Precision Measurements of Tune-out Wavelengths with an Atom Interferometer

Tune-out wavelengths occur were there is a root in the dynamic polarizability between two resonances. Precision measurements of tune-out wavelengths serve as a benchmark test for atomic structure calculations of ratios of dipole matrix elements. We present a new measurement of the longest tune-out wavelength in potassium, with a preliminary result of $\lambda_{\mathrm{zero}} \quad =$ 768.9702(8) nm. We describe experimental improvements such as adding an optical cavity that allows us to reach sub-picometer precision. We discuss systematic errors due to broadband laser light and the Earths' rotation. We also show preliminary results for Rb.