Effective Hubbard parameters for programmable tweezer arrays

The experimental realization of Fermi-Hubbard tweezer arrays with lithium-6 atoms in 1- and 2-D (?PRL128,223202, PRL129,123201) opens a new stage for studying fermionic matter and fermionic quantum computing, where programmable lattice geometries and Hubbard model parameters are paired with single-site imaging. ?In order to use these versatile experimental Fermi-Hubbard models as quantum simulators, it is crucial to know the Hubbard parameters describing them, which are difficult to set to desired values and require laborious calibration without theoretical guidance. Here we present calculations of Hubbard model parameters of arbitrary 2-D lattice geometries, including tunneling , onsite potential and interaction , and compare results with experimental measurements. The Hubbard parameters can be obtained for both bosonic and fermionic tweezer arrays. The calculations are not limited to single band as well, and may be used to engineer multi-band Hubbard models. We also present procedures ?to solve the inverse problem: finding lattice geometries that realize desired Hubbard parameters. The simplest case is to find geometries realizing uniform Hubbard parameters. Our calculations contribute to evaluate and optimize 2-D Fermi-Hubbard tweezer array experiments, and further help on developing fermionic quantum simulation platforms.