Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

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.

References

  1. Boyd, M. M. et al. Nuclear spin effects in optical lattice clocks. Phys. Rev. A 76, 022510 (2007).

    Article  ADS  Google Scholar 

  2. Campbell, G. K. et al. Probing interactions between ultracold fermions. Science 324, 360–363 (2009).

    Article  ADS  Google Scholar 

  3. Lemke, N. D. et al. Spin-1/2 optical lattice clock. Phys. Rev. Lett. 103, 063001 (2009).

    Article  ADS  Google Scholar 

  4. Fukuhara, T., Takasu, Y., Kumakura, M. & Takahashi, Y. Degenerate fermi gases of ytterbium. Phys. Rev. Lett. 98, 030401 (2007).

    Article  ADS  Google Scholar 

  5. Reichenbach, I. & Deutsch, I. H. Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms. Phys. Rev. Lett. 99, 123001 (2007).

    Article  ADS  Google Scholar 

  6. Hayes, D., Julienne, P. S. & Deutsch, I. H. Quantum logic via the exchange blockade in ultracold collisions. Phys. Rev. Lett. 98, 070501 (2007).

    Article  ADS  Google Scholar 

  7. Daley, A. J., Boyd, M. M., Ye, J. & Zoller, P. Quantum computing with alkaline-earth-metal atoms. Phys. Rev. Lett. 101, 170504 (2008).

    Article  ADS  Google Scholar 

  8. Gorshkov, A. V. et al. Alkaline-earth-metal atoms as few-qubit quantum registers. Phys. Rev. Lett. 102, 110503 (2009).

    Article  ADS  Google Scholar 

  9. Kugel, K. I. & Khomskii, D. I. Crystal structure and magnetic properties of substances with orbital degeneracy. Sov. Phys. JETP 37, 725–730 (1973).

    ADS  Google Scholar 

  10. Arovas, D. P. & Auerbach, A. Tetrahis(dimethylamino)ethylene-C60: Multicomponent superexchange and Mott ferromagnetism. Phys. Rev. B 52, 10114–10121 (1995).

    Article  ADS  Google Scholar 

  11. Li, Y. Q., Ma, M., Shi, D. N. & Zhang, F. C. SU(4) theory for spin systems with orbital degeneracy. Phys. Rev. Lett. 81, 3527–3530 (1998).

    Article  ADS  Google Scholar 

  12. Pati, S. K., Singh, R. R. P. & Khomskii, D. I. Alternating spin and orbital dimerization and spin-gap formation in coupled spin–orbital systems. Phys. Rev. Lett. 81, 5406–5409 (1998).

    Article  ADS  Google Scholar 

  13. Tokura, Y. & Nagaosa, N. Orbital physics in transition-metal oxides. Science 288, 462–468 (2000).

    Article  ADS  Google Scholar 

  14. Ruderman, M. A. & Kittel, C. Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev. 96, 99–102 (1954).

    Article  ADS  Google Scholar 

  15. Coqblin, B. & Schrieffer, J. R. Exchange interaction in alloys with cerium impurities. Phys. Rev. 185, 847–853 (1969).

    Article  ADS  Google Scholar 

  16. Doniach, S. The Kondo lattice and weak antiferromagnetism. Physica B+C 91, 231–234 (1977).

    Article  ADS  Google Scholar 

  17. Coleman, P. 1/N expansion for the Kondo lattice. Phys. Rev. B 28, 5255–5262 (1983).

    Article  ADS  Google Scholar 

  18. Tsunetsugu, H., Sigrist, M. & Ueda, K. The ground-state phase diagram of the one-dimensional Kondo lattice model. Rev. Mod. Phys. 69, 809–863 (1997).

    Article  ADS  Google Scholar 

  19. Assaad, F. F. Quantum Monte Carlo simulations of the half-filled two-dimensional Kondo lattice model. Phys. Rev. Lett. 83, 796–799 (1999).

    Article  ADS  Google Scholar 

  20. Tokura, Y. (ed.) Colossal Magnetoresistive Oxides (Gordon and Breach, 2000).

  21. Oshikawa, M. Topological approach to Luttinger’s theorem and the Fermi surface of a Kondo lattice. Phys. Rev. Lett. 84, 3370–3373 (2000).

    Article  ADS  Google Scholar 

  22. Senthil, T., Sachdev, S. & Vojta, M. Fractionalized Fermi liquids. Phys. Rev. Lett. 90, 216403 (2003).

    Article  ADS  Google Scholar 

  23. Duan, L.-M. Controlling ultracold atoms in multi-band optical lattices for simulation of Kondo physics. Europhys. Lett. 67, 721–727 (2004).

    Article  ADS  Google Scholar 

  24. Paredes, B., Tejedor, C. & Cirac, J. I. Fermionic atoms in optical superlattices. Phys. Rev. A. 71, 063608 (2005).

    Article  ADS  Google Scholar 

  25. Coleman, P. in Handbook of Magnetism and Advanced Magnetic Materials Vol. 1 (eds Kronmüller, H. & Parkin, S.) 95–148 (Wiley, 2007).

    Google Scholar 

  26. Gegenwart, P., Si, Q. & Steglich, F. Quantum criticality in heavy-fermion metals. Nature Phys. 4, 186–197 (2008).

    Article  ADS  Google Scholar 

  27. Read, N. & Sachdev, S. Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets. Phys. Rev. Lett. 62, 1694–1967 (1989).

    Article  ADS  Google Scholar 

  28. Marston, J. B. & Affleck, I. Large-n limit of the Hubbard–Heisenberg model. Phys. Rev. B 39, 11538–11558 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  29. Harada, K., Kawashima, N. & Troyer, M. Néel and spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets. Phys. Rev. Lett. 90, 117203 (2003).

    Article  ADS  Google Scholar 

  30. Assaad, F. F. Phase diagram of the half-filled two-dimensional SU(N) Hubbard–Heisenberg model: A quantum Monte Carlo study. Phys. Rev. B 71, 075103 (2005).

    Article  ADS  Google Scholar 

  31. Paramekanti, A. & Marston, J. B. SU(N) quantum spin models: a variational wavefunction study. J. Phys. Condens. Matter 19, 125215 (2007).

    Article  ADS  Google Scholar 

  32. Greiter, M. & Rachel, S. Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap. Phys. Rev. B 75, 184441 (2007).

    Article  ADS  Google Scholar 

  33. Xu, C. & Wu, C. Resonating plaquette phases in SU(4) Heisenberg antiferromagnet. Phys. Rev. B 77, 134449 (2008).

    Article  ADS  Google Scholar 

  34. Hermele, M., Gurarie, V. & Rey, A. M. Mott insulators of ultracold fermionic alkaline earth atoms: Underconstrained magnetism and chiral spin liquid. Phys. Rev. Lett. 103, 135301 (2009).

    Article  ADS  Google Scholar 

  35. Wu, C., Hu, J. P. & Zhang, S. C. Exact SO(5) symmetry in the spin-3/2 fermionic system. Phys. Rev. Lett. 91, 186402 (2003).

    Article  ADS  Google Scholar 

  36. Honerkamp, C. & Hofstetter, W. Ultracold fermions and the SU(N) Hubbard model. Phys. Rev. Lett. 92, 170403 (2004).

    Article  ADS  Google Scholar 

  37. Rapp, A., Hofstetter, W. & Zarand, G. Trionic phase of ultracold fermions in an optical lattice: A variational study. Phys. Rev. B 77, 144520 (2008).

    Article  ADS  Google Scholar 

  38. Affleck, I., Arovas, D. P., Marston, J. B. & Rabson, D. A. SU(2n) quantum antiferromagnets with exact C-breaking ground states. Nucl. Phys. B 366, 467–506 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  39. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

    Article  ADS  Google Scholar 

  40. Altman, E., Demler, E. & Lukin, M. D. Probing many-body states of ultracold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004).

    Article  ADS  Google Scholar 

  41. Hofstetter, W., Cirac, J. I., Zoller, P., Demler, E. & Lukin, M. D. High-temperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett. 89, 220407 (2002).

    Article  ADS  Google Scholar 

  42. Werner, F., Parcollet, O., Georges, A. & Hassan, S. R. Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices. Phys. Rev. Lett. 95, 056401 (2005).

    Article  ADS  Google Scholar 

  43. Schneider, U. et al. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520–1525 (2008).

    Article  ADS  Google Scholar 

  44. Fukuhara, T., Sugawa, S., Sugimoto, M., Taie, S. & Takahashi, Y. Mott insulator of ultracold alkaline-earth-metal-like atoms. Phys. Rev. A 79, 041604(R) (2009).

    Article  ADS  Google Scholar 

  45. Ni, K. K. et al. A high phase-space-density gas of polar molecules. Science 322, 231–235 (2008).

    Article  ADS  Google Scholar 

  46. Rey, A. M., Gorshkov, A. V. & Rubbo, C. Many-body treatment of the collisional frequency shift in fermionic atoms. Phys. Rev. Lett. 103, 260402 (2009).

    Article  ADS  Google Scholar 

  47. Cazalilla, M. A., Ho, A. F. & Ueda, M. Ultracold gases of ytterbium: Ferromagnetism and Mott states in an SU(6) Fermi system. New J. Phys. 11, 103033 (2009).

    Article  ADS  Google Scholar 

  48. Gorshkov, A. V., Jiang, L., Greiner, M., Zoller, P. & Lukin, M. D. Coherent quantum optical control with subwavelength resolution. Phys. Rev. Lett. 100, 093005 (2008).

    Article  ADS  Google Scholar 

  49. Ciuryło, R., Tiesinga, E. & Julienne, P. S. Optical tuning of the scattering length of cold alkaline-earth-metal atoms. Phys. Rev. A 71, 030701(R) (2005).

    Article  ADS  Google Scholar 

  50. Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007).

    Article  ADS  Google Scholar 

Download references

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

Authors
  1. A. V. Gorshkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Hermele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Gurarie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. S. Julienne
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. Zoller
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. E. Demler
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. M. D. Lukin
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. A. M. Rey
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed extensively to the work presented in this paper.

Corresponding author

Correspondence to A. V. Gorshkov.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 829 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1535

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing