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Physical Review Letters

Neutron Interferometric Observation of Noncyclic Phase

Apoorva G. Wagh, Veer Chand Rakhecha, Peter Fischer, A. Ioffe

Published Sep 1, 1998• 89 citations
Publisher

Abstract

Using polarized neutrons, we have determined phases as well as interference amplitudes for noncyclic spinor evolutions in static magnetic fields. Both these quantities depend on the angle subtended by the neutron spin with the field. This experiment elucidates the subtle, and widely misunderstood, concepts involved.
DOI
10.1103/physrevlett.81.1992

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Observing pancharatnam phases and amplitudes

Apoorva G. Wagh, Veer Chand Rakhecha

In the mid-l950s, Pancharamam [l] propounded an exact prescription for the phase acquired in a completely general evolution of a quanta1 system. Without any loss of generality, we highlight this phase prescription here for spin-polarized neutrons, a two-state system, and describe an interferometric experiment observing phases and associated interference amplitudes in noncyclic evolutions.

Neutron News•Jan 1, 2001•0 citations

Comment on “Neutron Interferometric Observation of Noncyclic Phase”

Rajendra Bhandari

A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].

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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
A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].
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.