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Symmetry breaking and singularity structure in Bose-Einstein condensates

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find t...

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Bibliographic Details
Main Authors: Commeford, K. A. (Author) , Carr, Lincoln D. (Author)
Format: Article (Journal)
Language:English
Published: 22 August 2012
In: Physical review. A, Atomic, molecular, and optical physics
Year: 2012, Volume: 86, Issue: 2, Pages: 1-12
ISSN:1094-1622
DOI:10.1103/PhysRevA.86.023627
Online Access:Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevA.86.023627
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevA.86.023627
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Author Notes:K.A. Commeford, M.A. Garcia-March, A. Ferrando and Lincoln D. Carr

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520 |a We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005. 
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