Effective inertial frame in an atom interferometric test of the equivalence principle

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. We demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a factor of 100 and enables a precise measurement of these differences. We realize a relative precision of $\Delta g / g \approx 6 \times 10^{-11}$ per shot, which improves on the best previous result for a dual-species atom interferometer by more than three orders of magnitude. By suppressing gravity gradient systematic errors to below one part in $10^{13}$, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.