Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

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A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity Omegac₂ occurs when the intervortex separation b becomes comparable with the vortex core radius xi. For a radial harmonic trap, the loss of confinement as Omega approaches omegaₚerp implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which Omegac₂ is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of Omegac₂ arises not only from decreasing b but also from increasing xi caused by the vanishing of the chemical potential as Omega approaches Omegac₂.