The effect of electromagnetic potentials on the interference fringes in electron interferometers in which electron beams are split into separate component beams which travel along spatially separated paths before being recombined are examined. By using a quantum theory interpretation of these fringe observations, it is shown that these potentials contribute significantly to the stability of the the fringe pattern. (C.J.G.)
The effect of electromagnetic potentials on the interference fringes in electron interferometers in which electron beams are split into separate component beams which travel along spatially separated paths before being recombined are examined. By using a quantum theory interpretation of these fringe observations, it is shown that these potentials contribute significantly to the stability of the the fringe pattern. (C.J.G.)
In the so-called electric Aharonov-Bohm effect, a quantum interference pattern shift is produced when electrons move in an electric field-free region but, at the same time, under the presence of a time-dependent electric potential. Analogous fringe shifts are observed in interference experiments where electrons, travelling through an electrostatic field, suffer a classical lag effect produced by electric forces. Since these experiments are reported mainly in specialized journals, it could be rather difficult and time consuming for a student to attain a comprehensive overview of the subject. Therefore, particular attention has been addressed to reviewing the theory, to describing a couple of experiments and to the interpretation of the results. We believe that students can be suitably introduced to exploring the “paradoxical” aspects of the interaction of electrons with electric potentials and fields.
A new class of electron interferometers is proposed that make use of a laser-modulated electron beam. The observable interference arises in second-order processes, since the first-order interference oscillates rapidly and averages to zero. It is shown that the detected signal varies sinusoidally with the separation of two sequential modulators, thus generating a fringe pattern with peak-to-peak spacing that may be smaller or larger than the laser wavelength. It is suggested that such devices could be used to detect and study the modulation process and, because they operate with massive charged particles, to perform a wide variety of new experiments and high-precision measurements.
The cordus concept is shown to be able to explain wave behaviour in gaps, and fringes in the double slit device. This is useful because one of the enigmas of the double-slit device is that single photons form fringe patterns. Cordus explains fringes in terms of force lines called hyperfine fibrils (hyff) and their interaction with the edges of the light path. This also explains beam divergence and near-field effects. The results show that it is conceptually possible to create a solution for fringes based on a particuloid interpretation of light, without using the concept of interference. The biggest difference between Wave theory and the cordus explanation is their interpretation of the mechanism for fringes. Wave theory explains fringes as �interference�: two separate waves of light differing by full (half) fractions of wavelengths and thus constructively (destructively) interfering. From the Cordus perspective photons do not actually interfere or add together, and 'interference' is only a convenient analogy. The Cordus explanation is that fringes are caused instead by interaction of the photon hyff with opaque edges. This bracket of papers therefore offers a resolution of wave-particle duality by anticipating the internal cordus structure of the photon and the associated cordus mechanics. From this perspective wave and particle behaviours are simply the different output behaviours that the internal system shows depending on how it is measured. Thus Cordus offers a deeper mechanics that subsumes both quantum mechanics and wave theory. Surprisingly, Cordus suggests that the next deeper level of reality is deterministic.
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.
An experiment in which decoherence, i.e. the transition from quantum to classical behaviour, can be studied in detail was proposed by Anglin and Zurek [1] and has now been realized. An electron beam in a biprism interferometer is split into two parts both of which travel over a plate made of a highly resistive material at the same, small height. The induced charges inside the plate move along with the beam electron, therefore a current results which encounters ohmic resistance. This process leads to a disturbance in the electron and phonon gas in the plate. As this disturbance is different for the two parts of the beam, entanglement between beam electron and plate is formed. The strength of decoherence, represented by the visibility of the interference fringes, varies as a function of two parameters, the height above the plate and the lateral separation of the beams. Allowing electrons of different height to reach the fluorescent screen successively, 'photos' of the quantum-classical border (continuous decrease of contrast with decreasing height above the plate) are built up.
The interference pattern of coherent electrons is effected by coupling to the quantized electromagnetic field. The amplitudes of the interference maxima are changed by a factor which depends upon a double line integral of the photon two-point function around the closed path of the electrons. The interference pattern is sensitive to shifts in the vacuum fluctuations in regions from which the electrons are excluded. Thus this effect combines aspects of both the Casimir and the Aharonov-Bohm effects. The coupling to the quantized electromagnetic field tends to decrease the amplitude of the interference oscillations, and hence is a form of decoherence. The contributions due to photon emission and to vacuum fluctuations may be separately identified. It is to be expected that photon emission leads to decoherence, as it can reveal which path an electron takes. It is less obvious that vacuum fluctuations also can cause decoherence. What is directly observable is a shift in the fluctuations due, for example, to the presence of a conducting plate. In the case of electrons moving parallel to conducting boundaries, the dominant decohering influence is that of the vacuum fluctuations. The shift in the interference amplitudes can be of the order of a few percent, so experimental verification of this effect may be possible. The possibility of using this effect to probe the interior of matter, e.g., to determine the electrical conductivity of a rod by means of electrons encircling it is discussed. (Presented at the Conference on Fundamental Problems in Quantum Theory, University of Maryland, Baltimore County, June 18-22, 1994.)