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arXiv:0710.2289 · Physical Review A

Decoherence induced by Smith-Purcell radiation

Ezequiel Álvarez, Francisco Diego Mazzitelli

Published Mar 25, 2008• 5 citations
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Abstract

The interaction between charged particles and the vacuum fluctuations of the electromagnetic field induces decoherence, and therefore affects the contrast of fringes in an interference experiment. In this article we show that if a double slit experiment is performed near a conducting grating, the fringe visibility is reduced. We find that the reduction of contrast is proportional to the number of grooves in the conducting surface, and that for realistic values of the parameters it could be large enough to be observed. The effect can be computed and understood in terms of the Smith-Purcell radiation produced by the surface currents induced in the conductor.

DOI
10.1103/physreva.77.032113

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The interaction between charged particles and the vacuum fluctuations of the electromagnetic field induces decoherence, and therefore affects the contrast of fringes in an interference experiment. In this article we show that if a double slit experiment is performed near a conducting grating, the fringe visibility is reduced. We find that the reduction of contrast is proportional to the number of grooves in the conducting surface, and that for realistic values of the parameters it could be large enough to be observed. The effect can be computed and understood in terms of the Smith-Purcell radiation produced by the surface currents induced in the conductor.
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.
We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
When individual particles pass through a double slit, a fringe pattern appears on a screen. If an observer detects the path of the particle, the interference fringes disappear. This is called the quantum decoherence. In this paper, we discuss a parameter estimation problem using the quantum decohenrece in the double-slit experiment. As a simple model, we consider a massive scalar field interacting with the particle which have passed through the double slit. The scalar field, as well as the observer, can induce the loss of the fringe pattern of the particle. Because the interference fringes of the particle depend on the field mass and coupling, we can estimate the field parameters from the fringes. For qualitative analysis, we introduce the interferometric visibility of the fringe pattern and the Fisher information (FI) matrix of the field mass and coupling. Using the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the FI matrix. Also if we focus on FI of the mass, then we find that FI characterizes the wave-particle duality in the double-slit experiment.
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.