Two-electron quantum walks can probe entanglement and decoherence in an electron microscope

Classical physics is often a good approximation for quantum systems composed of many interacting particles, although wavepacket dispersion and scattering processes continuously induce delocalization and entanglement. According to decoherence theory, an entangled ensemble can appear classical when only a subset of all particles is observed. This emergence of macroscopic phenomena from quantum interactions is, for example, relevant for phase transitions, quantum thermalization, hydrodynamics, spin liquids, or time crystals. However, entanglement and decoherence in free electrons have not yet been explored, although the electron is a fundamental elementary particle with extraordinary technological relevance. Here, we investigate the degree of coherence and entanglement in a free-space electron gas in the beam of an ultrafast electron microscope. We introduce a two-electron quantum walk that transforms the quantum state into different bases for quantum state tomography of entangled or partially entangled electron-electron pairs. We apply this novel diagnostic to study quantum effects in short pulses of hundreds of electrons under strong Coulomb correlation. We observe a high contrast interference in the electron-electron correlations but no significant signs of electron-electron entanglement which we explain by limited purity of the initial states and decoherence effects from unmeasured reservoir electrons. The ability to characterize quantum states of multiple free electrons may allow verification of electron-electron entanglement for use in fundamental studies and quantum electron microscopy.