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 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 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 magnetism^7,8 and the Kondo effect^3,9.