Precision measurement and few-body physics with lattice-trapped Fermi-degenerate gases of strontium

We implement high resolution clock spectroscopy and spatially resolved readout of Fermi-degenerate strontium in a three-dimensional optical lattice. Here, correlations in the atomic signal between different spatial regions of the sample enable the most rapid evaluation of lattice induced clock shifts and a record fractional frequency precision of $2.5 \times 10^{-19}$. Additionally, spectrally resolved interactions enable us to isolate $n$-atom lattice sites, where we observe the onset of multi-body interactions as both a density-dependent clock shift that is non-linear in the occupation-number, and three-body recombination loss. Furthermore, careful characterization of the lattice potential enables a precise extraction of the two- and three-body interaction parameters. In future work, these techniques can be directly applied to tests of general relativity at the millimeter scale and studies of magnetic correlations in large-spin quantum materials.