  We study the signatures of rotational and phase symmetry breaking in small
rotating clouds of trapped ultracold Bose atoms by looking at rigorously
defined condensate wave function. Rotational symmetry breaking occurs in narrow
frequency windows, where the ground state of the system has degenerated with
respect to the total angular momentum, and it leads to a complex wave function
that exhibits vortices clearly seen as holes in the density, as well as
characteristic vorticity. Phase symmetry (or gauge symmetry) breaking, on the
other hand, is clearly manifested in the interference of two independent
rotating clouds.
