Multiple ionization in strong laser fields

With the ultrashort laser pulses available today, intensities which exceed the binding electrical field of an atom by several orders of magnitude are routinely achieved. As a consequence, it is possible to remove (ionize) one electron or several electrons from an atom within one pulse. The intensity dependence of laser-induced ionization is highly nonlinear and is mostly studied with chemically inert noble gases, using pulses with frequencies in the visible or near-infrared range. For intensities above 10^14 W/cm^2 and femtosecond pulse durations, single ionization (A->A+) can be described very well as a tunneling process with subsequent classical motion of the electron in the laser field. Ionization of \textit{two} electrons can be expressed in terms of two independent single ionization steps (sequential double ionization, A->A+->A2+) if the intensity is high enough (e.g. I>10^15 W/cm^2 for neon). However, for smaller intensities, the measured A2+ ion yields are several orders of magnitude larger than those expected from the sequential mechanism and the transition to the sequential regime leads to a characteristic knee structure in the intensity dependence of the yield. The ionization pathway responsible for the increased production of A2+ ions, i.e. the simultaneous ejection of two electrons (A->A2+), is called nonsequential double ionization (NSDI). For the description of this process, a semiclassical rescattering mechanism has proved successful. According to the rescattering mechanism, an electron tunnels from the atomic potential, is accelerated by the laser field and driven back to the ion where, in an inelastic collision, a second electron is released. With respect to the final momenta of the ionized electrons, the rescattering mechanism also allows for quantitative predictions which are in good agreement with experimental results. The mechanisms of double ionization can be generalized to ionization of an arbitrary number of electrons, with all pathways deviating from the sequential one being referred to as nonsequential multiple ionization. An understanding of triple ionization is of special interest since it is the first case for which several competing nonsequential pathways exist, i.e. simultaneous ionization of three electrons described by the rescattering mechanism (I: A->A3+) and the two combinations of single ionization with NSDI by rescattering (II: A->A+->A3+ and III: A->A2+->A3+). Considering the nonlinear dependence of the tunneling probability on the ionization energies of the participating charge states, one expects that only the pathways I and II contribute significantly to the A3+ yield in the nonsequential intensity regime (e.g. IA+->A2+->A3+), respectively. Based on the predictions of the rescattering mechanism, these transitions should also manifest themselves in the momentum distributions of the A3+ ions. Since experiments could only partially confirm the above expectations, a detailed theoretical investigation of triple ionization is desirable. In this work, quantum mechanical simulations of triple ionization with laser pulses of visible and near-infrared frequencies are presented. To allow for efficient numerical calculations, the motion of the electrons is restricted to a three-dimensional subspace of the full configuration space. This modeling approach has already proved successful in the qualitative investigation of double ionization. From the quantum mechanical wave function of the model, several quantities are calculated which can also be measured experimentally (ion yields, electron and ion momentum distributions) and their dependence on the laser parameters (intensity, frequency, pulse duration) is studied. The main goal of this work is to understand the pathways and mechanisms of triple ionization in the different intensity regimes. For this purpose, we first study the ion yields as a function of intensity. Using one- and two-electron approximations, the yields of the pathways II - IV can be written as products of the yields of the intermediate charge states. This way, it is possible to quantitatively understand the A3+ yields in a wide range of intensities. To quantify the remaining pathway I, rescattering of an electron is analyzed classically (by performing trajectory studies) and quantum mechanically (by considering the time-dependent probability flux). Finally, the insights gained from the product yields and the rescattering analysis are used to interpret the A3+ ion momentum distributions which reflect the change of the prevalent ionization pathway more clearly than the yields. A major result of this work is the importance of classical thresholds for simultaneous multiple ionization. For example, the onset of the regime where the intensity-dependent A3+/A+ yield ratio is approximately constant can be identified with the threshold intensity of simultaneous triple ionization where the energy of the rescattered electron is equal to the sum of the two ionization energies of the A+ ion. Furthermore, the investigation of the A3+ yields indicates that the pathway III plays a much more important role for triple ionization in the nonsequential intensity regime than previously thought. Finally, one has to emphasize the ability of the model to qualitatively reproduce the essential experimental observations on triple ionization