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Two-orbital S U(N) magnetism with ultracold alkaline-earth atoms

Nature Physics volume 6, pages 289–295 (2010)Cite this article

Abstract

Fermionic alkaline-earth atoms have unique properties that make them attractive candidates for the realization of atomic clocks and degenerate quantum gases. At the same time, they are attracting considerable theoretical attention in the context of quantum information processing. Here we demonstrate that when such atoms are loaded in optical lattices, they can be used as quantum simulators of unique many-body phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement many-body systems with an unprecedented degree of symmetry, characterized by the S U(N) group with N as large as 10. Moreover, the interplay of the nuclear spin with the electronic degree of freedom provided by a stable optically excited state should enable the study of physics governed by the spin–orbital interaction. Such systems may provide valuable insights into the physics of strongly correlated transition-metal oxides, heavy-fermion materials and spin-liquid phases.

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Figure 1: Interaction parameters between g and e atoms loaded in the lowest vibrational state of the corresponding optical lattice.
Figure 2: Young diagrams describing the irreducible representations of SU(N) on individual sites.
Figure 3: The ground-state phase diagram for the S U(N=2) Kugel–Khomskii model restricted to two wells, left and right.
Figure 4: Probing the phases of the SU(N) antiferromagnet on a 2D square lattice.
Figure 5: KLM for the case N=2.

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Acknowledgements

We gratefully acknowledge conversations with M. M. Boyd, A. J. Daley, S. Fölling, W. S. Bakr, J. I. Gillen, L. Jiang, G. K. Campbell, Y. Qi and N. Blümer. This work was supported by NSF, CUA, DARPA, the Packard Foundation, AFOSR MURI and NIST.

Author information

Authors and Affiliations

  1. Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA

    A. V. Gorshkov, C. Xu, E. Demler & M. D. Lukin

  2. Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

    M. Hermele & V. Gurarie

  3. Joint Quantum Institute, NIST and University of Maryland, Gaithersburg, Maryland 20899-8423, USA

    P. S. Julienne

  4. and Department of Physics, JILA, NIST, University of Colorado, Boulder, Colorado 80309, USA

    J. Ye & A. M. Rey

  5. Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria

    P. Zoller

  6. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria

    P. Zoller

  7. Institute for Theoretical Atomic, Molecular and Optical Physics, Harvard–Smithsonian Center of Astrophysics, Cambridge, Massachusetts 02138, USA

    E. Demler & M. D. Lukin

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  1. A. V. Gorshkov
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Gorshkov, A., Hermele, M., Gurarie, V. et al. Two-orbital S U(N) magnetism with ultracold alkaline-earth atoms. Nature Phys 6, 289–295 (2010). https://doi.org/10.1038/nphys1535

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