Title: Effective inertial frame in an atom interferometric test of the equivalence principle,
Abstract: 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.