Vortex nucleation in mesoscopic Bose superfluid and breaking of the parity symmetry

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.