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.
Highlights
On-demand coherent manipulation of the transverse electron wave function in electron beams is of fundamental interest to improve spatial resolution in transmission electron microscopes
This effect, which can be attributed to fluctuations characterizing the quantum electromagnetic field, could be experimentally measured by means of either interference or diffraction of electron beams using an electron microscope
The recombination of the two parts of the electron wave function ψj eiχj following different paths j = 1, 2 that are affected by their corresponding phases χj leads to an electron probability at the detector ∝ |ψ1|2 + |ψ2|2 + 2 Re{ψ1ψ2∗ ei(χ1−χ2)}; when one of the paths passes near a 12 nm gold particle, the phase-shift difference can be as large as |χ1 − χ2| ∼ 3◦, which could be resolved in an electron holography setup
Summary
Keywords: electron microscopy, vacuum fluctuations, photonic nanostructures, light–matter interaction Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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