State-dependent potentials for the ¹𝑆₀ and ³𝑃₀ clock states of neutral ytterbium atoms

We thank C. Bachorz, D. Gröters, B. Hebbe Madhusudhana, T. Marozsak, and D. Robledo for technical contributions to the experiment. We further acknowledge fruitful discussions with V. A. Dzuba, S. Blatt, Y. Takahashi, and G. Pasqualetti. We thank V.A. Dzuba, Y. Takahashi, and F. Scazza for careful reading of the manuscript and S. Fölling, G. Pasqualetti, and O. Bettermann for providing their clock laser as a frequency reference for identifying the zero crossing of our ULE cavity. We also thank the team of Hübner Photonics for the broad frequency-tunable laser source, C-WAVE VIS+IR Low Power [86]. This project has received funding from the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy (EXC-2111 Grant No. 390814868), from the European Research Council under the European Union's Horizon 2020 research and innovation program (Grant No. 803047), from the German Federal Ministry of Education and Research (BMBF) via the funding program quantum technologies (from basic research to market, Grant No. 13N15895 FermiQP), and from the initiative Munich Quantum Valley from the State Ministry for Science and the Arts as part of the High-Tech Agenda Plus of the Bavarian State Government.