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.

  • Article
  • Published:

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions

Nature Physics volume 10, pages 779–784 (2014)Cite this article

Subjects

A Corrigendum to this article was published on 02 June 2015

This article has been updated

Abstract

Spin-exchanging interactions govern the properties of strongly correlated electron systems such as many magnetic materials. When orbital degrees of freedom are present, spin exchange between different orbitals often dominates, leading to the Kondo effect, heavy fermion behaviour or magnetic ordering. Ultracold ytterbium or alkaline-earth ensembles have attracted much recent interest as model systems for these effects, with two (meta-) stable electronic configurations representing independent orbitals. We report the observation of spin-exchanging contact interactions in a two-orbital SU(N)-symmetric quantum gas realized with fermionic 173Yb. We find strong inter-orbital spin exchange by spectroscopic characterization of all interaction channels and demonstrate SU(N = 6) symmetry within our measurement precision. The spin-exchange process is also directly observed through the dynamic equilibration of spin imbalances between ensembles in separate orbitals. The realization of an SU(N)-symmetric two-orbital Hubbard Hamiltonian opens the route to quantum simulations with extended symmetries and with orbital magnetic interactions, such as the Kondo lattice model.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Two-orbital interacting states of fermions in a lattice.
Figure 2: Clock transition spectroscopy of a two-component Fermi gas in a 3D lattice.
Figure 3: Magnetic field dependence of clock transition frequencies in the presence of two-orbital on-site interactions.
Figure 4: Spin-exchange dynamics between |g〉 and |e〉 atoms in 2D ensembles.

Similar content being viewed by others

Change history

  • 20 May 2015

    In the version of this Article originally published the assignment of states with symmetric electronic wavefunctions (|eg+〉) and with antisymmetric electronic wavefunctions (|eg−〉) to the observed spectral lines was inverted throughout. These errors have been corrected online 20 May 2015.

References

  1. Gorshkov, A. V. et al. Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms. Nature Phys. 6, 289–295 (2010).

    Article  ADS  Google Scholar 

  2. Sugawa, S. et al. Interaction and filling-induced quantum phases of dual Mott insulators of bosons and fermions. Nature Phys. 7, 642–648 (2011).

    Article  ADS  Google Scholar 

  3. Taie, S., Yamazaki, R., Sugawa, S. & Takahashi, Y. An SU(6) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling. Nature Phys. 8, 825–830 (2012).

    Article  ADS  Google Scholar 

  4. Martin, M. J. et al. A quantum many-body spin system in an optical lattice clock. Science 341, 632–636 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  5. Pagano, G. et al. A one-dimensional liquid of fermions with tunable spin. Nature Phys. 10, 198–201 (2014).

    Article  ADS  Google Scholar 

  6. Hinkley, N. et al. An atomic clock with 10−18 instability. Science 341, 1215–1218 (2013).

    Article  ADS  Google Scholar 

  7. Bloom, B. J. et al. An optical lattice clock with accuracy and stability at the 10−18 level. Nature 506, 71–75 (2014).

    Article  ADS  Google Scholar 

  8. Foss-Feig, M., Hermele, M. & Rey, A. M. Probing the Kondo lattice model with alkaline-earth-metal atoms. Phys. Rev. A 81, 051603(R) (2010).

    Article  ADS  Google Scholar 

  9. Gerbier, F. & Dalibard, J. Gauge fields for ultracold atoms in optical superlattices. New J. Phys. 12, 033007 (2010).

    Article  ADS  Google Scholar 

  10. 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 

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

    Article  ADS  Google Scholar 

  12. 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 

  13. Tsunetsugu, H., Sigrist, M. & Ueda, K. The ground-state phase diagram of the one-dimensional Kondo lattice model. Rev. Mod. Phys. 69, 809–864 (1997).

    Article  ADS  Google Scholar 

  14. Foss-Feig, M., Hermele, M., Gurarie, V. & Rey, A. M. Heavy fermions in an optical lattice. Phys. Rev. A 82, 053624 (2010).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Coleman, P. Handbook of Magnetism and Advanced Magnetic Materials Vol. 1 95–148 (Wiley, 2007).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Boyd, M. M. et al. Optical atomic coherence at the 1-second time scale. Science 314, 1430–1433 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. 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 

  22. Cazalilla, M., Ho, A. & 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 

  23. Hermele, M. & Gurarie, V. Topological liquids and valence cluster states in two-dimensional SU(N) magnets. Phys. Rev. B 84, 174441 (2011).

    Article  ADS  Google Scholar 

  24. Banerjee, D. et al. Atomic quantum simulation of U(N) and SU(N) non-abelian lattice gauge theories. Phys. Rev. Lett. 110, 125303 (2013).

    Article  ADS  Google Scholar 

  25. Kitagawa, M. et al. Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s-wave scattering lengths. Phys. Rev. A 77, 012719 (2008).

    Article  ADS  Google Scholar 

  26. Ludlow, A. D. et al. Cold-collision-shift cancellation and inelastic scattering in a Yb optical lattice clock. Phys. Rev. A 84, 052724 (2011).

    Article  ADS  Google Scholar 

  27. Lemke, N. D. et al. p-wave cold collisions in an optical lattice clock. Phys. Rev. Lett. 107, 103902 (2011).

    Article  ADS  Google Scholar 

  28. Yamaguchi, A., Uetake, S., Hashimoto, D., Doyle, J. M. & Takahashi, Y. Inelastic collisions in optically trapped ultracold metastable ytterbium. Phys. Rev. Lett. 101, 233002 (2008).

    Article  ADS  Google Scholar 

  29. Kato, S., Sugawa, S., Shibata, K., Yamamoto, R. & Takahashi, Y. Control of resonant interaction between electronic ground and excited states. Phys. Rev. Lett. 110, 173201 (2013).

    Article  ADS  Google Scholar 

  30. 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 

  31. Stellmer, S., Grimm, R. & Schreck, F. Detection and manipulation of nuclear spin states in fermionic strontium. Phys. Rev. A 84, 043611 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Busch, T., Englert, B., Rza̧żewski, K. & Wilkens, M. Two cold atoms in a harmonic trap. Found. Phys. 28, 549–559 (1998).

    Article  Google Scholar 

  34. Will, S. et al. Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature 465, 197–201 (2010).

    Article  ADS  Google Scholar 

  35. Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).

    ADS  Google Scholar 

  36. Zürn, G. et al. Fermionization of two distinguishable fermions. Phys. Rev. Lett. 108, 075303 (2012).

    Article  ADS  Google Scholar 

  37. Barber, Z. W. et al. Optical lattice induced light shifts in an Yb atomic clock. Phys. Rev. Lett. 100, 103002 (2008).

    Article  ADS  Google Scholar 

  38. Taie, S. et al. Realization of a SU(2) × SU(6) system of fermions in a cold atomic gas. Phys. Rev. Lett. 105, 190401 (2010).

    Article  ADS  Google Scholar 

  39. Zhang, X. et al. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism. Preprint at http://arxiv.org/abs/1403.2964 (2014)

Download references

Acknowledgements

We gratefully acknowledge contributions by C. Schweizer, E. Davis and P. Ketterer during the construction of the experiment, and helpful discussions with A.M. Rey, M. Wall and A. Daley. This work was supported by the EU through the ERC Synergy Grant UQUAM and through the Marie Curie program (fellowship to P.C.D.G.).

Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany

    F. Scazza, C. Hofrichter, M. Höfer, P. C. De Groot, I. Bloch & S. Fölling

  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

    F. Scazza, C. Hofrichter, M. Höfer, P. C. De Groot, I. Bloch & S. Fölling

Authors
  1. F. Scazza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Hofrichter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Höfer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. C. De Groot
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. Bloch
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. S. Fölling
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.S., C.H., M.H., P.C.D.G. and S.F. conceived the experiment, built the set-up, carried out the measurements and analysed the data. All authors contributed extensively to the discussion of the results and to the writing of the manuscript.

Corresponding author

Correspondence to S. Fölling.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 658 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Scazza, F., Hofrichter, C., Höfer, M. et al. Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions. Nature Phys 10, 779–784 (2014). https://doi.org/10.1038/nphys3061

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3061

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