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Physical Review A

Neutron interferometric search for quaternions in quantum mechanics

Helmut Kaiser, E. A. George, S. Werner

Published Apr 1, 1984• 70 citations
Publisher

Abstract

Following a proposal by Asher Peres we have carried out a neutron interferometer experiment searching for quaternion noncommutative contributions to the neutron-nuclear scattering amplitude. Using slabs of Ti and Al we find that the phase shift experienced by one of the beams in our interferometer is invariant under the interchange of the two slabs to an accuracy of 1 part in 30 000.

DOI
10.1103/physreva.29.2276

Related papers

Two-wavelength-difference measurement of gravitationally induced quantum interference phases

Kenneth C. Littrell, Brendan E. Allman, S. Werner

One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.

Physical Review A•Sep 1, 1997•117 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

Observation of geometric and dynamical phases by neutron interferometry

Brendan E. Allman, Helmut Kaiser, S. A. Werner +3 more

The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.

Physical Review A•Dec 1, 1997•44 citations

Spectral filtering in neutron interferometry

S. A. Werner, R. Clothier, Helmut Kaiser +2 more

We have demonstrated experimentally that the contrast lost, due to placing slabs of a material having a neutron optical potential in one leg of a neutron interferometer, can be restored by spectral filtering of the beams leaving the interferometer immediately before detection. The non-Gaussian spectral distribution of the neutrons traversing the interferometer in our experiment leads to an unexpected phase reversal of the interferograms.

Physical Review Letters•Aug 5, 1991•33 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

Test of quantum mechanics by neutron interferometers

H. Rauch

Since its advent in 1974, the neutron interferometry technique is a powerful tool for tests of quantum mechanics by matter waves. High order interference pattern could be observed and an upper limit for nonlinear terms in the Schroedinger equation has been given. The 4..pi..-symmetry of a spinor wave function was verified in 1975. Afterwards a precision measurement of this 4..pi..-symmetry effect has been performed which yields, after corrections for the new values of the fundamental constants, a periodicity factor of ..cap alpha.. = 715.87 +- 3.8 deg which does not include the expected 720 deg within its simple error limits. Alternative formulations of quantum mechanics predict a deviation of the 4..pi..-periodicity factor in the region of strong interaction. Therefore, a precision measurement of the influence of strong interactions is proposed where the spinor rotation is observed within the region of additional strong interactions caused by a nonmagnetic material of heavy nuclei inserted alternatively into the beam paths of the interferometer. It is expected to reach an accuracy concerning the additional phase shift in the range of 10/sup -5/ which corresponds to deviation factors within the region of strong interactions of about 20% from the standard formulation. Various factors limiting themore » accuracy are discussed.« less

Hadronic J.; (United States)•Apr 1, 1982•2 citations
Following a proposal by Asher Peres we have carried out a neutron interferometer experiment searching for quaternion noncommutative contributions to the neutron-nuclear scattering amplitude. Using slabs of Ti and Al we find that the phase shift experienced by one of the beams in our interferometer is invariant under the interchange of the two slabs to an accuracy of 1 part in 30 000.
One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.
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.
The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.
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.
Since its advent in 1974, the neutron interferometry technique is a powerful tool for tests of quantum mechanics by matter waves. High order interference pattern could be observed and an upper limit for nonlinear terms in the Schroedinger equation has been given. The 4..pi..-symmetry of a spinor wave function was verified in 1975. Afterwards a precision measurement of this 4..pi..-symmetry effect has been performed which yields, after corrections for the new values of the fundamental constants, a periodicity factor of ..cap alpha.. = 715.87 +- 3.8 deg which does not include the expected 720 deg within its simple error limits. Alternative formulations of quantum mechanics predict a deviation of the 4..pi..-periodicity factor in the region of strong interaction. Therefore, a precision measurement of the influence of strong interactions is proposed where the spinor rotation is observed within the region of additional strong interactions caused by a nonmagnetic material of heavy nuclei inserted alternatively into the beam paths of the interferometer. It is expected to reach an accuracy concerning the additional phase shift in the range of 10/sup -5/ which corresponds to deviation factors within the region of strong interactions of about 20% from the standard formulation. Various factors limiting themore » accuracy are discussed.« less