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


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.

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Figure 1: Energy spectrum as a function of Ω.
Figure 2: Variation of the angular momentum with rotation frequency Ω.
Figure 3: Density of the ground state and phase maps of ψ1 and ψ2.
Figure 4: Structure of the ground state.


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We acknowledge discussions with I. Cirac and the support of the EU SCALA and ESF Fermix Programs, Spanish MEC grants (FIS 2005-03169/04627, QOIT) and the French programs ANR and IFRAF.

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Correspondence to N. Barberán.

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Dagnino, D., Barberán, N., Lewenstein, M. et al. Vortex nucleation as a case study of symmetry breaking in quantum systems. Nature Phys 5, 431–437 (2009).

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