Gravitational and Coriolis forces in crystal neutron interferometry. I. Theory

The proof that neutron interference is possible using split-crystal interferometers opens the way to extended arm separation and length and to new experiments exploring quantum mechanics and gravity. Therefore, this paper reexamines the effect of gravitational and Coriolis forces on the Laue diffraction of neutrons by perfect crystals and the operation of crystal interferometers. We give in analytical form the transfer matrices for the propagation of the neutron quantum state, either pure or mixed and subjected to gravity and Coriolis force, in free space and perfect crystals. They are used to study the effect of interferometer aberrations on the quantum-mechanical phase due to the Earth's gravity. We also give an alternative way to understand the impact of gravitational and Coriolis forces in terms of the crystal displacements and tilts perceived by the neutron.