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Vortex Rings in Bose-Einstein Condensates Carretero, Ricardo


We review recent results for the emergence, existence, dynamics and interactions of vortex rings in Bose-Einstein condensates (BECs) modelled by the Gross-Pitaevskii equation (GPE). We focus our attention on the two opposite regimes of low and high atomic density limits in the BEC as well as in the intermediate transition between these two limits. In the low density limit, corresponding to the linear limit, we study the emergence of single and multiple vortex rings emanating from planar 3D dark solitons through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach, and find good qualitative and quantitative agreement with our Bogoliubov-de Gennes (BdG) numerical analysis. Under appropriate conditions for the trapping strengths, we find that vortex rings might be stabilized for large enough atomic densities (large chemical potentials). On the other hand, in the large density limit, the vortex rings acquire stability and are effec- tively robust coherent structures. We study different single and multi-vortex-ring configurations together with their (normal) modes of vibration. Exotic structures such as Hopfions, the one- component counterpart to Skyrmions, are also constructed and tested for stability. Finally, we discuss some interactions dynamics between vortex rings such as periodic leapfrogging of co-axial vortex rings and the scattering behavior for co-planar collisions between vortex rings. Work in collaboration with: P.G. Kevrekidis, D.J. Frantzeskakis, Wenlong Wang, R.M. Caplan, J.D. Talley, R.N. Bisset, C. Ticknor, and L.A. Collins.

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