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 p hase shift due to potential gradients such as gravity across a perfect -silicon-crystal Mach-Zehnder interferometer for neutrons is complicat ed by the highly dispersive nature of the dynamical diffraction proces s describing the propagation of neutrons through a perfect crystal. Th rough dynamical diffraction, a coherent monochromatic incident beam of neutrons that does not exactly satisfy the Bragg condition is split i nto two currents within each crystal so that there are 16 possible coh erent interfering trajectories by which the neutron can traverse the i nterferometer. In this work, previous calculations of the effects of d ynamical diffraction on gravitationally induced phase-shift measuremen ts are extended to include effects in all exit beams and internal effe cts within the subbeams for both symmetric and skew-symmetric interfer ometers. For the interferometers used in a recent experiment in which the gravitationally induced phase shift of the neutron is measured wit h a statistical uncertainty of the order of 1 part in 1000, it is foun d that these effects predict an increase of a few percent in the magni tude of the phase shift. Additionally, some consequences on the phase and contrast of restricting the beams within and after the interferome ter are discussed. Agreement of this theory with experiment and the ge neral applicability of the model is discussed.