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

A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity Omega (c2) 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-->omega (perpendicular to) implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which Omega (c2) is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of Omega (c2) arises not only from decreasing b but also from increasing xi caused by the vanishing of the chemical potential as Omega-->Omega (c2).