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Physical Review A

Null Fizeau effect for thermal neutrons in moving matter

M. Arif, Helmut Kaiser, S. Werner, Alberto Cimmino, W. A. Hamilton, A. G. Klein, G. I. Opat

Published Feb 1, 1985• 53 citations
Publisher

Abstract

We have carried out an interferometer experiment to determine the phase shift of slow neutrons caused by the motion of a material medium. Within experimental error, we confirm the theoretical prediction of a null result for the case when the medium moves inside stationary boundaries. Upper limits on the energy dependence of neutron-nucleus potential and on the wavelength dependence of s-wave neutron scattering lengths are deduced.

DOI
10.1103/physreva.31.1203

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Abstract The fundamental dual nature of neutrons –sometimes a particle (when detected) and sometimes a wave (when traversing the interferometer) – is wonderfully mani-fested by the non-local nature of the neutron interferometry experiments discussed in this chapter. We begin with a discussion of the series of experiments, called gravitationally induced quantum interference, in Section 7.1. Then in Section 7.2, the effect of the Earth’s rotation on the phase of a neutron de Broglie wave is described. This is the quantum mechanical analogue of the Michelson et al. (1925) experiment with light. An experiment in which this Sagnac phase shift was observed due to rotation of the interferometer on a turntable phase within the laboratory frame is also discussed (Atwood et al. 1984). An experiment related to the small effective mass of the neutron propagating in a crystal under Bragg reflecting conditions and its deflection due to the Coriolis force is discussed in Section 7.2.3 (Raum et al. 1997). Acceleration-induced interference, which is related to the gravity experiments by the principle of equivalence, is discussed in Section 7.3 (Bonse and Wroblewski 1983). Phase shifts caused by the motion of matter within the interferometer are related to the optical Fizeau effect. Several neutron Fizeau-type experiments are discussed in Section 7.4.

•Aug 10, 2000•1 citation
We have carried out an interferometer experiment to determine the phase shift of slow neutrons caused by the motion of a material medium. Within experimental error, we confirm the theoretical prediction of a null result for the case when the medium moves inside stationary boundaries. Upper limits on the energy dependence of neutron-nucleus potential and on the wavelength dependence of s-wave neutron scattering lengths are deduced.
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.
For thermal neutrons we have measured the Fizeau effect to 1.5% accuracy. The quoted accuracy was achieved by use of a newly designed neutron interferometer. Four fast-moving samples, all parts of a single, four-winged, aluminum, rotating propeller, could be made to engage simultaneously in the interfering beams. Our experiment complements and exceeds two recent Fizeau experiments, one of which was performed with cold neutrons and much lower accuracy and the other with a moving medium inside stationary boundaries resulting in a null Fizeau effect.
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.
Energies, wave vectors, and amplitudes of waves that are generated when a neutron is incident onto a moving parallel-sided plate are calculated by solving Schr\"odinger's equation. It is shown that the wave entering the plate and those reflected at the plate surfaces suffer energy (frequency) changes due to ``inelastic'' interaction with the moving plate. The motion-induced phase shift caused by such a plate in a neutron interferometer is evaluated, including the contribution which arises in the presence of dispersion of the coherent scattering length, e.g., near a resonance or as a result of local-field effects. With thermal neutrons the amplitudes of reflected waves are about ${10}^{\mathrm{\ensuremath{-}}4}$ of the incident wave amplitude. Energy changes amount to 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ (reflected waves) and to less than ${10}^{\mathrm{\ensuremath{-}}6}$ (entering wave) for neutrons with a 4-A\r{} wavelength. Nonlinear contributions to the interferometric phase shift have to be taken into account when the plate and/or the medium velocity exceed 1% of the neutron velocity.
Abstract The fundamental dual nature of neutrons –sometimes a particle (when detected) and sometimes a wave (when traversing the interferometer) – is wonderfully mani-fested by the non-local nature of the neutron interferometry experiments discussed in this chapter. We begin with a discussion of the series of experiments, called gravitationally induced quantum interference, in Section 7.1. Then in Section 7.2, the effect of the Earth’s rotation on the phase of a neutron de Broglie wave is described. This is the quantum mechanical analogue of the Michelson et al. (1925) experiment with light. An experiment in which this Sagnac phase shift was observed due to rotation of the interferometer on a turntable phase within the laboratory frame is also discussed (Atwood et al. 1984). An experiment related to the small effective mass of the neutron propagating in a crystal under Bragg reflecting conditions and its deflection due to the Coriolis force is discussed in Section 7.2.3 (Raum et al. 1997). Acceleration-induced interference, which is related to the gravity experiments by the principle of equivalence, is discussed in Section 7.3 (Bonse and Wroblewski 1983). Phase shifts caused by the motion of matter within the interferometer are related to the optical Fizeau effect. Several neutron Fizeau-type experiments are discussed in Section 7.4.