Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.
Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.
Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the 2nd 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 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 described in some detail. The book 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. Quantum interference experiments with massive particles have direct consequences on the discussion of epistemological questions since they show explicitly the wave-particle duality, and the entanglement and the contextuality of various parameters governing our modern view of nature.
Abstract The fundamental dual nature of neutrons –sometimes a particle (when detected) and sometimes a wave (when traversing the interferometer) – is wonderfully mani-fested by the non-local nature of the neutron interferometry experiments discussed in this chapter. We begin with a discussion of the series of experiments, called gravitationally induced quantum interference, in Section 7.1. Then in Section 7.2, the effect of the Earth’s rotation on the phase of a neutron de Broglie wave is described. This is the quantum mechanical analogue of the Michelson et al. (1925) experiment with light. An experiment in which this Sagnac phase shift was observed due to rotation of the interferometer on a turntable phase within the laboratory frame is also discussed (Atwood et al. 1984). An experiment related to the small effective mass of the neutron propagating in a crystal under Bragg reflecting conditions and its deflection due to the Coriolis force is discussed in Section 7.2.3 (Raum et al. 1997). Acceleration-induced interference, which is related to the gravity experiments by the principle of equivalence, is discussed in Section 7.3 (Bonse and Wroblewski 1983). Phase shifts caused by the motion of matter within the interferometer are related to the optical Fizeau effect. Several neutron Fizeau-type experiments are discussed in Section 7.4.
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.
Abstract Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the 2nd 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 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 described in some detail. The book 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. Quantum interference experiments with massive particles have direct consequences on the discussion of epistemological questions since they show explicitly the wave-particle duality, and the entanglement and the contextuality of various parameters governing our modern view of nature.
Abstract The quantum interference of DeBroglie matter waves is probably one of the most startling and fundamental aspect 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. This book provides the reader with a detailed account of neutron interferometry experiments. The basic ideas and experiments related to coherence properties of matter waves and 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 are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are topics of this book. It includes the theoretical motivations as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The book is written in a style that will be suitable at the beginning graduate level, and will excite many students and researchers in neutron physics, quantum optics, 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.
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.