Coherent ionization dynamics induced by intense X-ray free-electron laser pulses

Coherent ionization dynamics induced by intense X-ray free-electron laser pulses In this dissertation, theoretical models of atoms, clusters, and solids irradiated by ultrashort and intense pulses from an (X-ray) free-electron laser are investigated with the objective to find appropriate conditions where coherent dynamics manifests itself in physical observables. The ionization dynamics induced by an X-ray or extreme ultraviolet laser pulse is typically dominated by inner-shell one-photon absorption and subsequent relaxation processes, ultimately leading to sequential multiphoton ionization. If atoms are exposed to laser pulses with a photon energy well separated from absorption edges, a rate-equation description is generally sufficient for describing the temporal evolution of charge states. As this thesis is geared towards coherent ionization dynamics, scenarios have been selected for further analysis where the energy of incident photons is either in the vicinity of or below the most relevant absorption edge. Resonant two-photon absorption is discussed within a generic model comprising a twolevel system plus an energetically separated continuum of states. The two discrete states are in resonance with the electric field of a laser pulse; the ground state energy (relative to the lowest continuum state) is less than twice the photon energy, allowing for an ionization process based on the absorption of two photons. Under these circumstances, the results of two distinct approaches are compared. In the Markovian theory, on the one hand, the coupling to the continuum is reduced to the rate-equation level while possible Rabi cycling between the two discrete states is fully taken into account. The rate-equation approach, on the other hand, further simplifies the situation by treating the two-level system analogous to the Einstein rate equations. It is demonstrated that the ionization probability grows quadratically with increasing number of incident photons for weak pulses, which goes over into a linear scaling behavior for more intense pulses. This finding is supported by both approaches despite the fact that the underlying mechanisms are fundamentally different in the Markovian and the rate-equation theory. The observed phenomenon is attributed to either Rabi cycling or equal populations induced by an equilibrium of absorption and stimulated emission. Even though the ionization yield does not allow drawing a conclusion which of the two theories is more adequate over a broad intensity range, they turn out to be still distinguishable with regard to the crossover between these two intensity regimes of quadratic and linear scaling. If, for instance, the Markovian theory is applicable, the onset of the transition is hence governed by the Rabi frequency instead of the photon number. Finally, it is shown that the Rabi frequency as a key variable in this scenario is subject to a renormalization due to the coupling to the continuum. Furthermore, an atomic crystal is simulated in one space dimension (1d) based on a KronigPenney model while disregarding the electron-electron interaction. Correspondingly, emphasis is placed on the short-time dynamics during suband few-femtosecond pulses, where the Auger processes are assumed to be virtually frozen. The direct one-photon absorption is allowed in all cases, but the photon energy is always chosen to have similar values as the K-edge, thus generating only slow photoelectrons. As long as the analyses are confined to the short times before the onset of relaxation processes, the rate equations for independent atoms would yield no dependence of the ionization probability on the pulse duration if the total photon number is kept constant. In contrast, time-dependent Schrödinger equation calculations demonstrate a