Direct evidence of a continuous transition between waves and particles

TL;DR

This paper provides direct experimental evidence of a continuous transition between wave-like and particle-like behaviors in electrons, linking quantum coherence, interference, and energy loss.

Contribution

It demonstrates the spatial delocalization of electron wave packets correlates with their energy-dependent coherence length, bridging wave and particle descriptions.

Findings

Delocalization matches the coherence length of electron wave packets.

Wave packets shrink to particle-like dimensions at high energy losses.

Self-interference during Coulomb interactions influences electron behavior.

Abstract

The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent, self-coherence length of propagating wave packets that obey the time-dependent Schr\"odinger equation and undergo a Goos-H\"anchen shift. In the Heisenberg limit they are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase {\Delta}{\phi} = 0.5 rad and shrink to particle-like dimensions for energy losses of more than 1000 eV.