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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Dynamical diffraction effects in noninertial neutron interferometry

U. Bonse, Thomas Wroblewski

Published Sep 15, 1984• 41 citations
Publisher

Abstract

Neutron interferometry performed in a noninertial frame is essentially influenced by dynamical diffraction effects occurring in the interferometer crystal which hitherto have not been taken into account. We have developed a corresponding theory from which a corrected phase shift is obtained which applies likewise to interferometry performed under the influence of gravity or on an accelerated neutron interferometer. The theory also predicts fading of interference contrast with increasing acceleration as was observed in the Colella-Overhauser-Werner gravity experiments but could not be explained unambiguously.

DOI
10.1103/physrevd.30.1214

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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
Neutron interferometry performed in a noninertial frame is essentially influenced by dynamical diffraction effects occurring in the interferometer crystal which hitherto have not been taken into account. We have developed a corresponding theory from which a corrected phase shift is obtained which applies likewise to interferometry performed under the influence of gravity or on an accelerated neutron interferometer. The theory also predicts fading of interference contrast with increasing acceleration as was observed in the Colella-Overhauser-Werner gravity experiments but could not be explained unambiguously.
Neutron interferometry has been performed on an accelerated interferometer under conditions where gravitational effects on the interfering beams very nearly compensate each other. The observed neutron phase shift is found to be in excellent agreement with that calculated from Schr\"odinger's equation transformed to the accelerated frame where it is found essential to include the spherical wave aspect. The present experiment thus verifies the validity of the classical transformation laws for noninertial frames also in the quantum limit.
The authors discuss the coherence properties of neutron scattering from perfect crystals and apply them to the splitting and coherent recombination of a neutron beam in a Laue-type interferometer. They also point out the difference between neutron and x-ray scattering in such devices and discuss the effect of a relative displacement of the various interferometer slabs on the fringe pattern. All this can be done without using the detailed dynamical theory of x-ray scattering. Various experiments are discussed, especially the neutron-gravity experiment of Colella, Overhauser, and Werner, which is analyzed both in the laboratory frame and in a frame freely falling with the neutron beam. The older electron diffraction experiment of Marton et al., and its relevance to the Aharonov---Bohm effect, is also discussed and reinterpreted, because the standard interpretation is not consistent with the results of the neutron experiment. An Appendix presents a general discussion of the transformation to a uniformly accelerated reference frame, as a guide to help analyze future such experiments.
Dynamical diffraction leads to an interesting, unavoidable set of interference effects for neutron interferometers. This experiment studies the interference signal from two and three successive Bragg diffractions in the Laue geometry. We find that intrinsic Bragg-plane misalignment in monolithic, "perfect" silicon neutron interferometers is relevant between successive diffracting crystals, as well as within the Borrmann fan for typical interferometer geometries. We show that the dynamical phase correction employed in the Colella, Overhauser, and Werner gravitationally induced quantum interference experiments is attenuated by slight, intrinsic misalignments between diffracting crystals, potentially explaining the long-standing 1% discrepancy between theory and experiment. This systematic may also impact precision measurements of the silicon structure factor, affecting previous and future measurements of the Debye-Waller factor and neutron-electron scattering length as well as potential fifth-force searches. For the interferometers used in this experiment, Bragg planes of different diffracting crystals were found to be misaligned by 10 to 40 nrad.
The phase shift in interferometry due to the space-time curvature is computed in nonrelativistic and relativistic physics. This treatment is applied to an interferometer analogous to the perfect crystal interferometer used in the Colella-Overhauser-Werner experiment with thermal neutrons, an interferometer consisting of only horizontal mirrors, suitable for ultracold neutrons, and optical interferometry. Experiments are proposed to detect the effect of the tidal forces of the Earth, Moon, and the Sun, for the first time in interferometry. The phase shift in neutron interferometry due to terrestrial objects is considered and an experiment is proposed with superfluid helium as the source of gravity. This would provide, for the first time, direct evidence concerning the gravitational interaction between two quantum-mechanical states. The possibility of detecting purely general-relativistic effects due to curvature, by means of neutron interferometry, is also explored.
The proper analysis of experiments to measure the quantum-mechanical phase shift due to potential gradients such as gravity across a perfect-silicon-crystal Mach–Zehnder interferometer for neutrons is complicated by the highly dispersive nature of the dynamical diffraction process describing the propagation of neutrons through a perfect crystal. Through dynamical diffraction, a coherent monochromatic incident beam of neutrons that does not exactly satisfy the Bragg condition is split into two currents within each crystal so that there are 16 possible coherent interfering trajectories by which the neutron can traverse the interferometer. In this work, previous calculations of the effects of dynamical diffraction on gravitationally induced phase-shift measurements are extended to include effects in all exit beams and internal effects within the subbeams for both symmetric and skew-symmetric interferometers. For the interferometers used in a recent experiment in which the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of the order of 1 part in 1000, it is found that these effects predict an increase of a few percent in the magnitude of the phase shift. Additionally, some consequences on the phase and contrast of restricting the beams within and after the interferometer are discussed. Agreement of this theory with experiment and the general applicability of the model is discussed.
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.