# Probing Quantum Optical Excitations with Fast Electrons

## TL;DR

This paper theoretically investigates how fast electrons interact with localized optical modes, revealing that electron spectra depend on the quantum statistics and populations of sample excitations, enabling quantum characterization at nanometer scales.

## Contribution

It introduces a quantum-optics framework to analyze electron spectra interactions with optical modes, linking spectral features to quantum statistics and populations of excitations.

## Key findings

- Electron spectra depend on the quantum statistics of excitations.
- Ratios of electron gain intensities reveal autocorrelation functions.
- Feasible experiments can probe quantum properties of excitations.

## Abstract

Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Electron microscopes currently offer the unparalleled ability of rendering spatially-resolved electron spectra with combined meV and sub-nm resolution, while the use of ultrafast optical pulses enables fs temporal resolution and exposure of the electrons to ultraintense confined optical fields. Here, we theoretically investigate fundamental aspects of the interaction of fast electrons with localized optical modes that are made possible by these advances. We use a quantum-optics description of the optical field to predict that the resulting electron spectra strongly depend on the statistics of the sample excitations (bosonic or fermionic) and their population (Fock, coherent, or thermal), whose autocorrelation functions are directly retrieved from the ratios of electron gain intensities. We further explore feasible experimental scenarios to probe the quantum characteristics of the sampled excitations and their populations.