### 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 clocks^{1}, quantum information processing^{2} and quantum simulation^{3}. Few-particle systems of such atoms provide opportunities to observe the emergence of complex many-body phenomena with increasing system size^{4}. 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 matter^{5,6}, 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 ^{87}Sr 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 magnetism^{7,8} and the Kondo effect^{3,9}.

Original language | English |
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Pages (from-to) | 369-373 |

Number of pages | 5 |

Journal | Nature |

Volume | 563 |

Issue number | 7731 |

DOIs | |

Publication status | Published - 2018 Nov 15 |

Externally published | Yes |

### ASJC Scopus subject areas

- General

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## Cite this

*Nature*,

*563*(7731), 369-373. https://doi.org/10.1038/s41586-018-0661-6