Rapidly rotating Bose-Einstein condensates in an anharmonic confinement

We examine a rapidly rotating Bose-Einstein condensate in an anharmonic confinement and find that many properties such as the critical rotating frequency and phase diagram are quite different from those in a harmonic trap. We investigate the phase transitions by means of average-vortex-approximation. We find that the vortex lattice consists of a vortex array with a hole in the center of the cloud as the rotating frequency $\Omega$ increases and the vortex becomes invisible when $\Omega$ reaches some value.