Doctor of Philosophy / Department of Physics / Uwe Thumm / Although the latest and most powerful supercomputer today, Tianhe-2 in China, can finish 33.86 quadrillion floating-point operations per second (www.top500.org), it is still a big challenge to simulate the simplest few-electron system - the helium atom - a threebody system with one nucleus and two electrons. Within the fixed-nucleus approximation and time-dependent close coupling (TDCC) approach, we developed software to solve the time-dependent Schrödinger equation (TDSE) accurately, implementing the finite-element discrete-variable representation (FE-DVR) scheme. The general idea of the method is to expand the wave functions in the eigenvectors of the angular momentum operator, which further transform the six-dimensional TDSE to a set of infinite two-dimensional coupled equations. Although there are infinitely many coupled equations, they can be truncated to a finite number of equations by applying selection rules and physical requirements, and solved with our current computational resources. By numerically solving the TDSE in full dimensionality, we investigate the double photoionization of helium atoms in external fields. In co-planar emission geometry with and without the presence of a comparatively weak infrared (IR) laser pulse, we discuss the double ionization (DI) dynamics of helium atoms irradiated by ultrashort pulses of extreme ultraviolet (XUV) laser light. We first investigate the degree of electronic correlation by correlated photoelectron angular distributions for two-photon double ionization (TPDI) of helium atoms in the sequential and non-sequential DI regime. We quantify sequential and non-sequential contributions to TPDI driven by an XUV pulse with central photon energy hw[subscript]xuv near the sequential DI threshold. If the spectral width of the XUV pulse is broad enough, both the sequntial (hw[subscript]xuv > 54.4 eV) and non-sequential (hw[subscript]xuv < 54.4 eV) channels are open. Therefore, the sequential and non-sequential DI mechanisms are difficult to distinguish. By tracking the DI asymmetry in joint photoelectron angular distributions, we introduce the forward-backward-emission asymmetry as a measure that allows the distinction of sequential and non-sequential contributions. Specifically, for hw[subscript]xuv = 50 eV pulses with a sine-squared temporal profile, we find that the sequential DI contribution is the largest at a pulse length of 650 as (1 as = 10[superscript]−18 s), due to competing temporal and spectral constraints. In addition, we validate a simple heuristic expression for the sequential DI contribution in comparison with ab initio calculations. We then investigate the influence of the laser field on the DI of helium by a single XUV pulse. For IR-laser-assisted single-XUV-photon DI our joint angular distributions show that the IR-laser field enhances back-to-back electron emission and induces a characteristic splitting in the angular distribution for electrons that are emitted symmetrically relative to the identical linear polarization directions of the XUV and IR pulse. These IR-pulse-induced changes in photoelectron angular distributions are (i) imposed by different symmetry constraints for XUV-pulse-only and laser-assisted XUV-photon DI, (ii) robust over a large range of energy sharing between the emitted electrons, and (iii) consistent with the transfer of discrete IR-photon momenta to both photoelectrons from the assisting IR-laser field. While selection-rule forbidden at equal energy sharing, for increasingly unequal energy sharing we find back-to-back emission to become more likely and to compete with symmetric emission. To obtain a high level of accuracy, accurate quantum-mechanical calculations of three Coulomb interacting particales exposed to an intense XUV and weak IR field are at the limit of current computational power. Any direct extension (such as strong laser-field intensity, elliptically-polarized field, and laser-induced DI) of our approach to more complicated systems appears to be currently out of reach. At the end of this thesis, we give suggestions on how to improve the efficiency of TDSE calculations for simulations of these complicated many-photon processes.

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