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.
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.
Quantum theory provides us with the best account of microscopic components of matter as well as of radiation. It was introduced in the twentieth century and has experienced a wide range of success. Although the theory’s probabilistic predictions of final experimental outcomes is found to be correct with high precision, there is no general consensus regarding what is actually going on with a quantum system “en route”, or rather the perceivable intermediate behavior of a quantum system, e.g., the particle’s behavior in the double-slit experiment. Neutron interferometry using single silicon perfect crystals is established as a versatile tool to test fundamental phenomena in quantum mechanics, where an incident neutron beam is coherently split in two or three beam paths with macroscopic separation of several centimeters. Here, we present quantum optical experiments with these matter-wave interferometers, studying the effect of the quantum Cheshire Cat in some variants, the neutron’s presence in the paths of the interferometer as well as the direct test of a commutation relation. To reduce disturbances induced by the measurement, the interaction strength is lessened and so-called weak interactions are exploited by employing pre- and post-selection procedures. All results of the experiments confirm the predictions of quantum theory; the observed behaviors of the neutron between the pre- and post-selection in space and time emphasize striking and counter-intuitive aspects of quantum theory.
The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivations and explanations. The basic ideas and results of interference experiments related to coherence and decoherence of matter waves and certain post-selection variations, gravitationally induced quantum phase shifts, Berry's geometrical phases, spinor symmetry and spin superposition, and Bell's inequalities are all discussed and explained in this book. Both the scalar and vector Aharonov-Bohm topological interference effects and the neutron version of the Sagnac effect are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are also topics of this book. It includes the theoretical underpinning as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The observed phase shifts due to the Earth's gravity and rotation indicate a close connection to relativity theory. Neutron interferometry can be considered as a central technique of quantum optics with massive particles. It has stimulated the development of interferometry with atoms, molecules and clusters. The book is written in a style that will be suitable at the senior undergraduate and beginning of graduate level. It will interest and excite many students and researchers in neutron, nuclear, quantum, gravitational, optical, and atomic physics. Lecturers teaching courses in modern physics and quantum mechanics will find a number of interesting and historic experiments they may want to include in their lectures.
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.
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.
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.
In recent years there has been enormous progress in matter wave interferometry. The Colella-Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer are the prototypes of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question as to what extent the gravitational redshift and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the nonvanishing, nonrelativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.