Vortex Rings in Fast Rotating Bose-Einstein Condensates
arXiv:1009.1982 · doi:10.1007/s00205-011-0447-6
Abstract
When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex phase appears, that is the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii energy on the unit disc. In particular we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold there are vortices in the condensate. We prove that they gather along a particular circle on which they are evenly distributed. This is done by providing new upper and lower bounds to the GP energy.
to appear in Archive of Rational Mechanics and Analysis
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Cited by in corpus (11)
- Mathematical theory and numerical methods for Bose-Einstein condensation
- The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
- Rotating superfluids in anharmonic traps: From vortex lattices to giant vortices
- Critical Rotational Speeds for Superfluids in Homogeneous Traps
- On the Ginzburg--Landau Functional in the Surface Superconductivity Regime
- Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions
- Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
- Giant vortex phase transition in rapidly rotating trapped Bose-Einstein condensates
- Giant vortex in a fast rotating holographic superfluid
- Vortex Phases of Rotating Superfluids
- On the Third Critical Speed for Rotating Bose-Einstein Condensates