Abstract Coherence phenomena play an important role in any kind of interferometry (Gabor 1956; Glauber 1963; Mandel and Wolf 1965, 1995; Born and Wolf 1975; Walls and Milburn 1994; Mandel and Wolf 1995). In this chapter we summarize some known results, add some new ones obtained with neutrons, and analyse them in terms of general quantum optics, which can be applied to photon and matter waves as well. Indeed, neutrons have many well-known particle properties, but in interference experiments they behave like wave fields, which provides the connection to the quantum optical terminology. Coherence appears as a system property (neutron + apparatus) which persists as long as it does not become destroyed by statistical or dissipative effects.
Abstract Coherence phenomena play an important role in any kind of interferometry (Gabor 1956; Glauber 1963; Mandel and Wolf 1965, 1995; Born and Wolf 1975; Walls and Milburn 1994; Mandel and Wolf 1995). In this chapter we summarize some known results, add some new ones obtained with neutrons, and analyse them in terms of general quantum optics, which can be applied to photon and matter waves as well. Indeed, neutrons have many well-known particle properties, but in interference experiments they behave like wave fields, which provides the connection to the quantum optical terminology. Coherence appears as a system property (neutron + apparatus) which persists as long as it does not become destroyed by statistical or dissipative effects.
Neutron interferometry provides a powerful tool to investigate particle and wave features in quantum physics. Single particle interference phenomena can be observed with neutrons and the entanglement of degrees of freedom, i.e., contextuality can be verified and used in further experiments. Entanglement of two photons, or atoms, is analogous to a double slit diffraction of a single photon, neutron or atom. Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, they are subject to all basic interactions, and they are sensitive to topological effects, as well. The 4π-symmetry of spinor wave functions, the spin-superposition law and many topological phenomena can be made visible, thus showing interesting intrinsic features of quantum physics. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Neutron interferometry experiments based on post-selection methods renewed the discussion about quantum non-locality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle, but where and when a collapse of the wave-field occurs depends on the level of experiment.
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.
Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena. Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle systems shows that quantum correlations are to some extent more demanding than classical ones. In this case entanglement between external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden variable theories can be rejected by arguments based on the Kochen-Specker theorem.
Abstract This chapter describes a rather broad selection of neutron interferometry experiments whose theoretical description requires an understanding of the mutual coherence function, and the sensitive experimental techniques utilized. Within the interferometer the coherent beams can be influenced by interactions with fields and material media in space and time causing phase shifts and wave packet delays that substantially affect the outgoing beams. Post-selection experiments involving spectral filtering and time-of-flight analysis are described. The phase-echo effect is described; it is a generalization of the spin-echo effect. Placing statistical or deterministic absorbers within the interferometer affects the outgoing coherence properties of beams quite differently. Low counting rate interference experiments show time pair-correlation effects characteristic of Poissonian statistical beams. Decoherence effects are investigated to study the transition from a quantum to a classical regime.
Abstract Among the various areas of neutron optical research, neutron interferometry has provided some of the most challenging and spectacular developments. In most cases, separated coherent beams are used which are produced either by wavefront division (Young’s type) or by amplitude division (Mach− Zehnder type). These beams are subsequently coherently superposed after passing through regions of space where the neutron wavefunction is modified in phase and amplitude by various interactions: nuclear, magnetic, electromagnetic, gravitational, or by geometry and topology (as in Aharonov−Bohm-type experiments). Various types of neutron interferometers that have been tested are shown in Fig. 2.1. The first neutron interferometer was based upon wavefront division and biprism deflection, but it had several constraints for interferometric applications mainly due to the small beam separation (100 μm) (Maier-Leibnitz and Springer 1962). Nevertheless, this method gained further interest for diffraction experiments from macroscopic objects and for the detection of weak interaction effects where the long flight paths (10 m) enhance the sensitivity for the measurements of these effects (Gähler et al. 1980; Klein et al. 1981a). The perfect-crystal interferometer (Rauch et al. 1974) provides widely separated coherent beams and has become a standard method for advanced neutron optical investigations. The development of diffraction and phase grating interferometers extended the Mach-Zehnder interferometer method to very slow neutrons (loffe et al. 1985; Gruber et al. 1989). The superposition of spin-up and spin-down states in the longitudinal direction provides the basis for Larmor and Ramsey interferometry, where no lateral beam splitting is necessary. The well-known spin-echo systems (Mezei 1972) and zero-field spin-echo systems (Gähler and Golub 1987; Dubbers et al. 1989) are examples of such interferometers, which also play an important role in atom interferometry (Bord é 1989; Kasevich and Chu 1991; Riehle et al. 1991).
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.