This paper describes gravity experiments, where the outcome depends upon both the gravitational acceleration g and the Planck constant ℏ. We focus on the work performed with an elementary particle, the neutron.
We call attention to a feasible laboratory experiment with an outcome that depends necessarily on both Planck's constant and the gravitational constant. A neutron interferometer for which the two beams enclose an area of ~ 6 cm2 can be cut from a single crystal of silicon. A shift of ~ 10 fringes is anticipated when the interferometer is rotated 180\ifmmode^\circ\else\textdegree\fi{} about an axis parallel to both the earth's surface and the incident neutron beam.
Neutrons not only fall classically in the gravitational field of the Earth as potatoes and other normal objects do; at certain conditions, they reveal quantum behavior, or even form well defined gravitational quantum states. Due to the relative simplicity of quantum mechanical rules for solving this problem, we could predict analytically the motion of a neutron in a grav itational field in the vicinity of a reflecting surface. Such a bouncing neutron can have only certain, discrete values of energy. These extremely small energy values turn out to be very sensitive probes to the presence of even tiny extra interactions, in particular those between the neutron and the mirror. Moreover, several emerging fields of research profit from experi ence and knowledge gained in the recent experimental observation of gravitational quantum states of ultracold neutrons, and extend the developed methods to atoms and anti-atoms, to whispering-gallery effect and other domains, thus providing more and more application for the method. Quantum bouncing particles could play their role in quantum tests of the equivalence principle, in explorations of gravitational properties of antimatter, in searching for new funda mental short-range and other interactions beyond the Standard Model of particle physics, in surface and thin-layer physics, in chemistry, and so on. In this short note we mention results of a few previous years and project nearest developments ..
The experiments described in this paper probe the simultaneous effects of gravity, inertia, and quantum mechanics on the motion of the neutron. Using a neutron interferometer of the type developed by Bonse and Hart for x rays, we have observed quantum-mechanical interference phenomena induced by the gravitational field of the Earth and by the Earth's rotation relative to the fixed stars. The importance of these experiments with regard to the role of the principle of equivalence in quantum mechanics is discussed.
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.
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.