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 two-level 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 Kronig-Penney model while disregarding the electron-electron interaction. Correspondingly, emphasis is placed on the short-time dynamics during sub- and 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 strong dependence on the duration of transform-limited pulses. This observation is the combined result of different causes. Transform-limited subfemtosecond pulses are spectrally very broad, causing a large portion of the spectrum to overlap with the band gaps. Therefore, the ionization probability tends to decrease for short pulses or, conversely, longer pulse durations enhance the radiation damage to the crystal. This trend breaks for few-femtosecond pulses as soon as the energy selection rule becomes sufficiently strong so that fewer states are available for efficiently driven transitions. Hence, the radiation damage decreases with increasing pulse durations on the longer time scale. Provided that the relaxation of off-diagonal elements of the one-body reduced density matrix is not too fast, the ionization probability turns out to be close to zero for a certain pulse duration of a few femtoseconds. This is interesting because returning the sample back to its initial state by the very same pulse responsible for the excitation might open up entirely new experimental possibilities at free-electron lasers. Complicating a potential experimental realization, a heavy dependence on the pulse characteristics of this feature is seen. For stronger pulses, Rabi-like dynamics is observed, reflected in both the occupation numbers and the electron density, which exhibits characteristics of a standing wave before being partially reabsorbed. In this context, the tuning of the photon energy for systematically coming as close as possible to an ideal scenario for prominent Rabi-like dynamics is investigated. To address the discrepancies between the dynamics of the isolated atom and the model crystal with respect to the anticipated ionization probability, one investigates short ordered chains of atoms as an intermediate level between a single atom and an infinite crystal. For this purpose, all approximations from the model crystal are retained including the reduction to one space dimension so that the considered chains contain a crystal similar to the model system studied before in the limiting case of a large number of atoms. This approach deliberately disregards electrostatic trapping in order to identify another trapping mechanism based on a coherent time evolution, analogous to the findings obtained from the crystal model. Likewise, it is seen that the forming of standing waves inhibits the electron flux away from the atom chain and may lower the ionization probability via Pauli blocking, resulting in a localization effect and a reduced ionization. Focusing on the charge density in the vicinity of the middle atom, one surprisingly discovers that the infinite-crystal limit is reached for comparatively low number of atoms. Relatedly, a significant modification of the evolution of the charge density is seen for a chain comprising only three atoms, thereby clearly showing another trapping effect which does not originate from electrostatic interactions. Further simulations with reduced models indicate that these observations do neither require the buildup of a band structure --accompanied by a modified density of states-- nor efficient potential scattering of photoelectrons. It is concluded that the coherent trapping phenomenon can be traced back to quantum interferences. Moreover, two generalizations of the model address further questions. Firstly, it is demonstrated that introducing disorder to the chain only marginally affects the results. Secondly, a time-dependent Hartree-Fock approach, which takes electrostatic trapping into account, turns out to even weaken the localization effect in comparable scenarios. In particular, no enhancement of the trapping is seen by considering both mechanisms simultaneously. In summary, a pronounced impact of coherent dynamics is seen in all considered systems due to the choice of photon energies close to an absorption edge or a resonant transition. This condition is often met in the region of vacuum and extreme ultraviolet or in the soft X-ray region, and may also be fulfilled in the X-ray regime the presence of heavy atoms such as iron or highly charged ions.
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