Real Space-Real Time Evolution of Excitonic States Based on the Bethe-Salpeter Equation Method.

We introduce a method for constructing localized excitations and simulating the real time dynamics of excitons at the Many-Body Perturbation Theory Bethe-Salpeter Equation level. We track, on the femto-seconds scale, electron injection from a photoexcited dye into a semiconducting slab. From the time-dependent many-body wave function we compute the spatial evolution of the electron and of the hole; full electron injection is attained within 5 fs. Time-resolved analysis of the electron density and electron-hole interaction energy hints at a two-step charge transfer mechanism through an intermediary partially injected state. We adopt the Von-Neumann entropy for analyzing how the electron and hole entangle. We find that the excitation of the dye-semiconductor model may be represented by a four-level system and register a decrease in entanglement upon electron injection. At full injection, the electron and the hole exhibit only a small degree of entanglement indicative of pure electron and hole states.