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arXiv:1404.4571 · Physica A Statistical Mechanics and its Applications

Vortices in rotating Bose–Einstein condensates confined in homogeneous traps

Tanja Rindler-Daller

Published Nov 26, 2007• 9 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2007.11.017

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In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.
Abstract The ground-state phases of rotating spin-1 Bose-Einstein condensates in three different box traps are studied numerically. In circular or square box trap, influenced by the combined effects of spin-exchange interaction and rotation, traditional skyrmion vortex for a rotating spin-1 BEC in harmonic trap are replaced by the homogeneous coreless vortices layered with fourfold rotational symmetry, which are usually generated from the trap boundary every four. In a triangular box trap, one skyrmion vortex structure is firstly found in the trap center, while other vortices are all generated from the boundary and arrange parallel to the trap edge in the form of vortex chains .
We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.