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EXPERIMENTAL INVESTIGATION OF THE QUANTUM STRUCTURE OF ELECTROMAGNETIC FIELDS

Paul Feit, B. Fogarassy, Kalman Tompa

Published Nov 1, 1957• 0 citations
OpenAlex

Abstract

An experiment carried out in order to obtain a direct indication of the quantum structhre of a cm wavelength electromagnetic field is described. The interaction between tbe electromagnetic field generated in a cavity resonntor and an electron beam passing through it was studied. According to the theoretical calculations on which this experiment is based the electrons leaving the cavity as a result of the interaction should have a directional scattering of given value. In the experiment, however, no directional scattering was observed or more precisely if there were any directionnl scattering it was not more than 10% of the expected value. (auth)

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Quantum Effects in the Interaction between Electrons and High-Frequency Fields. II

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Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations
An experiment carried out in order to obtain a direct indication of the quantum structhre of a cm wavelength electromagnetic field is described. The interaction between tbe electromagnetic field generated in a cavity resonntor and an electron beam passing through it was studied. According to the theoretical calculations on which this experiment is based the electrons leaving the cavity as a result of the interaction should have a directional scattering of given value. In the experiment, however, no directional scattering was observed or more precisely if there were any directionnl scattering it was not more than 10% of the expected value. (auth)
The study of the appearance of quantum effects in an essentially classical experiment---involving the passage of an electron through a resonant cavity---as the frequency of the electromagnetic field increases, was begun in a previous paper, in which the electron velocity was examined. In the present paper, an analysis is made of the electric field in the same experiment. Both the expectation value of the field, and the expectation value of the square of the deviation from the expectation value (the dispersion) of the field are calculated to the lowest order in the electron charge. The expectation value of the field is seen to differ from the classical value by a small amount, the difference being due to the wave properties of the electron. The dispersion in the field is shown to consist of three parts: one due to the quantum-mechanical properties of the field alone, the second due to the wave properties of the electron, and the third due to the interaction between the quantum-mechanical properties of the field and the classical properties of the electron. The orders of magnitude of the three terms are shown to decrease in the order in which they are enumerated. A calculation is then made of the effect on the field of a number of electrons passing through the cavity, the interaction between the electrons being neglected. The number of electrons required in a "bunch" to produce a field comparable to the dispersion in the field is calculated, and, for a typical set of experimental conditions, it is seen that the highest frequency at which this requirement can be met is of the order of 3\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012/sec.
Since the first experiments of the quantum modulation of electron beams by lasers with a crystal as medium in the interaction area ~d1warz-Hora effect) were reported, extensive theoretical studies were performed.A very detaile/ rLproduction of these experiments was achieved (by Andrick and Langhans, further by Weingartshofer et al) where the medium in the interaction area was a gas.The initial clarification of the experiments with crystal as a quantum phenomenon is using a threshold defining a correspondence principle for electromagnetic interaction.Recent experiments by Weingartshofer et al independently confirm this correspondence principle.For two other experiments the ranges of quantum and classical regimes are elaborated to explain the basically differing character of observations.The discussion of the coherence for matter waves is followed up from the beginning of the Schwarz-Hora effect including developments reviewed by Hawkes and indicating further generalizations by the Hanbury-Brown/ Twiss effect.A consequent generalization of the scattering theory of the quantum modulation is presented based on a Green's function solution which results in the fact that far-field superpositions only lead to interferences.The problems of the re-emission of photons from quantum modulated electron beams is discussed and experiments on indirect observations of the phenomena in microwave amplification and in the 1/f noise Handel effect are reported.In the last case. . the self-interaction of electrons are involved in the Handel effect.A further second-quantised derivation and the coherent state Handel effect is presented.
The passage of an electron through a cavity resonator is considered for the purpose of studying the appearance of quantum mechanical effects in an essentially classical experiment as the frequency of the electromagnetic field becomes high. Both the electron and the field must be represented, initially, by wave packets---in space and momentum coordinates for the former, and in electric field and vector potential coordinates for the latter---in order to correspond to classically meaningful systems. The velocity of the electron at the output of the cavity is investigated. It is found that the expectation value of velocity has a quantum-mechanical correction term. A more significant effect, however, is the nonvanishing of the expectation value of the square of the deviation from the expectation value (mean square deviation from the mean) of the velocity. This deviation is a random phenomenon which will produce noise in an electron beam. An expression for the mean square deviation, in which the results of electron and field quantization are separately apparent, is derived, and its significance is discussed. An order-of-magnitude calculation is made for the ratio of minimum possible mean square deviation of velocity to velocity increment due to the field, and the frequency for which this ratio becomes unity is calculated for a particular set of conditions to be of the order of 3\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012/sec.