Vortex-ring solutions of the Gross-Pitaevskii equation for an axisymmtrically trapped Bose-Einstein condensate

C. H. Hsueh, S. C. Gou, T. L. Horng, Y. M. Kao

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross-Pitaevskii (GP) equation for an axisymmetrically trapped Bose-Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wavefunction of the vortex ring is determined by solving the ground state of the effective GP equation numerically. Application of our method to the formation of a three-dimensional Skyrmion in a trapped two-component BEC is demonstrated.

Original languageEnglish
Pages (from-to)4561-4571
Number of pages11
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Volume40
Issue number24
DOIs
Publication statusPublished - 2007 Dec 28

Fingerprint

vortex rings
Bose-Einstein condensates
ground state
profiles
energy

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics

Cite this

@article{05130d8ac51f4499a45a4a8045ec498e,
title = "Vortex-ring solutions of the Gross-Pitaevskii equation for an axisymmtrically trapped Bose-Einstein condensate",
abstract = "We propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross-Pitaevskii (GP) equation for an axisymmetrically trapped Bose-Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wavefunction of the vortex ring is determined by solving the ground state of the effective GP equation numerically. Application of our method to the formation of a three-dimensional Skyrmion in a trapped two-component BEC is demonstrated.",
author = "Hsueh, {C. H.} and Gou, {S. C.} and Horng, {T. L.} and Kao, {Y. M.}",
year = "2007",
month = "12",
day = "28",
doi = "10.1088/0953-4075/40/24/002",
language = "English",
volume = "40",
pages = "4561--4571",
journal = "Journal of Physics B: Atomic, Molecular and Optical Physics",
issn = "0953-4075",
publisher = "IOP Publishing Ltd.",
number = "24",

}

Vortex-ring solutions of the Gross-Pitaevskii equation for an axisymmtrically trapped Bose-Einstein condensate. / Hsueh, C. H.; Gou, S. C.; Horng, T. L.; Kao, Y. M.

In: Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 40, No. 24, 28.12.2007, p. 4561-4571.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Vortex-ring solutions of the Gross-Pitaevskii equation for an axisymmtrically trapped Bose-Einstein condensate

AU - Hsueh, C. H.

AU - Gou, S. C.

AU - Horng, T. L.

AU - Kao, Y. M.

PY - 2007/12/28

Y1 - 2007/12/28

N2 - We propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross-Pitaevskii (GP) equation for an axisymmetrically trapped Bose-Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wavefunction of the vortex ring is determined by solving the ground state of the effective GP equation numerically. Application of our method to the formation of a three-dimensional Skyrmion in a trapped two-component BEC is demonstrated.

AB - We propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross-Pitaevskii (GP) equation for an axisymmetrically trapped Bose-Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wavefunction of the vortex ring is determined by solving the ground state of the effective GP equation numerically. Application of our method to the formation of a three-dimensional Skyrmion in a trapped two-component BEC is demonstrated.

UR - http://www.scopus.com/inward/record.url?scp=36348962375&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36348962375&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/40/24/002

DO - 10.1088/0953-4075/40/24/002

M3 - Article

AN - SCOPUS:36348962375

VL - 40

SP - 4561

EP - 4571

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 24

ER -