Using Feynman Diagrams to Analytically Compute Higher Order Quantum Corrections to Atom Interferometer Phase Shifts*

In atom interferometry, the differential phase accumulated between two arms due to spatially varying gravitational fields is often analyzed under a semi-classical approximation that disregards the finite spatial extent of an atom's wavefunction. Deviations from this approximation have not yet been measured definitively, but as atom interferometers become more sensitive, higher order quantum corrections could potentially be observed. These measurements would offer insight into the connection between quantum mechanics and gravity and reveal a novel source of systematic error. We introduce a Feynman diagram based approach to analytically computing the phase shift in an atom interferometer which incorporates these higher-order quantum corrections. This approach can also be used to calculate phase shifts caused by spatially varying magnetic fields and optical potentials.