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Decoherence of electron beams by electromagnetic field fluctuations

Yehoshua B. Levinson

Published Jun 1, 2004• 0 citations
Publisher

Abstract

Electromagnetic field fluctuations are responsible for the destruction of electron coherence (dephasing) in solids and in vacuum electron beam interference. The vacuum fluctuations are modified by conductors and dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the beams can influence the beam coherence. We calculate the quenching of interference of two beams moving in vacuum parallel to a thick plate with permittivity $\\epsilon(\\omega)=\\epsilon_{0}+i 4\\pi\\sigma/\\omega$. In case of an ideal conductor or dielectric $(|\\epsilon|=\\infty)$ the dephasing is suppressed when the beams are close to the surface of the plate, because the random tangential electric field $E_{t}$, responsible for dephasing, is zero at the surface. The situation is changed dramatically when $\\epsilon_{0}$ or $\\sigma$ are finite. In this case there exists a layer near the surface, where the fluctuations of $E_{t}$ are strong due to evanescent near fields. The thickness of this near - field layer is of the order of the wavelength in the dielectric or the skin depth in the conductor, corresponding to a frequency which is the inverse electron time of flight from the emitter to the detector. When the beams are within this layer their dephasing is enhanced and for slow enough electrons can be even stronger than far from the surface.

DOI
10.1117/12.547345

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Electromagnetic field fluctuations are responsible for the destruction of electron coherence (dephasing) in solids and in vacuum electron beam interference. The vacuum fluctuations are modified by conductors and dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the beams can influence the beam coherence. We calculate the quenching of interference of two beams moving in vacuum parallel to a thick plate with permittivity epsilon(omega)=epsilon0+i4pisigma/omega\\epsilon(\\omega)=\\epsilon_{0}+i 4\\pi\\sigma/\\omegaepsilon(omega)=epsilon0​+i4pisigma/omega. In case of an ideal conductor or dielectric (∣epsilon∣=infty)(|\\epsilon|=\\infty)(∣epsilon∣=infty) the dephasing is suppressed when the beams are close to the surface of the plate, because the random tangential electric field EtE_{t}Et​, responsible for dephasing, is zero at the surface. The situation is changed dramatically when epsilon0\\epsilon_{0}epsilon0​ or sigma\\sigmasigma are finite. In this case there exists a layer near the surface, where the fluctuations of EtE_{t}Et​ are strong due to evanescent near fields. The thickness of this near - field layer is of the order of the wavelength in the dielectric or the skin depth in the conductor, corresponding to a frequency which is the inverse electron time of flight from the emitter to the detector. When the beams are within this layer their dephasing is enhanced and for slow enough electrons can be even stronger than far from the surface.
Electromagnetic field fluctuations are responsible for the destruction of electron coherence (dephasing) in solids and in vacuum electron beam interference. The vacuum fluctuations are modified by conductors and dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the beams can influence the beam coherence. We calculate the quenching of interference of two beams moving in vacuum parallel to a thick plate with permittivity (ω) = 0 + i4πσ/ω. In the case of an ideal conductor or dielectric (| | = ∞) the dephasing is suppressed when the beams are close to the surface of the plate, because the random tangential electric field E t , responsible for dephasing, is zero at the surface. The situation is changed dramatically when 0 or σ is finite. In this case there exists a layer near the surface, where the fluctuations of E t are strong due to evanescent near fields. The thickness of this near-field layer is of the order of the wavelength in the dielectric or the skin depth in the conductor, corresponding to a frequency which is the inverse electron time of flight from the emitter to the detector. When the beams are within this layer their dephasing is enhanced and slow enough electrons can be even stronger than far from the surface.
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.)
The influence of electromagnetic vacuum fluctuations in the presence of the perfectly conducting plate on electrons is studied with an interference experiment. The evolution of the reduced density matrix of the electron is derived by the method of influence functional. We find that the plate boundary anisotropically modifies vacuum fluctuations that in turn affect the electron coherence. The path plane of the interference is chosen either parallel or normal to the plate. In the vicinity of the plate, we show that the coherence between electrons due to the boundary is enhanced in the parallel configuration, but reduced in the normal case. The presence of the second parallel plate is found to boost these effects. The potential relation between the amplitude change and phase shift of interference fringes is pointed out. The finite conductivity effect on electron coherence is discussed.
The interaction between particles and the electromagnetic field induces decoherence generating a small suppression of fringes in an interference experiment. We show that if a double-slit-like experiment is performed in the vicinity of a conducting plane, the fringe visibility depends on the position (and orientation) of the experiment relative to the conductor's plane. This phenomenon is due to the change in the structure of vacuum induced by the conductor and is closely related to the Casimir effect. We estimate the fringe visibility both for charged and for neutral particles with a permanent dipole moment. The presence of the conductor may tend to increase decoherence in some cases and to reduce it in others. A simple explanation for this peculiar behavior is presented.
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.
Open system dynamics of an electron is studied in the presence of radiation field, confined between two parallel conducting pates. It has been suggested in previous works that the quantized zero-point modes of this field lead to finite decoherence effects, possibly due to the Casimir force. However, in this work it is shown that the decoherence found in previous works is due to the sudden switching on of the system-environment interaction and due to the acceleration of the electron enforced by the background paths whose superposition was analyzed. The work discusses important theoretical aspects of the setup and shows that, while coherence might be lost due to bremsstrahlung induced by an external or the image potential, it cannot be lost due to the mere presence of the quantum vacuum fluctuations between the plates.