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Emergence of multi-body interactions in a fermionic lattice clock

Nature volume 563, pages 369–373 (2018)Cite this article

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Abstract

Alkaline-earth atoms have metastable ‘clock’ states with minute-long optical lifetimes, high-spin nuclei and SU(N)-symmetric interactions, making them powerful platforms for atomic clocks1, quantum information processing2 and quantum simulation3. Few-particle systems of such atoms provide opportunities to observe the emergence of complex many-body phenomena with increasing system size4. Multi-body interactions among particles are emergent phenomena, which cannot be broken down into sums over underlying pairwise interactions. They could potentially be used to create exotic states of quantum matter5,6, but have yet to be explored in ultracold fermions. Here we create arrays of isolated few-body systems in an optical clock based on a three-dimensional lattice of fermionic 87Sr atoms. We use high-resolution clock spectroscopy to directly observe the onset of elastic and inelastic multi-body interactions among atoms. We measure the frequency shifts of the clock transition for varying numbers of atoms per lattice site, from n = 1 to n = 5, and observe nonlinear interaction shifts characteristic of elastic multi-body effects. These measurements, combined with theory, elucidate an emergence of SU(N)-symmetric multi-body interactions, which are unique to fermionic alkaline-earth atoms. To study inelastic multi-body effects, we use these frequency shifts to isolate n-occupied sites in the lattice and measure the corresponding lifetimes of the clock states. This allows us to access the short-range few-body physics without experiencing the systematic effects that are encountered in a bulk gas. The lifetimes that we measure in the isolated few-body systems agree very well with numerical predictions based on a simple model for the interatomic potential, suggesting a universality in ultracold collisions. By connecting these few-body systems through tunnelling, the favourable energy and timescales of the interactions will allow our system to be used for studies of high-spin quantum magnetism7,8 and the Kondo effect3,9.

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Fig. 1: Two-orbital interactions in a three-dimensional lattice and experimental sequence.
Fig. 2: Clock spectroscopy of a ten-component Fermi gas in a three-dimensional lattice.
Fig. 3: Effective multi-body clock shifts.
Fig. 4: Three-body loss rate and occupation-number-dependent lifetime.

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The data that support the findings of this study are available within the paper.

References

  1. Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).

    Article  ADS  CAS  Google Scholar 

  2. Daley, A. J. Quantum computing and quantum simulation with group-II atoms. Quantum Inform. Process. 10, 865–884 (2011).

    Article  Google Scholar 

  3. Cazalilla, M. A. & Rey, A. M. Ultracold Fermi gases with emergent SU(N) symmetry. Rep. Prog. Phys. 77, 124401 (2014).

    Article  ADS  Google Scholar 

  4. Wenz, A. N. et al. From few to many: observing the formation of a Fermi sea one atom at a time. Science 342, 457–460 (2013).

    Article  ADS  CAS  Google Scholar 

  5. Fradkin, E. H., Nayak, C., Tsvelik, A. & Wilczek, F. A Chern-Simons effective field theory for the Pfaffian quantum Hall state. Nucl. Phys. B 516, 704–718 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Büchler, H. P., Micheli, A. & Zoller, P. Three-body interactions with cold polar molecules. Nat. Phys. 3, 726–731 (2007).

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  9. Riegger, L. et al. Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions. Phys. Rev. Lett. 120, 143601 (2018).

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  11. Hofrichter, C. et al. Direct probing of the Mott crossover in the SU(N) Fermi-Hubbard model. Phys. Rev. X 6, 021030 (2016).

    Google Scholar 

  12. Scazza, F. et al. Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions. Nat. Phys. 10, 779–784 (2014); corrigendum 11, 514 (2015).

    Article  CAS  Google Scholar 

  13. Cappellini, G. et al. Direct observation of coherent interorbital spin-exchange dynamics. Phys. Rev. Lett. 113, 120402 (2014).

    Article  ADS  CAS  Google Scholar 

  14. Höfer, M. et al. Observation of an orbital interaction-induced Feshbach resonance in 173Yb. Phys. Rev. Lett. 115, 265302 (2015).

    Article  ADS  Google Scholar 

  15. Pagano, G. et al. Strongly interacting gas of two-electron fermions at an orbital Feshbach resonance. Phys. Rev. Lett. 115, 265301 (2015).

    Article  ADS  CAS  Google Scholar 

  16. Hammer, H.-W., Nogga, A. & Schwenk, A. Colloquium: Three-body forces: from cold atoms to nuclei. Rev. Mod. Phys. 85, 197–217 (2013).

    Article  ADS  CAS  Google Scholar 

  17. Johnson, P. R., Blume, D., Yin, X. Y., Flynn, W. F. & Tiesinga, E. Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons. New J. Phys. 14, 053037 (2012); corrigendum 20, 079501 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  19. Mark, M. J. et al. Precision measurements on a tunable Mott insulator of ultracold atoms. Phys. Rev. Lett. 107, 175301 (2011).

    Article  ADS  CAS  Google Scholar 

  20. Ferlaino, F. et al. Efimov resonances in ultracold quantum gases. Few-Body Syst. 51, 113–133 (2011).

    Article  ADS  CAS  Google Scholar 

  21. Fletcher, R. J. et al. Two- and three-body contacts in the unitary Bose gas. Science 355, 377–380 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  22. Greene, C. H., Giannakeas, P. & Pérez-Ríos, J. Universal few-body physics and cluster formation. Rev. Mod. Phys. 89, 035006 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  23. D’Incao, J. P. Few-body physics in resonantly interacting ultracold quantum gases. J. Phys. B 51, 043001 (2018).

    Article  ADS  Google Scholar 

  24. Wolf, J. et al. State-to-state chemistry for three body recombination in an ultracold rubidium gas. Science 358, 921–924 (2017).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  26. Marti, G. E. et al. Imaging optical frequencies with 100µHz precision and 1.1µm resolution. Phys. Rev. Lett. 120, 103201 (2018).

    Article  ADS  Google Scholar 

  27. Campbell, G. K. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006).

    Article  ADS  CAS  Google Scholar 

  28. Kato, S. et al. Laser spectroscopic probing of coexisting superfluid and insulating states of an atomic Bose–Hubbard system. Nat. Commun. 7, 11341 (2016).

    Article  ADS  CAS  Google Scholar 

  29. Zang, X.-P., Yang, M., Ozaydin, F., Song, W. & Cao, Z.-L. Generating multiatom entangled W states via light-matter interface based fusion mechanism. Sci. Rep. 5, 16245 (2015).

    Article  ADS  CAS  Google Scholar 

  30. Martinez de Escobar, Y. N. et al. Two-photon photoassociative spectroscopy of ultracold 88Sr. Phys. Rev. A 78, 062708 (2008).

    Article  ADS  Google Scholar 

  31. Burt, E. A. et al. Coherence, correlations, and collisions: what one learns about Bose-Einstein condensates from their decay. Phys. Rev. Lett. 79, 337–340 (1997).

    Article  ADS  CAS  Google Scholar 

  32. Söding, J. et al. Three-body decay of a rubidium Bose-Einstein condensate. Appl. Phys. B 69, 257–261 (1999).

    Article  ADS  Google Scholar 

  33. Wang, J., D’Incao, J. P., Wang, Y. & Greene, C. H. Universal three-body recombination via resonant d-wave interactions. Phys. Rev. A 86, 062511 (2012).

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge technical contributions from W. Milner, E. Oelker, J. Robinson, L. Sonderhouse and W. Zhang, and discussions with T. Bothwell, S. Bromley, C. Kennedy, D. Kedar, S. Kolkowitz, M. D. Lukin, A. Safavi-Naini and C. Sanner. This work was supported by NIST, DARPA, W911NF-16-1-0576 through ARO, AFOSR-MURI, AFOSR, NSF-1734006 and NASA. A.G. is supported by a postdoctoral fellowship from the Japan Society for the Promotion of Science and G.E.M. is supported by a postdoctoral fellowship from the National Research Council. J.P.D. acknowledges support from NSF Grant PHY-1607204.

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Author notes

  1. S. L. Campbell

    Present address: Molecular Biophysics and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

  2. S. L. Campbell

    Present address: Department of Physics, University of California, Berkeley, CA, USA

  3. G. E. Marti

    Present address: Department of Molecular and Cellular Physiology, Stanford University, Stanford, CA, USA

  4. These authors contributed equally: A. Goban, R. B. Hutson

Authors and Affiliations

  1. JILA, National Institute of Standards and Technology, University of Colorado, Boulder, CO, USA

    A. Goban, R. B. Hutson, G. E. Marti, S. L. Campbell, M. A. Perlin, J. P. D’Incao, A. M. Rey & J. Ye

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

    A. Goban, R. B. Hutson, G. E. Marti, S. L. Campbell, M. A. Perlin, J. P. D’Incao, A. M. Rey & J. Ye

  3. Joint Quantum Institute, NIST, University of Maryland, Gaithersburg, MD, USA

    P. S. Julienne

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Contributions

A.G., R.B.H., G.E.M., S.L.C. and J.Y. contributed to the experiments. M.A.P., P.S.J., J.P.D. and A.M.R. contributed to the development of the theoretical model. All authors discussed the results, contributed to the data analysis and worked together on the manuscript.

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Correspondence to A. Goban or J. Ye.

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Supplementary information

Supplementary Information

This file contains detailed discussions of low-energy effective multi-body theory, occupation number dependence of three-body lifetime, extracting free-space scattering lengths and calculations of three-body lifetimes based on a universal van der Waals model. It also includes Supplementary Figure 1 showing trap-depth dependence of multi-body clock shifts. The calculated shifts from the three-body theory show good agreement with the experimental data in the wide range of the mean trap depths.

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Goban, A., Hutson, R.B., Marti, G.E. et al. Emergence of multi-body interactions in a fermionic lattice clock. Nature 563, 369–373 (2018). https://doi.org/10.1038/s41586-018-0661-6

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