Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed Ω to exceed the radial harmonic frequency ω_⊥. In the regime Ωω_⊥, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity Ωₕ, a central hole appears in the condensate. Numerical studies confirm the predicted value of Ωₕ, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).