Quantum Interference to Measure Spacetime Curvature: A Proposed Experiment at the Intersection of Quantum Mechanics and General Relativity

An experiment in Low Earth Orbit (LEO) is proposed to measure components of the Riemann curvature tensor using atom interferometry. We show that the difference in the quantum phase $\mathrm{\Delta }\varphi$ of an atom that can travel along two intersecting geodesics is given by $m{R}_{0i0j}\mathrm{/}\mathrm{\hslash }$ times the spacetime volume contained within the geodesics. Our expression for $\mathrm{\Delta }\varphi$ also holds for gravitational waves in the long wavelength limit.