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Emergence of multi-body interactions in a fermionic lattice clock


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.

Data availability

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


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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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Authors and Affiliations



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).

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  • Multi-body Effects
  • Station Clock
  • Three-body Loss
  • Nuclear Spin Degrees
  • High Motivation Condition

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