Towards simulation of lattice gauge theories with ultracold ytterbium atoms in hybrid optical potentials

Gauge theories play a fundamental role for our understanding of nature, ranging from high-energy to condensed matter physics. Their formulation on a regularized periodic lattice geometry, so-called lattice gauge theories (LGTs), has proven invaluable for theoretical studies. Numerical studies on, e.g., their real-time dynamics are however computationally challenging. We report progress on developing a quantum simulator for LGTs using neutral ytterbium atoms. Ytterbium's internal level structure provides a ground and meta-stable clock state pair, and fermionic isotopes further host nuclear qubits. We combine optical lattice and optical tweezer technology that can enable robust and scalable implementation of LGTs. To realize state-selective control, we leverage magic and tune-out wavelengths. We present the first measurements of such wavelengths near the narrow cooling transition at 556 nm and discuss prospects in implementing local gauge invariance.