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

Nature Physics volume 5, pages 431–437 (2009)Cite this article

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.

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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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Acknowledgements

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.

Author information

Authors and Affiliations

  1. Dept. ECM, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain

    D. Dagnino & N. Barberán

  2. ICFO - Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, 08860 Barcelona, Spain

    M. Lewenstein

  3. ICREA– Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain

    M. Lewenstein

  4. Laboratoire Kastler Brossel, CNRS, UPMC, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

    J. Dalibard

Authors
  1. D. Dagnino
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  2. N. Barberán
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  3. M. Lewenstein
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  4. J. Dalibard
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All authors have contributed equally to this work.

Corresponding author

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). https://doi.org/10.1038/nphys1277

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