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Chinese Physics Letters

Aharonov-Bohm-Type Electron Interference in a Two-Mode Squeezed Vacuum Field

Bin Shao, Jian Zou

Published Jun 1, 1998• 0 citations
Publisher

Abstract

Electron interference related to Aharonov-Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of the temporal behavior of electron interference are discussed. It is shown that for the two-mode squeezed vacuum field the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR). In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.

DOI
10.1088/0256-307x/15/6/002

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Electron interference related to Aharonov-Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of the temporal behavior of electron interference are discussed. It is shown that for the two-mode squeezed vacuum field the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR). In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.
Electron interference related to Aharonov–Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of Shapiro steps, the visibility of the interference fringe and the temporal behavior of electron interference in correlated and uncorrelated two-mode radiation field are discussed. It is shown that for the correlated two-mode squeezed vacuum the integer Shapiro steps are obtained and the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR), while for the uncorrelated two-mode coherent state the fractional Shapiro steps are obtained and the CR phenomenon does not occur. In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.
Dynamic behaviour of Aharonov-Bohm-type electron interference in the presence of a nonclassical electromagnetic field is investigated. The visibility of the time-averaged interference pattern is discussed for SU(1,1) coherent state (CS) and a comparison with other states is made. It is shown that the dynamic behaviour of the electron interference exhibits collapse and revival (CR) phenomenon for SU(1,1) CS. It is also shown that CR phenomenon of electron interference is closely related to the fluctuation of a nonclassical electromagnetic field.
The coupling of the quantized electromagnetic field to coherent electrons is investigated. The effects both of photon emission and of the electromagnetic vacuum fluctuations upon electron interference are analyzed. The modifications of the vacuum fluctuations due to a conducting plate lead to a decrease in the amplitude of the interference oscillations. The possibility of observing this effect is discussed. It is also shown that there is an analogue of the Aharonov-Bohm effect in which electron interference is sensitive to vacuum fluctuations in regions from which the electrons are excluded.
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.)
Abstract Vacuum fluctuations are known to produce electron diffraction leading to decoherence and self-interference. These effects have so far been studied as either an extension of the Aharonov–Bohm effect in front of a planar perfect conductor or through path integral analysis. Here, we present a simpler, general, and rigorous derivation based on a direct solution of the quantum electrodynamic aloof interaction between the electron and a material structure in the temporal gauge. Our approach allows us to study dissipative media, for which we show examples of electron wave function shaping due to the interaction with real-metal surfaces. We further present a proof of the relation between the phase associated with vacuum fluctuations and the Aharonov–Bohm effect produced by the image self-interaction that is valid for arbitrary geometries. Besides their fundamental interest, our results could be useful for on-demand patterning of electron beams with potential application in nondestructive nanoscale imaging and spectroscopy.