Measurement of a magic-zero wavelength

Light at a magic-zero wavelength causes zero energy shift for an atom. We measured the longest magic-zero wavelength for ground state potassium atoms to be $\lambda_\textrm{zero}=768.971(1)$ nm, and we show how this provides an improved experimental benchmark for atomic structure calculations. This $\lambda_\textrm{zero}$ measurement determines the ratio of the potassium atom D1 and D2 line strengths with record precision. It also demonstrates a new application for atom interferometry, and we discuss how decoherence will fundamentally limit future measurements of magic-zero wavelengths.