  Recently a novel phase transition has been observed \cite{jalin} in a
rotating Bose-Einstein condensate when the rotating frequency $\Omega$ reaches
the transverse trap frequency $\omega_{\bot}$ and eventually crosses it. We
study certain aspects of this experiment in terms of the condensation of
composite bosons and the corresponding vortex formation using a Chern-Simon
Gross-Pitaevskii theory. %
