Article | Published:

Dynamics of interacting fermions under spin–orbit coupling in an optical lattice clock

Nature Physicsvolume 14pages399404 (2018) | Download Citation


Quantum statistics and symmetrization dictate that identical fermions do not interact via s-wave collisions. However, in the presence of spin–orbit coupling (SOC), fermions prepared in identical internal states with distinct momenta become distinguishable. The resulting strongly interacting system can exhibit exotic topological and pairing behaviours, many of which are yet to be observed in condensed matter systems. Ultracold atomic gases offer a promising pathway for simulating these rich phenomena, but until recently have been hindered by heating and losses. Here we enter a new regime of many-body interacting SOC in a fermionic optical lattice clock (OLC), where the long-lived electronic clock states mitigate unwanted dissipation. Using clock spectroscopy, we observe the precession of the collective magnetization and the emergence of spin-locking effects arising from an interplay between p-wave and SOC-induced exchange interactions. The many-body dynamics are well captured by a collective XXZ spin model, which describes a broad class of condensed matter systems ranging from superconductors to quantum magnets. Furthermore, our work will aid in the design of next-generation OLCs by offering a route for avoiding the observed large density shifts caused by SOC-induced exchange interactions.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

  2. 2.

    Barbarino, S., Taddia, L., Rossini, D., Mazza, L. & Fazio, R. Synthetic gauge fields in synthetic dimensions: interactions and chiral edge modes. New. J. Phys. 18, 035010 (2016).

  3. 3.

    Strinati, M. C. et al. Laughlin-like states in bosonic and fermionic atomic synthetic ladders. Phys. Rev. X 7, 021033 (2017).

  4. 4.

    Zeng, T.-S., Wang, C. & Zhai, H. Charge pumping of interacting fermion atoms in the synthetic dimension. Phys. Rev. Lett. 115, 095302 (2015).

  5. 5.

    Zhai, H. Degenerate quantum gases with spin–orbit coupling: a review. Rep. Prog. Phys. 78, 026001 (2015).

  6. 6.

    Goldman, N., Juzeliūnas, G., Öhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).

  7. 7.

    Celi, A. et al. Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett. 112, 043001 (2014).

  8. 8.

    Galitski, V. & Spielman, I. B. Spin-orbit coupling in quantum gases. Nature 494, 49–54 (2013).

  9. 9.

    Goldman, N., Dalibard, J., Aidelsburger, M. & Cooper, N. R. Periodically driven quantum matter:the case of resonant modulations. Phys. Rev. A 91, 033632 (2015).

  10. 10.

    Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Colloquium: artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).

  11. 11.

    Wall, M. L. et al. Synthetic spin-orbit coupling in an optical lattice clock. Phys. Rev. Lett. 116, 035301 (2016).

  12. 12.

    Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. A spin-orbit coupled Bose–Einstein condensate. Nature 471, 83–86 (2011).

  13. 13.

    Fu, Z. et al. Radio-frequency spectroscopy of a strongly interacting spin–orbit-coupled Fermi gas. Phys. Rev. A 87, 053619 (2013).

  14. 14.

    Ha, L.-C., Clark, L. W., Parker, C. V., Anderson, B. M. & Chin, C. Roton-Maxon excitation spectrum of Bose condensates in a shaken lattice. Phys. Rev. Lett. 114, 055301 (2015).

  15. 15.

    Li, J. R. et al. A stripe phase with supersolid properties in spin-orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

  16. 16.

    Tai, M. E. et al. Microscopy of the interacting Harper–Hofstadter model in the few-body limit. Nature 546, 519–523 (2017).

  17. 17.

    Kolkowitz, S. et al. Spin-orbit-coupled fermions in an optical lattice clock. Nature 542, 66–70 (2017).

  18. 18.

    Livi, L. F. et al. Synthetic dimensions and spin-orbit coupling with an optical clock transition. Phys. Rev. Lett. 117, 220401 (2016).

  19. 19.

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

  20. 20.

    Zhang, X. et al. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism. Science 345, 1467–1473 (2014).

  21. 21.

    Anderson, P. W. Random-phase approximation in the theory of superconductivity. Phys. Rev. 112, 1900–1916 (1958).

  22. 22.

    Matsunaga, R. et al. Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor. Science 345, 1145–1149 (2014).

  23. 23.

    Deutsch, C. et al. Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010).

  24. 24.

    Du, X., Luo, L., Clancy, B. & Thomas, J. E. Observation of anomalous spin segregation in a trapped Fermi gas. Phys. Rev. Lett. 101, 150401 (2008).

  25. 25.

    Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).

  26. 26.

    Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

  27. 27.

    Rey, A. M. et al. Probing many-body interactions in an optical lattice clock. Ann. Phys. 340, 311–351 (2014).

  28. 28.

    Bishof, M. et al. Inelastic collisions and density-dependent excitation suppression in a 87Sr optical lattice clock. Phys. Rev. A 84, 052716 (2011).

  29. 29.

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

  30. 30.

    Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998).

  31. 31.

    Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

  32. 32.

    Isaev, L., Schachenmayer, J. & Rey, A. M. Spin-orbit-coupled correlated metal phase in Kondo lattices: An implementation with alkaline-earth atoms. Phys. Rev. Lett. 117, 135302 (2016).

  33. 33.

    de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010).

  34. 34.

    Slichter, C. P. Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1996).

  35. 35.

    Schachenmayer, J., Pikovski, A. & Rey, A. M. Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: a phase-space Monte-Carlo study. New. J. Phys. 17, 065009 (2015).

Download references


We are grateful to M. Lukin, S. Yelin, V. Gurarie, M. Foster, S. L. Campbell, A. Goban, R. B. Hutson, G.E. Marti, E. Oelker, J. Robinson, L. Sonderhouse and D. G. Reed for stimulating discussions and technical contributions. We thank M. Norcia and A. Kaufman for their careful reading of the manuscript. This research is supported by NIST, DARPA, JILA Physics Frontier Center (NSF-PFC-1125844), AFOSR-MURI, and AFOSR. C.S. is partially supported by the JILA Visiting Fellow Program.

Author information

Author notes

    • M. L. Wall

    Present address: The Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA

  1. S. L. Bromley and S. Kolkowitz contributed equally to this work.


  1. JILA, NIST and Department of Physics, University of Colorado, Boulder, CO, USA

    • S. L. Bromley
    • , S. Kolkowitz
    • , T. Bothwell
    • , D. Kedar
    • , A. Safavi-Naini
    • , M. L. Wall
    • , A. M. Rey
    •  & J. Ye
  2. Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, Paris, France

    • C. Salomon


  1. Search for S. L. Bromley in:

  2. Search for S. Kolkowitz in:

  3. Search for T. Bothwell in:

  4. Search for D. Kedar in:

  5. Search for A. Safavi-Naini in:

  6. Search for M. L. Wall in:

  7. Search for C. Salomon in:

  8. Search for A. M. Rey in:

  9. Search for J. Ye in:


S.L.B., S.K., T.B., D.K. and J.Y. contributed to the executions of the experiments. A.S.-N., M.L.W. and A.M.R. developed the theory model. All authors discussed the results, contributed to the data analysis and worked together on the manuscript.

Competing interests

The authors have no competing financial interests.

Corresponding author

Correspondence to S. L. Bromley.

Supplementary information

  1. Supplementary Information

    Supplementary Figure 1–3

About this article

Publication history