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Electrons as waves - and what will come next?

Tomáš Tyc, Michal Lenc

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

The route from electron interference to correlations is
discussed. It is shown that multi-electron inteference will
probably have no applications in electron microscopy in the
near future.

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Electron Waves: Interference in an Atom

I. Peterson

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Based on the semiclassical analysis of photoionization microscopy, we study the ionization of the Rydberg hydrogen atom near a dielectric surface. The radial electron probability density distributions on a given detector plane are calculated at different scaled energies and near different dielectric surfaces. We find due to the interference effect of different types of electron trajectories arriving at a given point on the detector plane, oscillatory structures appear in the electron probability density distributions. With the increase in the scaled energy, more types of electron ionization trajectories appear and the oscillatory structure in the electron probability density distributions becomes complex. Besides, the dielectric constant of the dielectric surface can also affect the electron probability density distributions. Since the photoionization microscopy interference pattern recorded on the detector plane reflects the distribution of the square modulus of the transverse component of the electronic wave function, with the recorded interference pattern, we can investigate the ionization dynamics of the Rydberg atom near surfaces clearly. This study provides some reference values for the future experiment research on the photoionization microscopy of the Rydberg atom near dielectric surfaces.
The coherent interaction between free electrons and optical near-fields enables the active modulation of electron wave packets, a mechanism central to photon-induced near-field electron microscopy (PINEM). While existing theories effectively describe these interactions at high kinetic energies, the growing interest in low-energy ultrafast electron microscopy demands frameworks that explicitly account for finite wave packet geometries and recoil effects. In this paper, we develop a rigorous 3D quantum scattering theory for electron wave packets interacting with time-periodic potentials, capturing the case of optical near-field interaction. By mapping the time-dependent dynamics into an extended Floquet space, we formally connect the modulation process to time-independent multi-channel scattering. We evaluate the resulting scattering amplitudes using both an exact R-matrix approach and a multi-channel eikonal approximation. The latter analytical approach recovers PINEM-like probabilities weighted by the wave packet's transverse profile. Application of the theory to an oscillating potential demonstrates the generation of distinct energy sidebands, revealing that the modulation strength is sensitive to the transverse focusing of the incident electron pulse, underlining the importance of a fully 3D treatment.