The Effects of Dynamical Diffraction on the Measurement of Gravitationally Induced Quantum Phase Shifts by Neutron Interferometry

The proper analysis of experiments to measure the quantum-mechanical phase shift due to potential gradients such as gravity across a perfect-silicon-crystal Mach-Zehnder interferometer for neutrons is complicated by the highly dispersive nature of the dynamical diffraction process describing the propagation of neutrons through a perfect crystal. Through dynamical diffraction, a coherent monochromatic incident beam of neutrons that does not exactly satisfy the Bragg condition is split into two currents within each crystal so that there are 16 possible coherent interfering trajectories by which the neutron can traverse the interferometer. In this work, previous calculations of the effects of dynamical diffraction on gravitationally induced phase-shift measurements are extended to include effects in all exit beams and internal effects within the subbeams for both symmetric and skew-symmetric interferometers. For the interferometers used in a recent experiment in which the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of the order of 1 part in 1000, it is found that these effects predict an increase of a few percent in the magnitude of the phase shift. Additionally, some consequences on the phase and contrast of restricting the beams within and after the interferometer are discussed. Agreement of this theory with experiment and the general applicability of the model is discussed.