# Possibility to probe negative values of a Wigner function in scattering of a coherent superposition of electronic wave packets by atoms

## TL;DR

This paper demonstrates how to detect negative values of the Wigner function in electron scattering experiments using coherent superpositions of wave packets, revealing quantum effects like non-locality and entanglement.

## Contribution

It introduces a method to probe negative Wigner function values in electron scattering with superposed wave packets, advancing quantum tomography and microscopy techniques.

## Key findings

- Predicted azimuthal asymmetry up to 10% in scattered electrons.
- Proposed detection of non-positive Wigner functions in electron beams.
- Potential applications in quantum tomography and non-invasive microscopy.

## Abstract

Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays everywhere positive, which obscures such purely quantum phenomena as non-locality and entanglement. With the advent of the electron microscopes with subnanometer-sized beams one can enter a genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a non-vanishing impact-parameter between them (a Schr\"odinger's cat state) by atomic targets. For hydrogen in the ground $1s$ state, a small parameter of the problem, a ratio $a/\sigma_{\perp}$ of the Bohr radius $a$ to the beam width $\sigma_{\perp}$, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to $10 \%$ and argue that it can be reliably detected. Production of beams with the not-everywhere positive Wigner functions and probing such quantum effects can open new perspectives for non-invasive electron microscopy, quantum tomography, particle physics, etc.