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Physical Review Letters

Neutron Propagation in Moving Matter: The Fizeau Experiment with Massive Particles

A. G. Klein, G. I. Opat, Alberto Cimmino, Anton Zeilinger, W. Treimer, R. Gähler

Published Jun 15, 1981• 81 citations
Publisher

Abstract

Using a two-slit neutron interferometer, we have measured the shift of the interference pattern induced by the motion of a quartz rod. The measured shift is found to be in agreement with the quantum mechanical prediction derived from a relativity argument. Some peculiarities of the case of massive particles as compared with the classic Fizeau photon case are discussed.

DOI
10.1103/physrevlett.46.1551

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Using a two-slit neutron interferometer, we have measured the shift of the interference pattern induced by the motion of a quartz rod. The measured shift is found to be in agreement with the quantum mechanical prediction derived from a relativity argument. Some peculiarities of the case of massive particles as compared with the classic Fizeau photon case are discussed.
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.
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.
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.
Entanglement of two photons, or atoms is a complementary situation to a double slit situation of a single photon, neutron or atom. With neutrons single particle interference phenomena can be observed and the “entanglement of degrees of freedom”, i.e. contextuality can be verified. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions, and they are sensitive to topological effects, as well. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell‐type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger cat‐like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.
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.