### Abstract

We derive a general and exact equation of motion for a quantized vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single-vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.

Original language | English |
---|---|

Article number | 023617 |

Number of pages | 12 |

Journal | Physical Review A |

Volume | 97 |

Issue number | 2 |

DOIs | |

Publication status | Published - 12 Feb 2018 |

### Cite this

*Physical Review A*,

*97*(2), [023617]. https://doi.org/10.1103/PhysRevA.97.023617

}

*Physical Review A*, vol. 97, no. 2, 023617. https://doi.org/10.1103/PhysRevA.97.023617

**Motion of vortices in inhomogeneous Bose-Einstein condensates.** / Groszek, Andrew J.; Paganin, David M.; Helmerson, Kristian; Simula, Tapio P.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Motion of vortices in inhomogeneous Bose-Einstein condensates

AU - Groszek, Andrew J.

AU - Paganin, David M.

AU - Helmerson, Kristian

AU - Simula, Tapio P.

PY - 2018/2/12

Y1 - 2018/2/12

N2 - We derive a general and exact equation of motion for a quantized vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single-vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.

AB - We derive a general and exact equation of motion for a quantized vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single-vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.

UR - http://www.scopus.com/inward/record.url?scp=85042074588&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.97.023617

DO - 10.1103/PhysRevA.97.023617

M3 - Article

VL - 97

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 023617

ER -