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 intera..., We use absorption imaging of ultracold atoms to detect the relative populations of ground and clock atoms. These populations are used to determine the excitation fraction. We relate the excitation fraction to various physics effects as detailed in the manuscript. , , ## ‘Coherent evolution of superexchange interaction in seconds long optical clock spectroscopy’ dataset

 

## Description of the data and file structure

All experimental data presented in “Coherent evolution of superexchange interaction in seconds long optical clock spectroscopy” in both the main text and supplementary materials is provided. Each folder provided in ‘paper_data.zip’ is labelled by figure name and contains the data for each figure. Here we go folder-by-folder and specifically annotate each dataset.

 

### Fig 2:

**(B)** `plot_fig_2b.py` is the Python script to plot the data in Fig.2(B).

Left panel: ‘dark_times’ are the Ramsey interferometer dark times in seconds.  ‘C_’ are the Ramsey fringe contrasts. A detailed explanation of Ramsey spectroscopy is provided in the main text of our manuscript. Our method of determining these contrasts is in the section ‘Ellipse fitting analysis’ in the Supplemental materials. ‘C_errs’ are one standard deviation error bars for the ‘C_...