Neutral-atom arrays offer a promising path for quantum simulation, yet the potential of fermionic ${}^{40}\mathrm{K}$ remains largely constrained by state-dependent light shifts that degrade cooling and detection fidelities. This problem can be resolved by working at a magic wavelength, where the differential light shift vanishes. We report the first experimental determination of the magic wavelength for the $D_1$ transition in fermionic ${}^{40}\mathrm{K}$ at 1227.54(4) nm. Using in-trap loss spectroscopy in a wavelength-tunable optical tweezer, we map the differential ac Stark shift across a range of trapping powers and wavelengths. By converting these shifts to differential scalar polarizabilities, we find excellent agreement with relativistic all-order calculations. Benchmark measurements at 1064.49 nm further quantify the intensity-sampling systematics inherent to standard trapping wavelengths, contrasting with the “mechanically clean” environment provided by the magic condition. Our results provide an important step toward high-fidelity in-trap $D_1$ cooling, fluorescence imaging, and light-assisted loading, establishing a robust path toward scaling fermionic neutral-atom arrays for quantum information science.

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• Lineshapes & shifts
• Stark effect
• Polarizability
• Cooling & trapping
• Optical tweezers