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Physical Review A

Observation of a motion-induced phase shift of neutron de Broglie waves passing through matter near a nuclear resonance

M. Arif, Helmut Kaiser, R. Clothier, S. Werner, W. A. Hamilton, Alberto Cimmino, Andrew G. Klein

Published Feb 1, 1989• 20 citations
Publisher

Abstract

We report the results of a neutron interferometry experiment where for the first time (to our knowledge) a phase shift of a neutron de Broglie wave induced by moving matter has been successfully measured. This experiment is the quantum-mechanical analog of the optical Fizeau effect. The observed phase shift is caused by the motion of matter itself, and not by the motion of its boundaries. The experimental results are found to be in good agreement with the theoretical predictions. Some unexpected and previously unreported neutron wave interference effects observed during the experiment are also reported.

DOI
10.1103/physreva.39.931

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We report the results of a neutron interferometry experiment where for the first time (to our knowledge) a phase shift of a neutron de Broglie wave induced by moving matter has been successfully measured. This experiment is the quantum-mechanical analog of the optical Fizeau effect. The observed phase shift is caused by the motion of matter itself, and not by the motion of its boundaries. The experimental results are found to be in good agreement with the theoretical predictions. Some unexpected and previously unreported neutron wave interference effects observed during the experiment are also reported.
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One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.
The effects of a moving medium on the phase of a massive particle are studied theoretically. The discussion explains a recently published Fizeau-type neutron-interferometer experiment. It is shown explicitly that the physics of this experiment can be described either as a manifestation of a time-dependent potential in the Schr\"odinger equation or as a verification of the Galilean-transformation properties of Schr\"odinger waves. An intriguing consequence of these considerations is that for most materials no Fizeau phase shift occurs if the boundaries of the moving medium are at rest. However, we point out that such would not be the case in an experiment involving a medium whose potential is velocity dependent.
The phase shift of matter wave due to the Earth's rotation and gravity has been demonstrated in the neutron-interferometry experiments where the Bragg reflection of the neutron wave from crystals is used to form a closed path. In the literature, the rotation-induced phase shift is ascribed to an extra energy term associated with angular momentum in the Hamiltonian. In this investigation, based on a classical treatment of the collision of neutrons with the lattice planes, the modifications in the particle velocity due to the Earth's rotation as well as those due to gravity are calculated. Then, in conjunction with the relation between the particle velocity and the propagation vector of matter wave, it is shown that the corresponding phase shifts in matter wave are in accord with the interference experiments. Thereby, based on the velocity modification due to collision, a reinterpretation of the effects of the Earth's rotation and gravity on the neutron-wave interference is presented. Meanwhile, a null effect of the Earth's orbital motion is predicted.