Metastable quantum phase transitions in a periodic one-dimensional Bose gas: Mean-field and Bogoliubov analyses

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schroumldinger equation, and linear perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.