Using an Atom Interferometer to Measure Changes in Tune-Out Wavelength caused by Rotation and Acceleration

Measurements of tune-out wavelengths made with an atom interferometer are shown to change by 150 pm due to inertial displacements. Because tune-out wavelengths can be measured with picometer precision in our laboratory, we explore how to use shifts in tune-out wavelengths to measure rotation rates with respect to an inertial frame. For example, measuring the earth's rotation rate with an uncertainty of 1{\%} appears possible with this technique. The origin of shifts in measured tune-out wavelengths ($\lambda _{zero,\, lab})$ as compared to tune-out wavelengths in an inertial frame ($\lambda_{zero})$ is explained by dispersive inertial phase shifts, the vector dynamic polarizability $\alpha^{v}(\omega )$, and dispersion compensation. An atom beam with a velocity spread and an ensemble of atomic spin states is required. Because accurate measurements of $\lambda _{zero}$ can be used for reporting ratios of dipole matrix elements, we also discuss methods for reducing systematic errors in measurements of $\lambda_{zero}$.