Coexistence of Vortex Liquid and Solid in Rotating Bose-Einstein Condensate

We perform computer simulations for the Gross-Pilaevskii equation with a tiny damping in order to study the condensate wave-function in 3-D rotating Bose-Einstein condensate under the trapping potential. We find that the wave-function is divided into two kinds of phases in terms of its coherent feature. The first one is a coherent phase which is characterized by the static vortex lattice located close to the center of the trapping potential, and the second one is an incoherent one which lies outside the first coherent phase and shows vortex liquid like behaviors. The boundary between the two phases is quite sharp like the phase interface as seen in the first-order phase transition. This result suggests that the melting seen in type II superconductors spatially occurs in the rotating Bose-Einstein condensate since the wave-function amplitude decreases with departing from the center of the trap and its coherent feature is overcome by intrinsic fluctuations at a certain distance.