Vortices in a rotating Bose-Einstein condensate under extreme elongation in a harmonic plus quartic trap

The behaviors of a rapid rotating Bose-Einstein condensate under extreme elongation in a 2D anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $\mathrm{\Omega }\ge {\omega }_{\perp }$ (${\omega }_{\perp }$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive s-wave interaction ($g$). When $g$ is present, the interplay between $g$ and the quartic trap potential can lead to rich vortex lattice transition states as a function of $\mathrm{\Omega }$, to which vortex lattices vanish eventually at some higher $\mathrm{\Omega }$.