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

Abstract

We analyze vortex nucleation in mesoscopic two-dimensional 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 ${\ensuremath{\Omega}}_{c}$, the system undergoes an extra symmetry change or breaking. Well below ${\ensuremath{\Omega}}_{c}$, the ground state is properly described by the mean-field theory with an even condensate wave function. Well above ${\ensuremath{\Omega}}_{c}$, the mean-field solution works also well, but the order parameter becomes odd. This phenomenon involves therefore a discrete parity symmetry breaking. In the critical region, the mean-field 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.