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Physical Review A

Thermal-neutron propagation in moving media

U. Bonse, Andreas Rumpf

Published Feb 1, 1988• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.37.1059

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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
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\ensuremath−4{10}^{\mathrm{\ensuremath{-}}4}10\ensuremath−4 of the incident wave amplitude. Energy changes amount to 4\ifmmode\times\else\texttimes\fi{}10\ensuremath−3{10}^{\mathrm{\ensuremath{-}}3}10\ensuremath−3 (reflected waves) and to less than 10\ensuremath−6{10}^{\mathrm{\ensuremath{-}}6}10\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.
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.
Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.
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.
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.
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.