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Classical and Quantum Gravity

Gravitational, rotational and topological quantum phase shifts in neutron interferometry

Samuel A. Werner

Published Jun 1, 1994• 53 citations
Publisher

Abstract

Experiments involving quantum interference of neutron de Broglie waves, having a wavelength A , extending over macroscopic distances of order are described. In particular I discuss interference induced by the Earth's gravitational field and by its rotation (Sagnac effect), the topological phase shifts resulting from the diffraction of the neutron, carrying its magnetic moment , around a charged electrode (Aharonov--Casher effect) and then finally during its passage through a pulsed magnetic field (scalar Aharonov--Bohm effect).

DOI
10.1088/0264-9381/11/6a/016

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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, 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.

•Jan 1, 2000•37 citations
Experiments involving quantum interference of neutron de Broglie waves, having a wavelength A , extending over macroscopic distances of order are described. In particular I discuss interference induced by the Earth's gravitational field and by its rotation (Sagnac effect), the topological phase shifts resulting from the diffraction of the neutron, carrying its magnetic moment , around a charged electrode (Aharonov--Casher effect) and then finally during its passage through a pulsed magnetic field (scalar Aharonov--Bohm effect).
The special and unique techniques of neutron interferometry have been used to observe a number of topological effects. These include the quantum mechanical phase shift of a neutron due to the Earth's rotation (the quantum analog of the Michelson–Gale–Pearson experiment with light), the phase shift of a particle carrying a magnetic moment (a neutron) encircling a line charge (the Aharonov–Casher effect) and the scalar Aharonov–Bohm effect, observed with a pulsed magnetic field solenoid and time-of-flight neutron detection. On the occasion of the 50th anniversary of the Aharonov–Bohm paper, we provide an overview of the neutron interferometry technique and a description of these three historic experiments.
The phase shift predicted by Aharonov and Casher for a magnetic dipole diffracting around a charged electrode has been observed for the case of thermal neutrons, using a neutron interferometer containing a 30-kV/mm vacuum electrode system. The judicious use of the Earth's gravitational field introduces a spin-independent phase shift which enables unpolarized neutrons to be used. A supplementary magnetic bias field of the correct magnitude allows first-order sensitivity to be achieved; even so, the theoretically predicted phase shift is only 1.50 mrad for the geometry and conditions of the experiment. We observe a phase shift of 2.19\ifmmode\pm\else\textpm\fi{}0.52 mrad.
The usual vector Aharonov–Bohm effect involves the quantum interference of electrons encircling a solenoid due to the magnetic vector potential. The analogous Aharonov–Casher effect was predicted for the neutron, which carries a magnetic dipole moment, encircling a line of electric charge . It was first observed by neutron interferometry, as described in this chapter. An analogous effect using neutrons and a pulsed magnetic solenoid in one leg of the interferometer has also been observed. This experiment using both polarized and unpolarized neutrons is described in this chapter. It is the first observation of the scalar Aharonov-Bohm effect. The idea of geometric phases was later shown to be pervasive in physics. These ideas were brought to full fruition in a neutron interferometry experiment in the late 1990s. The connections of this experiment with the helical field experiment of Bitter and Dubbers and the absorption experiment of Hasegawa are also discussed. The confinement-induced phase when neutrons move between narrow plates is another example of a non-local interaction of neutrons.
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.
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.
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.