Neutron Interferometry: Lessons in Experimental Quantum Mechanics

by Helmut Rauch and Samuel A. Werner
448 pp. Clarendon Press, Oxford, 2000

Reviewed in American Journal of Physics by Mark P. Silverman

It is all too easy, when one reads standard textbooks of quantum mechanics, to focus so intently on abstract state vectors in Hilbert space or on mathematical techniques for solving the Schrödinger equation, that one loses track of (or perhaps never encounters) the fascinating experiments on real physical particles for which the principles of quantum mechanics are required. Neutron Interferometry helps motivate the theoretical side of quantum mechanical instruction by disclosing a world of experimental detail, centered on the neutron, that calls for and tests the principles of quantum theory. The book is not a textbook, but I have recently used it, together with my own book on the quantum interference of electrons (both free and bound in atoms), for instructive, thought-provoking examples - some for mathematical analysis, others for qualitative discussion - in a junior-senior level course of quantum mechanics.

The authors, who have, both independently and in collaboration, made pioneering contributions to neutron interferometry, begin with the analogy between neutron optics and light optics, and from there develop seminal concepts relating to coherence, diffraction, and interference. I find this approach congenial to my own way of teaching quantum mechanics, which, in brief, is to begin with the analogy to classical optics rather than with ties to classical mechanics. In this way, students may find that certain aspects of quantum mechanics are not as unintuitive as physics popularizers, or even quantum mechanics teachers, are wont to claim, if by "intuitive" one means the capacity to predict qualitatively the behavior of a system on the basis of past experience. With classical optics (instead of classical mechanics) as past experience, a variety of single-particle quantum phenomena, e.g. those involving step potentials, barriers, and wells, become reasonably intuitive.

Although quantum mechanics takes its name from the discreteness - quantization - of energy, angular momentum, and other dynamical observables, I believe a good case can be made (and I have made it elsewhere) that what distinguishes quantum mechanics most from classical mechanics is superposition and interference. If interference is to occur, then the superposing waves (or states) must exhibit some degree of coherence. Ironically, for all its fundamentality as the concept underlying quantum interference, I have not found many quantum mechanics textbooks in which the term coherence even appears in the index (apart, perhaps, from the topic of coherent oscillator states), let alone in the discussion of interference phenomena. Students all too frequently may be left with an erroneous impression that it is the de Broglie wavelength that sets the size scale for objects or apertures to give rise to interference effects. By contrast, Neutron Interferometry gives a thorough discussion of the important coherence parameters (longitudinal coherence length, transverse coherence length, coherence volume, coherence time, and so forth) that enter into an analysis of quantum interference, as well as experimental procedures for measuring these coherence parameters in the case of neutron beams.

For readers looking for satisfyingly detailed descriptions of quantum interference phenomena, Neutron Interferometry is a gold mine of illustrative examples. As in my own book whose title asserts that, contrary to Feynman's oft-quoted remark, there is more to the "mystery" of quantum mechanics than two-slit interference, Rauch and Werner outline the basic theory and experimental features of various inequivalent categories of quantum interference phenomena involving spin superposition, topological phase, gravitational and noninertial effects, nonlinearity of the Schrödinger equation, particle-antiparticle oscillations, quantum statistics, quantum entanglement, and much more. Some of these examples are experiments that have already been done (in fact, many years ago), and others are speculative experiments waiting for appropriate advances in technology. Because book reviews are expected to be reasonably brief, I will comment on only a few of the numerous experiments that have interested me most and which represent quantum interference phenomena conceptually different from the standard example of two-slit interference that one encounters most often in textbooks.

The Aharonov-Bohm (AB) effect is a quantum interference effect that depends on spatial topology and can be manifested only by particles endowed with electric charge. A split electron beam, for example, made to pass in field-free space around (and not through) a region of space within which is a confined magnetic flux, will, upon recombination, exhibit a flux-dependent pattern of fringes. Thus, by a judicious adjustment of the magnetic flux, one can produce an interference minimum in the forward direction, even though the optical path length difference of the two beam components is null. The electrons do not experience a magnetic field locally, and therefore are not acted upon by a classical Lorentz force. As neutral particles, neutrons do not exhibit what is traditionally regarded as the AB effect. However, neutrons have a magnetic moment and give rise to a companion topological phenomenon known as the Aharonov-Casher (AC) effect. In the latter, a split neutron beam is made to pass around a region of space within which is a confined electric charge and, upon recombination, gives rise to a charge-dependent interference pattern. The experimental confirmation of this effect, which may be interpreted as an example of spin-orbit coupling, was performed at the University of Missouri Research Reactor in 1991. Rauch and Werner summarize the theoretical interpretations and experimental features of the AC effect and its variants very well.

All particles, quantum as well as classical, are subject to the attractive force of gravity. In quantum mechanics, however, potential differences in the absence of classical forces can give rise to quantum interference effects (as just illustrated above in the case of a topological phase). In their book, the authors describe the so-called COW experiments (for Colella-Overhauser-Werner) in which a beam of neutrons, coherently split into two components moving parallel, but displaced vertically from one another, are recombined to yield an interference pattern that depends on the gravitational potential difference of the two beams. Here is an example where, ideally, the net work done by gravity on the two beams is the same, as well as is the optical path length difference of the two beams. There is a gravitationally-induced quantum interference in the absence of a net gravitational force. Quite by chance, I was lecturing on the COW experiments to my quantum mechanics class at about the time (2002) when the first experiments reporting the quantization of neutron energy states in a gravitational field were reported in Nature - an experiment that I hope will be included in the next edition of this book.

The AB, AC, and COW experiments are examples of single-particle self-interference. Among the entries in the chapter on "forthcoming and speculative experiments" is the neutron analogue of the optical Hanbury Brown-Twiss (HBT) experiments that demonstrated the correlated "wave noise" in chaotic light. From a quantum perspective, such correlations are known as photon bunching and represent a type of quantum interference attributable to the bosonic nature of the photon. Neutrons, however, like electrons, are fermions and are therefore governed by Fermi-Dirac statistics. A neutron HBT experiment would show a negative correlation or antibunching effect. In my own book I analyzed a variety of HBT experiments on free electron beams and had come to the conclusion that the degeneracy parameter of the most coherent field-emission electron sources available was marginally large enough for such experiments to be performed. (The degeneracy parameter is a measure of the mean number of electrons per cell of phase space.) The much lower (by orders of magnitude) degeneracy of known neutron sources led me to conclude that a neutron HBT experiment was virtually hopeless. Rauch and Werner point out, however, the very interesting possibility of obtaining correlated neutrons from the deuteron disintegration reactions D(n,p)2n and D(p-, g)2n, a proposition similar to my proposal of obtaining correlated electrons from the disintegration of the exotic ion m+e-e- (the muonic analogue of H-).

Throughout their book, the authors describe clearly and objectively the successful applications of quantum mechanics to neutron interferometry, eschewing philosophical digressions over such matters as the completeness or interpretation of the quantum mechanical formalism. In the final chapter, however, they give a comprehensive neutral summary of the principal positions that have emerged in answer to the epistemological questions: (a) What is the meaning of the wavefunction? (b) How is the measurement process described? (c) How can a classical world appear out of quantum mechanics? (d) How can non-locality be explained? That such questions remain after more than 75 years of extensive use and meticulous testing of quantum mechanics testifies to how odd the quantum world can be - a world humorously, and not inaptly, mirrored in the Charles Addams cartoon that decorates the cover of the book: the skier who in some mysterious way has left one ski track around each side of a tall pine tree.

About the author

Mark P. Silverman is Jarvis Professor of Physics at Trinity College. He wrote of his investigations of light, electrons, nuclei, and atoms in his books Waves and Grains: Reflections on Light and Learning (Princeton, 1998), Probing the Atom (Princeton, 2000), and A Universe of Atoms, An Atom in the Universe (Springer, 2002). His latest book Quantum Superposition (Springer, 2008) elucidates principles underlying the strange, counterintuitive behaviour of quantum systems.