  We analyze vortex nucleation in mezoscopic 2D Bose superfluid in a rotating
trap. We explicitly include a weakly anisotropic stirring potential, breaking
thus explicitly the axial symmetry. As the rotation frequency passes the
critical value $\Omega_c$ the system undergoes an extra symmetry
change/breaking. Well below $\Omega_c$ the ground state is properly described
by the mean field theory with an even condensate wave function. Well above
$\Omega_c$ the MF solution works also well, but the order parameter becomes
odd. This phenomenon involves therefore a discrete parity symmetry breaking. In
the critical region the MF solutions exhibit dynamical instability. The true
many body state is a strongly correlated entangled state involving two
macroscopically occupied modes (eigenstates of the single particle density
operator). We characterize this state in various aspects: i) the eligibility
for adiabatic evolution; ii) its analytical approximation given by the
maximally entangled combination of two single modes; and finally iii) its
appearance in particle detection measurements.
