Atom-interferometric test of the equivalence principle at the $10^{-12}$ level

Does gravity influence local measurements? We use a dual-species atom interferometer with $2\,\text{s}$ of free-fall time to measure the relative acceleration between $^{85}$Rb and $^{87}$Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an E\"otv\"os parameter of $\eta = [1.6\; \pm\; 1.8\; \text{(stat)}\; \pm \; 3.4 \; \text{(sys)}] \times 10^{-12}$, consistent with zero violation of the equivalence principle. With a resolution of up to $1.4 \times 10^{-11} \, g$ per shot, we demonstrate a sensitivity to $\eta$ of $5.4 \times 10^{-11}\,/\sqrt{\text{Hz}}$.