Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale

The relation between the energy-dependent particle and wave descriptions of electron-matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrodinger equation, and underwent a Goos-Hanchen shift. The findings support the view that wave packets are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase close to Delta phi = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure-function relationships on the nanoscale.

Automated summary

The relation between energy-dependent particle and wave descriptions of electron-matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field. The study found that the spatial extension of the field coincided with the energy-dependent self-coherence length of propagating wave packets. The findings suggest that wave packets are created by self-interferences during coherent-inelastic Coulomb interactions, and exhibit particle-like behavior for high electron energy losses.