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

Abstract

A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity ${\ensuremath{\Omega}}_{c2}$ occurs when the intervortex separation b becomes comparable with the vortex-core radius $\ensuremath{\xi}.$ For a radial harmonic trap, the loss of confinement as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which ${\ensuremath{\Omega}}_{c2}$ is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of ${\ensuremath{\Omega}}_{c2}$ arises not only from decreasing b but also from increasing $\ensuremath{\xi}$ caused by the vanishing of the chemical potential as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\Omega}}_{c2}.$