Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Reviews of Modern Physics

Coherence effects in neutron diffraction and gravity experiments

Daniel M. Greenberger, A. W. Overhauser

Published Jan 1, 1979• 188 citations
Publisher

Abstract

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.

DOI
10.1103/revmodphys.51.43

Related papers

Dynamical diffraction effects in noninertial neutron interferometry

U. Bonse, Thomas Wroblewski

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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 15, 1984•41 citations

The Effects of Dynamical Diffraction on the Measurement of Gravitationally Induced Quantum Phase Shifts by Neutron Interferometry

Kenneth C. Littrell, Brendan E. Allman, Olexei I. Motrunich +1 more

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.

Acta Crystallographica Section A Foundations of Crystallography•Sep 1, 1998•11 citations

Neutron interferometer crystallographic imperfections and gravitationally induced quantum interference measurements

B. Heacock, M. Arif, Robert W. Haun +3 more

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.

Physical Review A•Jan 25, 2017•15 citations

Neutron Interferometry: Lessons in Experimental Quantum Mechanics

H Rauch and S Werner

The first successful operation of a perfect crystal neutron interferometer by Rauch, Treimer and Bonse (1974) in Vienna opened up new vistas; intricate quantum mechanical concepts that could only be dealt with in thought experiments during the Einstein-Bohr era, now became accessible to direct tests in the laboratory. In the following decade, Helmut Rauch and co-workers implemented interferometric verifications of 4π spinor symmetry, up-down spin superposition and stochastic versus deterministic absorption. On the other side of the Atlantic, Colella, Overhauser and Werner (COW 1975) made the first observation of a quantal phase produced by the weak force of gravity. Samuel Werner and co-workers proceeded to observe the Sagnac, AC and scalar AB effects. The field proliferated and became the subject matter of several conferences and review articles. A book on the topic, however, was not yet available. The two stalwarts, Rauch and Werner, have now spent four painstaking years writing Neutron Interferometry: Lessons in Experimental Quantum Mechanics, a `yearbook' comprising 365 pages of documentation followed by a 25-page reference list. The book presents this advanced subject from the experimenter's viewpoint, in keeping with the latter half of its title, at an elementary level suitable for graduate students. For teachers and researchers, the book should serve as a ready-reference reckoner for the broad range of topics covered. The book begins by bringing out the analogy between neutron optics and photon optics, illustrated with results of milestone neutron experiments. It surveys various types of neutron interferometers, providing details of perfect crystal interferometer set-ups at ILL, MURR and NIST. All known interactions of the neutron are succinctly reviewed and their observations described. Coherence properties of neutron beams are characterized in the light of partial beam detection and post-selection experiments. An in-depth portrayal of Rauch and Werner's own experiments, whether verifying counterintuitive quantal phenomena such as the up-down spin superposition, the AC and scalar AB effects or observing phases originating from the Earth's gravitation and rotation and from longitudinal and transverse motion of the medium, is made with insight. The first experimental separation of geometric and dynamical phases as well as the observation of noncyclic phases and amplitudes are briefly touched upon. The book provides a gist of interferometric tests of quantum features ranging from linearity of the Schrodinger equation to Bell nonlocality. Applications to condensed matter physics, neutron diffraction in single crystals and various interpretations of quantum mechanics are also described. Numerous references to related fields, e.g. atom interferometry, nuclear physics, general relativity and geometric phase, have been cited for the interested reader. It is a pity that such a beautiful book is not free of blemishes. The book credits the Vienna group (1997) with a direct polarimetric(!) verification of Pauli anticommutation (p 75), though polarimetry is incapable of sensing a π phase shift implied by anticommutation. Rauch and Werner persist with the Vienna group's incorrect claims on geometric phase, made in 1990 (p 206), 1994 (pp 186, 203) and 1996 (p 15, pp 206-10). The list of neutron interferometry experiments (p 15) is known within the interference community as the USA [Uncle Sam (Werner)'s Ad]. While incorrectly including the Vienna-Berlin (1996) work as a `topological phase' observation, the list leaves out several landmark achievements of neutron interferometry. The first direct verification of Pauli anticommutation (1997) and the first observation of Pancharatnam amplitudes and phases in noncyclic evolutions (1998) are just two of the glaring omissions. The 1993 erratum (Phys. Rev. Lett. 70 250) to the Missouri-Melbourne (1992) paper (p 194) on the scalar AB effect is conspicuous by its absence. The book cites a 1999 criticism (p 204) of the neutron interferometric observation of noncyclic phases, but turns a Nelson's eye to the accompanying reply (Phys. Rev. Lett. 83 2090 (1999)). Incidentally, the experiment was performed with polarized neutrons - as it ought to be - and not unpolarized neutrons, as the book states. Overhauser and Colella's classic 1974 paper (Phys. Rev. Lett. 33 1237) - a precursor to the COW (1975) experiment proper - gets disposed of in three words (p 211) and vanishes mysteriously from the list of references. The invocation of the `Feynman-Dirac prescription' (p 215) is inappropriate. The most serious `lapse' appears in Section 8.12 (pp 268-74). Wagh and Rakhecha 1997 (p 273) were the first to derive the exact spinor evolution for polarized neutrons accelerating in uniform electric and magnetic fields, and to disprove the conclusion of Casella and Werner 1992 (p 269). Rauch and Werner's book omits to acknowledge this fact and offers `its own' explanation of the phenomenon in Figs 8.6 and 8.7, based on ideas borrowed directly from Figs 4 and 2 respectively in Wagh and Rakhecha (1997). Barring such lapses, and a number of typographical errors*, Rauch and Werner have completed their Herculean task admirably to come up with this comprehensive sourcebook on neutron interferometry and its contributions to the epistemological understanding of the quantum world. The Oxford University Press has produced the book with its customary high-quality standards. The book has a smart appearance and an attractive front cover, adorned by a famous New Yorker cartoon depicting a skizzical quantal sojourn past a tree. I have no hesitation in recommending Neutron Interferometry as a must-read book to young and old physicists and philosophers hailing from a wide spectrum of disciplines. The book has already occupied pride of place on the shelf of every practitioner of neutron interferometry. So happy reading, experimenters and theoreticians - and happier interfering! Apoorva G Wagh *Use of the symbol δ to represent a partial differential (pp 2, 21), the incorrect sign for a power of 10 in Table 1.2 (p 3), a value close to unity cited for 1 - n (p 8), the word charge(s) misprinted as `change(s)' (p 193) and missing exponents ½ and 2 in Eqs (7.49) and (7.51) respectively (p 242) provide a random sample of the typographical errors in the book.

Measurement Science and Technology•Feb 16, 2001•83 citations

Neutron interferometric tests of quantum mechanics

H. Rauch

Since the invention of perfect crystal neutron interferometry this technique has become an important tool in the realization of many textbook experiments in quantum mechanics. Widely separated coherent beams of thermal neutrons are produced and superposed by dynamical Bragg diffraction from a properly shaped perfect crystal. The observed interference patterns show the characteristic coherence properties of matter waves which arc influenced by the individual particle and by the properties of the experimental device. The verification of the 4π-periodicity of spinor wavefunctions and the realization of thc spin-superposition experiment on B macroscopic scale has become feasible by this technique. A new kind of a quantum beat effect with an energy sensitivity of 2.7 × 20−-19 eV has been observed in a double coil resonance experiment. The influence of gravity and of the Earth's rotation on the wavefunction become visible at a level of an elementary particle with non-zero mass. All the results are in agreement with the formulation of quantum mechanics but, nevertheless, they stimulate discussion about its interpretation. The particle-wave dualism becomes obvious on a macroscopic scale and with a beam of massive particles.

Contemporary Physics•Jul 1, 1986•28 citations

The neutron interferometer as a device for illustrating the strange behavior of quantum systems

Daniel M. Greenberger

The neutron interferometer is a unique instrument that allows one to construct a neutron wave packet of macroscopic size, divide it into two components separated by centimeters, and then coherently recombine them. A number of experiments clearly showing the difference between quantum and classical theory have been performed with it, which are suitable for presentation in elementary quantum courses. This article presents a simple mathematical model of the interferometer, which can be used to illustrate clearly many of the surprising features of quantum systems. For example, one can describe an experiment to determine which component beam the neutron takes (an analog of the two-slit electron experiment). One can then trace in detail the loss of coherence of the wave function, rather than merely invoke the usual "handwaving" uncertainty arguments. The author discusses the effect of gravity on the neutron beam [the classic COW (Colella, Overhauser, and Werner) experiment], including a simple analysis in an accelerated reference frame, and its relation to the equivalence principle, the red shift, and the twin paradox. Also described are the effect of rotation of the neutron by 360\ifmmode^\circ\else\textdegree\fi{} to change its phase, the effect on the wave function of measuring the absence of the particle from a beam ("Dicke's paradox"), and a realizable version of Wheeler's "delayed-choice" experiments, as well as their relation to the problem of "Schr\"odinger's cat." The treatment is suitable for bright undergraduates and first-year graduate students.

Reviews of Modern Physics•Oct 1, 1983•144 citations
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.
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.
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.
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 first successful operation of a perfect crystal neutron interferometer by Rauch, Treimer and Bonse (1974) in Vienna opened up new vistas; intricate quantum mechanical concepts that could only be dealt with in thought experiments during the Einstein-Bohr era, now became accessible to direct tests in the laboratory. In the following decade, Helmut Rauch and co-workers implemented interferometric verifications of 4π spinor symmetry, up-down spin superposition and stochastic versus deterministic absorption. On the other side of the Atlantic, Colella, Overhauser and Werner (COW 1975) made the first observation of a quantal phase produced by the weak force of gravity. Samuel Werner and co-workers proceeded to observe the Sagnac, AC and scalar AB effects. The field proliferated and became the subject matter of several conferences and review articles. A book on the topic, however, was not yet available. The two stalwarts, Rauch and Werner, have now spent four painstaking years writing Neutron Interferometry: Lessons in Experimental Quantum Mechanics, a `yearbook' comprising 365 pages of documentation followed by a 25-page reference list. The book presents this advanced subject from the experimenter's viewpoint, in keeping with the latter half of its title, at an elementary level suitable for graduate students. For teachers and researchers, the book should serve as a ready-reference reckoner for the broad range of topics covered. The book begins by bringing out the analogy between neutron optics and photon optics, illustrated with results of milestone neutron experiments. It surveys various types of neutron interferometers, providing details of perfect crystal interferometer set-ups at ILL, MURR and NIST. All known interactions of the neutron are succinctly reviewed and their observations described. Coherence properties of neutron beams are characterized in the light of partial beam detection and post-selection experiments. An in-depth portrayal of Rauch and Werner's own experiments, whether verifying counterintuitive quantal phenomena such as the up-down spin superposition, the AC and scalar AB effects or observing phases originating from the Earth's gravitation and rotation and from longitudinal and transverse motion of the medium, is made with insight. The first experimental separation of geometric and dynamical phases as well as the observation of noncyclic phases and amplitudes are briefly touched upon. The book provides a gist of interferometric tests of quantum features ranging from linearity of the Schrodinger equation to Bell nonlocality. Applications to condensed matter physics, neutron diffraction in single crystals and various interpretations of quantum mechanics are also described. Numerous references to related fields, e.g. atom interferometry, nuclear physics, general relativity and geometric phase, have been cited for the interested reader. It is a pity that such a beautiful book is not free of blemishes. The book credits the Vienna group (1997) with a direct polarimetric(!) verification of Pauli anticommutation (p 75), though polarimetry is incapable of sensing a π phase shift implied by anticommutation. Rauch and Werner persist with the Vienna group's incorrect claims on geometric phase, made in 1990 (p 206), 1994 (pp 186, 203) and 1996 (p 15, pp 206-10). The list of neutron interferometry experiments (p 15) is known within the interference community as the USA [Uncle Sam (Werner)'s Ad]. While incorrectly including the Vienna-Berlin (1996) work as a `topological phase' observation, the list leaves out several landmark achievements of neutron interferometry. The first direct verification of Pauli anticommutation (1997) and the first observation of Pancharatnam amplitudes and phases in noncyclic evolutions (1998) are just two of the glaring omissions. The 1993 erratum (Phys. Rev. Lett. 70 250) to the Missouri-Melbourne (1992) paper (p 194) on the scalar AB effect is conspicuous by its absence. The book cites a 1999 criticism (p 204) of the neutron interferometric observation of noncyclic phases, but turns a Nelson's eye to the accompanying reply (Phys. Rev. Lett. 83 2090 (1999)). Incidentally, the experiment was performed with polarized neutrons - as it ought to be - and not unpolarized neutrons, as the book states. Overhauser and Colella's classic 1974 paper (Phys. Rev. Lett. 33 1237) - a precursor to the COW (1975) experiment proper - gets disposed of in three words (p 211) and vanishes mysteriously from the list of references. The invocation of the `Feynman-Dirac prescription' (p 215) is inappropriate. The most serious `lapse' appears in Section 8.12 (pp 268-74). Wagh and Rakhecha 1997 (p 273) were the first to derive the exact spinor evolution for polarized neutrons accelerating in uniform electric and magnetic fields, and to disprove the conclusion of Casella and Werner 1992 (p 269). Rauch and Werner's book omits to acknowledge this fact and offers `its own' explanation of the phenomenon in Figs 8.6 and 8.7, based on ideas borrowed directly from Figs 4 and 2 respectively in Wagh and Rakhecha (1997). Barring such lapses, and a number of typographical errors*, Rauch and Werner have completed their Herculean task admirably to come up with this comprehensive sourcebook on neutron interferometry and its contributions to the epistemological understanding of the quantum world. The Oxford University Press has produced the book with its customary high-quality standards. The book has a smart appearance and an attractive front cover, adorned by a famous New Yorker cartoon depicting a skizzical quantal sojourn past a tree. I have no hesitation in recommending Neutron Interferometry as a must-read book to young and old physicists and philosophers hailing from a wide spectrum of disciplines. The book has already occupied pride of place on the shelf of every practitioner of neutron interferometry. So happy reading, experimenters and theoreticians - and happier interfering! Apoorva G Wagh *Use of the symbol δ to represent a partial differential (pp 2, 21), the incorrect sign for a power of 10 in Table 1.2 (p 3), a value close to unity cited for 1 - n (p 8), the word charge(s) misprinted as `change(s)' (p 193) and missing exponents ½ and 2 in Eqs (7.49) and (7.51) respectively (p 242) provide a random sample of the typographical errors in the book.
Since the invention of perfect crystal neutron interferometry this technique has become an important tool in the realization of many textbook experiments in quantum mechanics. Widely separated coherent beams of thermal neutrons are produced and superposed by dynamical Bragg diffraction from a properly shaped perfect crystal. The observed interference patterns show the characteristic coherence properties of matter waves which arc influenced by the individual particle and by the properties of the experimental device. The verification of the 4π-periodicity of spinor wavefunctions and the realization of thc spin-superposition experiment on B macroscopic scale has become feasible by this technique. A new kind of a quantum beat effect with an energy sensitivity of 2.7 × 20−-19 eV has been observed in a double coil resonance experiment. The influence of gravity and of the Earth's rotation on the wavefunction become visible at a level of an elementary particle with non-zero mass. All the results are in agreement with the formulation of quantum mechanics but, nevertheless, they stimulate discussion about its interpretation. The particle-wave dualism becomes obvious on a macroscopic scale and with a beam of massive particles.
The neutron interferometer is a unique instrument that allows one to construct a neutron wave packet of macroscopic size, divide it into two components separated by centimeters, and then coherently recombine them. A number of experiments clearly showing the difference between quantum and classical theory have been performed with it, which are suitable for presentation in elementary quantum courses. This article presents a simple mathematical model of the interferometer, which can be used to illustrate clearly many of the surprising features of quantum systems. For example, one can describe an experiment to determine which component beam the neutron takes (an analog of the two-slit electron experiment). One can then trace in detail the loss of coherence of the wave function, rather than merely invoke the usual "handwaving" uncertainty arguments. The author discusses the effect of gravity on the neutron beam [the classic COW (Colella, Overhauser, and Werner) experiment], including a simple analysis in an accelerated reference frame, and its relation to the equivalence principle, the red shift, and the twin paradox. Also described are the effect of rotation of the neutron by 360\ifmmode^\circ\else\textdegree\fi{} to change its phase, the effect on the wave function of measuring the absence of the particle from a beam ("Dicke's paradox"), and a realizable version of Wheeler's "delayed-choice" experiments, as well as their relation to the problem of "Schr\"odinger's cat." The treatment is suitable for bright undergraduates and first-year graduate students.