Quantum gas in-situ state measurements of orbital and SU(N) Fermi-Hubbard Models with ytterbium

The Fermi-Hubbard Model (FHM) has long been a focus of both experimental and theoretical work in both condensed matter and cold atom physics. The extension of the FHM to multi-orbital or higher symmetry systems has less widely studied in the atomic quantum gas context. Advances in recent years both on the experimental side using alkaline-earth like quantum gases, as well as on the theoretical with new approaches and improved numerical methods, have made these more accessible and more tractable for quantitative study.

In our experiments, we realize Fermi-Hubbard Models with multiple orbitals, using state-dependent lattices as well as gases with extended SU(N) symmetries with N>2. The systems are probed by in-situ imaging, allowing for direct comparison with state-of-the-art theoretical modeling of the Hamiltonian using multiple observables.

This approach allows e.g. for the evaluation the equation of state (EoS) of the SU(N) Fermi-Hubbard Model (FHM) in a 2D square lattice for values of N up to 6, while probing the site occupation patterns, densities and compressibilities. This is then directly compared to numerical methods including determinantal quantum Monte Carlo (DQMC) and numerical linked cluster expansion (NLCE). In addition, in-situ temperatures can be determined, allowing for an extensive access to the precise state of the quantum gas.