Vortex nucleation as a case study of symmetry breaking in quantum systems

Abstract

Mean-field methods are a very powerful tool for investigating weakly interacting many-body systems in many branches of physics. In particular, they describe with excellent accuracy trapped Bose–Einstein condensates. A generic, but difficult question concerns the relation between the symmetry properties of the true many-body state and its mean-field approximation. Here, we address this question by considering, theoretically, vortex nucleation in a rotating Bose–Einstein condensate. A slow sweep of the rotation frequency changes the state of the system from being at rest to the one containing one vortex. Within the mean-field framework, the jump in symmetry occurs through a turbulent phase around a certain critical frequency. The exact many-body ground state at the critical frequency exhibits strong correlations and entanglement. We believe that this constitutes a paradigm example of symmetry breaking in—or change of the order parameter of—quantum many-body systems in the course of adiabatic evolution. A potentially general mechanism for symmetry breaking in mesoscopic quantum systems is revealed in a theoretical study, which shows how, in a rotating Bose–Einstein condensate, the symmetry properties of the true many-body state are related to those of its mean-field approximation.