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The thesis analyses the process of pair annihilation into one photon in a laser pulse. The theory of how to include pulse shapes in Strong Field QED and the resulting cross section is presented. The cross section is calculated and estimated for lasers of ELI and XFEL facilites. It is found that the effect may be experimentally verifiable at high frequency XFEL facilities for very finely tuned particle kinematics, but negligible at high intensity optical laser facilities such as ELI.

For the first time, a full-dimensional quantum-mechanical description of excitation, dissociation and ionization of H2+ in intense laser fields is presented. The quantum-mechanical propagation of the nuclei is carried out approximately using time-dependent Floquet surfaces and the Coulomb surface, switching between these surfaces is possible stochastically (”hopping”). The impact of quantum effects in the nuclear dynamics on dissociation and ionization as well as their interplay is investigated in detail. The results are in excellent agreement with experimental data. It is shown in particular that quantum effects in the nuclear dynamics are essential for the description and interpretation of the experiments.

For the first time, a full-dimensional quantum-mechanical description of excitation, dissociation and ionization of H2+ in intense laser fields is presented. The quantum-mechanical propagation of the nuclei is carried out approximately using time-dependent Floquet surfaces and the Coulomb surface, switching between these surfaces is possible stochastically (”hopping”). The impact of quantum effects in the nuclear dynamics on dissociation and ionization as well as their interplay is investigated in detail. The results are in excellent agreement with experimental data. It is shown in particular that quantum effects in the nuclear dynamics are essential for the description and interpretation of the experiments.:1 Introduction 1 2 Theory 3 2.1 Methods for the description of H+ 3 2.2 Hopping between potential surfaces 5 2.3 Equations of motion 9 2.3.1 The classical equations of motion for the nuclei 11 2.3.2 The Schr¨odinger equation for the electronic part 12 2.3.3 The connection between classical and quantum mechanical propagation 13 2.4 Calculation and discussion of required quantities 15 2.4.1 Born-Oppenheimer states and Born-Oppenheimer surfaces 15 2.4.2 Floquet states and Floquet surfaces 16 2.4.3 Initial conditions 22 2.5 Dissociation 24 2.5.1 Hopping between Floquet surfaces 25 2.5.2 Comparison with full quantum-mechanical results 29 2.6 Ionization 32 2.6.1 Hopping to the Coulomb surface 32 2.6.2 Comparison with NA-QMD results 37 3 Application: Fragmentation dynamics of H+ in short, intense laser pulses 41 3.1 Dissociation and ionization probabilities 43 3.1.1 Time resolved probabilities 43 3.1.2 Intensity resolved probabilities 44 3.1.3 Angular resolved probabilities 48 3.2 Kinetic energy release (KER) 50 3.2.1 Angular integrated KER 50 3.2.2 Angular resolved KER 54 3.2.3 Distribution of the ionization hops 56 3.3 The role of rotationally excited initial conditions 57 3.4 Comparison with experimental data 61 3.4.1 Dissociation KER 62 3.4.2 Angular distribution of dissociating fragments 64 3.4.3 ionization KER 65 Summary, conclusion, and outlook 67 Appendices 69 Bibliography 83