Real-time Entanglement of Auger and XPS-electrons: a preliminary investigation

Abstract: In this work, we employ a semi-classical approach to light matter interaction to describe and char- acterize spin configurations resulting from quantum correlations between electrons created by a photoemission event and by the following Auger decay. The system studied consists of three atomic levels and two continua. Initially, an external classical light field, in the form of a narrow Gaussian packet, perturbs the system, and transfers the density of charge, corresponding to one electron (the photoelectron), from the core level to the continuum. The Auger decay then occurs, whereby an electron from either of the valence levels decay to the core while, at the same time, another electron (the Auger electron) is emitted to the continuum. The description of the system is performed in the time domain, by time-evolving the many-particle wave function. Tracking the density of charge in the atomic levels and the continuum levels allows for a description of the dynamics of photoe- mission and Auger decay. Calculating the concurrence, as measure of entanglement, between the photoelectron and the Auger electron, gives insight about the correlation between their spins. We consider two scenarios; altering the relative strengths of the matrix elements responsible for anti-parallel and parallel spin configuration while keeping the interaction between the photoelectron and the Auger electron fixed, and secondly varying the interaction while keeping all the matrix elements fixed. The effect of increasing the strength of the parallel-spin configuration can be seen in the concurrence decreasing, diminishing the correlation between the spin of the photo- and the Auger electron. Furthermore, we find that the interactions between the electrons in the continuum strongly affect the modality of entanglement. While giving a rather simplistic description of a realistic atomic system, our results support the scope of the model to give valuable conceptual insight, into novel qualitative aspects of the temporal dynamics of the Auger decay.