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Communications in Theoretical Physics

Quantum Interference Effect in General Rotating Systems

Hong-Hua Xu, Chien-hua Tsai

Published Jan 1, 1990• 0 citations
Publisher

Abstract

As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrary time varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.

DOI
10.1088/0253-6102/13/1/134

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As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrary time varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.
As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrarily time-varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.
In recent years there has been significant activity in research and development of high sensitivity accelerometers and gyroscopes using atom interferometers. In these devices, a fringe shift in the interference of atom de Broglie waves indicates the rotation rate of the interferometer relative to an inertial frame of reference. In both optical and atomic conventional Sagnac interferometers, the resultant phase difference due to rotation is independent of the wave velocity. However, we show that if an atom interforemeter is enclosed in a Faraday cage which is at some potential, the phase difference of the counter-propagating waves is proportional to the inverse square of the particle velocity and it is proportional to the applied potential. This is due to Aharonov-Bohm effect and it can be used to increase the rotation sensitivity of atom interferometers.
Recent works showed that the Aharonov-Bohm (AB) phase difference for a quantum charged particle can be written in terms of electric and magnetic fluxes in a space-time surface whose boundaries are the possible particle worldlines in the interferometer, relative to the possible paths. After presenting this result in a more detailed way, reinforcing its topological nature, we study the magnetic and electric versions of the AB effect in different inertial reference frames. We find a particular reference frame for a magnetic AB effect where the magnetic flux has a null contribution for the AB phase difference, which is entirely due to an electric flux. Also, we find a particular reference frame for an electric AB effect where the electric flux has a null contribution for the AB phase difference, which is entirely due to a magnetic flux. In this sense, the nomenclatures magnetic AB effect and electric AB effect lose their meaning. We have electromagnetic AB effects.