Exchange-Mediated Mutual Correlation and Dephasing in Free-Electron and Light Interactions

The quantum world distinguishes itself from the classical world by being governed by probability amplitudes rather than probabilities. On a single-particle level, quantum phases can be manipulated leading to observable interference patterns that can be used as a probe e.g. in matter wave microscopy. But the quantum world bears even more fascinating effects when it comes to the interplay between more than one particle. Correlations between quantum particles such as entanglement can be exploited to speed up computational algorithms or enable secure cryptography. Here, we propose and numerically explore a thought experiment to address the question whether quantum correlations between particles can be used in matter wave microscopy. Specifically, we address the following questions: How can information be transferred between two mutually spin-correlated free-electron wavepackets? Can Coulomb and exchange correlations be linked to the decoherence mechanism of matter waves? Using a time-dependent Hartree-Fock algorithm, we will show that the exchange term has a substantial role in transferring the information between two mutually spin-correlated electrons, whereas the Hartree potential (or mean-field Coulomb potential) dominates the dephasing on a single-particle level. Our findings might facilitate fermionic matter-wave interferometry experiments in which it is possible to retrieve information about non-classical correlations and the mechanism of decoherence in open versus closed quantum systems.