Neutron Interferometry: Lessons in Experimental Quantum Mechanics

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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, Berr&ygrave;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.

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Editorial Reviews

For beginning graduate students of neutron, quantum, and atomic physics Rauch (U. of Austria, Vienna) and Werner (physics, U. of Missouri-Columbia) explain the theoretical motivation, instrumentation, and the result analysis of experimentally observing interference between coherently split, well-separated beams of matter waves. They discuss the experiments in terms of various post-selection criteria, gravitationally induced phase shifts, Berry's geometrical phase, spinor symmetry and spin superposition, Aharonov-Bohm topological interference effects, and the neutron version of the Sagnac effect. The interferometry they describe is of perfect crystals, artificial lattices, and spin-echo systems. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Meet the Author

Helmut Rauch, Professor Emeritus, Technical University of Vienna,Samuel A. Werner, Curators' Professor Emeritus, University of Missouri; Guest Researcher, Neutron Physics Group, NIST

Helmut Rauch completed his PhD in 1965 and become full Professor in 1972. He spent one sabbatical year at KFA Juelich/Germany and worked regularly at the Institute Laue-Langevin in Grenoble/France. His scientific interests are: neutron physics, quantum optics, foundations of quantum mechanics, and reactor physics. He invented together with U. Bonse and W. Treimer the perfect crystal neutron interferometer, and has published more than 350 papers in refereed journals. He was Director of the Atomic Institute in Vienna, President of the Austrian Science Foundation and twice President of the Austrian Physical Society. He is member of the Austrian and German Physical Society, the Austrian Academy of Sciences, and the German Academy of Sciences "Leopoldina" in Halle. Honours include the Erwin Schrodinger Award of the Austrian Academy of Sciences, and the Ludwig Wittgenstein Award of the Austrian Research Association.

Samuel Werner received his AB degree at Dartmouth College in 1959 and his PhD degree at the University of Michigan in 1965. He was a staff scientist in the Physics Department of the Scientific Laboratory of the Ford Motor Company for 10 years. He became Professor of Physics at the University of Missouri in 1975. Upon his retirement from Missouri in 2000 he moved to Gaithersburg, MD to become a guest researcher at NIST. His scientific interests are: neutron scattering, neutron physics, spin density waves (CDW) and charge density waves (SDW) in solids. He received the President's Award for Outstanding Research at the University of Missouri in 1980, the Outstanding Alumnus Award of the Nuclear Engineering Department at the University of Michigan in 1980, and an Exceptional Service Award of the Neutron Scattering Society of America in 2012. He was the first President of the NSSA. He is a Fellow of the NSSA, the American Physical Society, and the American Association for the Advancement of Science.

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Table of Contents

1 Introduction 1
1.1 Neutron optics and the analogy with light optics 1
1.2 The quantum phase shift of matter waves 9
1.3 Basic neutron diffraction phenomena 18
2 Neutron interferometers and apparatus 23
2.1 The perfect silicon crystal interferometer 23
2.2 Interferometer setups 32
2.3 Interferometers based upon cold and ultra-cold neutrons 37
2.4 Larmor interferometry 45
3 Neutron interactions and coherent scattering lengths 54
3.1 Nuclear interaction 54
3.2 Electromagnetic interactions 74
3.3 Parity-violating interactions 85
3.4 External influences 86
4 Coherence properties 93
4.1 Basic relations 95
4.2 Coherence measurements 99
4.3 Partial beam path detection 113
4.4 Counting statistics 125
4.5 Post-selection experiments 137
5 Spinor symmetry and spin superposition 165
5.1 Spinor symmetry 165
5.2 Spin superposition 169
5.3 Time-dependent spinor superposition 173
5.4 Double coil experiments and the magnetic Josephson effect 176
5.5 Multi-photon exchange experiments 184
6 Topological and geometric phases 189
6.1 Aharonov-Casher effect (vector Aharonov-Bohm effect) 189
6.2 Scalar Aharonov-Bohm effect 194
6.3 Topological phases 200
7 Gravitational, non-inertial, and motional effects 211
7.1 Gravitationally induced quantum interference 211
7.2 Sagnac effect 229
7.3 Acceleration-induced interference 236
7.4 Connections with photons 237
7.5 Neutron Fizeau effects 238
8 Forthcoming and more speculative experiments 256
8.1 Non-linearity of the Schrodinger equation 256
8.2 Aharonov-Bohm analogue 257
8.3 Quaternions in quantum mechanics 258
8.4 Non-ergodic effects 259
8.5 Wheeler delayed-choice experiments 260
8.6 Neutron-antineutron oscillations 261
8.7 Non-Newtonian gravity effects 262
8.8 Spin-rotation coupling 262
8.9 Hanbury Brown-Twiss analogue 263
8.10 The search for nuclear quantum entanglement 265
8.11 Confinement and gravity quantized phases 265
8.12 The Anandan acceleration 268
8.13 Search for basic dissipative terms 274
8.14 Bell type non-locality experiments 275
9 Solid state physics applications 278
9.1 Contrast reduction due to inhomogeneities 278
9.2 Phase contrast topography and tomography 283
9.3 Neutron Fourier spectroscopy 287
10 Perfect-crystal neutron optics 294
10.1 The transition from kinematic to dynamical diffraction 294
10.2 Dynamical diffraction for the symmetric Laue case 295
10.3 Anomalous transmission, angle amplification, and high collimation effects 304
10.4 Pendellosung interference effects 312
10.5 Primary extinction and the width of a Bragg reflection 316
10.6 The Takagi-Taupin equations 317
10.7 Theory of the perfect crystal neutron interferometer 324
11 Interpretational questions 350
References 366
Index 392
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