  We study a Bose-Einstein condensate trapped in an asymmetric double well
potential. Solutions of the time-independent Gross-Pitaevskii equation reveal
intrinsic loops in the energy (or chemical potential) level behavior when the
shape of the potential is varied. We investigate the corresponding behavior of
the quantum (many-body) energy levels. Applying the two-mode approximation to
the bosonic field operators, we show that the quantum energy levels create an
anti-crossing net inside the region bounded by the loop of the mean field
solution.
