Evolution of entanglement in electron–electron collisions

Abstract

The collision between two electrons is treated in a time-dependent three-dimensional approach involving a two-electron wave packet, which is composed of stationary solutions of the two-electron Schroedinger equation with Coulomb interaction. As a quantitative measure of the entanglement between the two electrons we employ a renormalized linear entropy, which is readily obtainable from the one-electron reduced density matrix in real space. Starting with a non-entangled initial state consisting of two separate one-electron packets, the scattering process is visualized on a femtosecond time scale by a sequence of snap shots of the one-electron density. The corresponding evolution of the linear entropy is shown for several energy values up to 200 eV (per electron in the center-of-mass system). The maximal entanglement, which is characterized by the asymptotic value of the linear entropy, is found to decrease strongly with increasing energy. The entropy for anti-parallel spins turns out to be almost the same as for parallel spins, which means that spin entanglement is vastly dominated by spatial entanglement.