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

Abstract

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 Schrödinger equation, and underwent a Goos–Hänchen 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 Δφ = 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.

Exploring TEM Coherence Properties via Speckle Contrast Analysis in Coherent Electron Scattering of Amorphous Material

“…The ability to probe nanoscale phenomena requires a thorough understanding of how beam interactions with the sample [38], environment, and control parameters [39] affect the electron beam coherence properties. Recently, the delivery of ultrashort electron pulses, enabled by femtosecond-induced photoemission, allows probing structural dynamics occurring at nano-to femtosecond timescales.…”