Bose-Einstein Condensates with Large Number of Vortices

We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a ''quantum Hall'' regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z . The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters