Data from: Coherent evolution of superexchange interaction in seconds long optical clock spectroscopy

Measurement science now connects strongly with engineering of quantum
coherence, many-body states, and entanglement. To scale up the performance
of an atomic clock using a degenerate Fermi gas loaded in a
three-dimensional optical lattice, we must understand complex many-body
Hamiltonians to ensure meaningful gains for metrological applications. In
this work, we use a highly filled Sr 3D lattice to study the effect of a
tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit
coupling spiral phase and breaks the isotropy of superexchange
interactions, changing the Heisenberg spin model into one exhibiting
XXZ-type spin anisotropy. By tuning the lattice confinement and applying
imaging spectroscopy we map out favorable atomic coherence regimes. With
weak transverse confinement, both s- and p-wave interactions contribute to
decoherence and atom loss, and their contributions can be balanced. At
deep transverse confinement, we directly observe coherent superexchange
interactions, tunable via on-site interaction and site-to-site energy
shift, on the clock Ramsey fringe contrast over timescales of multiple
seconds. This study provides a groundwork for using a 3D optical lattice
clock to probe quantum magnetism and spin entanglement.