### 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 language | English |
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Pages (from-to) | 4561-4571 |

Number of pages | 11 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 40 |

Issue number | 24 |

DOIs | |

Publication status | Published - 2007 Dec 28 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 40, no. 24, pp. 4561-4571. https://doi.org/10.1088/0953-4075/40/24/002

**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.

Research output: Contribution to journal › Article

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

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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 -