physreva.85.013627