Die Erzeugung immer kürzerer und energiereicherer Laserimpulse ist eine der wichtigsten Aufgaben der Laserphysik, um physikalische Phänomene in bisher unerreichten elektrischen Feldstärkebereichen zugängig zu machen und Beobachtungen auf kleinster Zeitskala zu ermöglichen. Mit Hilfe der Nachkompression verstärkter, in edelgasgefüllten Hohlfasern selbstphasenmodulierter Ti:Saphir-Laserimpulse werden die momentan kürzesten Impulse des sichtbaren Spektralbereiches erzeugt, die nur noch wenige Schwingungszyklen des elektrischen Feldes umfassen. Ebenso notwendig wie ein solcher Schritt der Impulskompression ist der verlässliche Nachweis seines Ergebnisses. Allerdings wächst auch die physikalische und technische Herausforderung einer präzisen und vollständigen Messung des ultrakurzen Laserimpulses mit zunehmender Komplexität und Breite des Impulsspektrums. Die vorliegende Arbeit stellt sowohl auf dem Gebiet der Kompression von Sub-10-fs Impulsen als auch auf dem der vollständigen Charakterisierung solcher Impulse optimierte aber auch neue Verfahrenstechniken vor. In Experimenten an einem zweistufigen Hohlfaserkompressor wird die Erzeugung der momentan kürzesten, nicht adaptiv komprimierten Impulse mit einer Dauer von lediglich 3,8 fs demonstriert. Eine elegante Alternative zu bisherigen Kompressionsmethoden zeigt der Nachweis effektiver Selbstkompression von mJ-Impulsen auf unter 8 fs in einem selbstführenden Edelgasfilament auf. Zur Kontrolle erfolgreicher Impulskompression und für eine phasenempfindliche Untersuchung des Prozesses der Dispersionskompensation über spektrale Bandbreiten von bis zu einer Oktave mussten etablierte Impulsmesstechniken wie das SPIDER- (Spectral Phase Interferometry for Direct Electric-field Reconstruction) und das FROG- (Frequency-Resolved Optical Gating) Verfahren weiterentwickelt werden. So wird mit der Realisierung und vollständigen Analyse interferometrischer FROG-Messungen ein neues phasenempfindliches Impulsmessverfahren vorgestellt. / One challenge of today’s laser physics is the stable compression of more and more intense laser pulses to the shortest possible pulse duration to enable new high-field laser experiments and to investigate fast atomic or molecular dynamics. At present, the shortest laser pulses of the visible spectral region envelop only a few cycles of the electric field. The state of the art method to generate such short pulses behind a Ti:sapphire amplifier laser system is by means of successive steps of spectral broadening inside a gas-filled hollow fibre and dispersion compensation. However, a reliable pulse characterization is as important as the pulse compression. The more spectral bandwidth the pulse covers the more technically challenging is the measurement of the pulse’s electric field structure. In this work, new concepts of compression and characterization of pulses down to durations below 10 fs are demonstrated as well as further optimization of established techniques. Due to modern, chirped-mirror based dispersion compensation pulses as short as 3.8 fs were generated with a two-stage hollow fibre compressor. At present, these are the shortest pulses of the visible spectral region, compressed without adaptive means for dispersion compensation. For the first time the effect of self-compression of mJ-pulses to below 8 fs in a self-guiding noble gas filament is demonstrated experimentally and determined by numerical simulations. Advanced pulse characterization schemes were needed for a phase-sensitive investigation of dispersion compensation and pulse compression of white light pulses. An optimized design of the SPIDER (Spectral Phase Interferometry for Direct Electric-field Reconstruction) technique is demonstrated that facilitates the measurement of the pulse’s spectral phase in case of broadband structured spectra. With the implementation of an interferometric FROG (Frequency-Resolved Optical Gating) a new phase-sensitive pulse characterization method is introduced.

We utilize the exact factorization of the electron-nuclear wave function [Abedi et al., PRL 105 123002 (2010)] to illuminate several aspects of laser-driven molecular dynamics in intense femtosecond laser pulses. Above factorization allows for a splitting of the full molecular wave function and leads to a time-dependent Schrödinger equation for the nuclear subsystem alone which is exact in the sense that the absolute square of the corresponding, purely nuclear, wave function yields the exact nuclear N-body density of the full electron-nuclear system. As one remarkable feature, this factorization provides the exact classical force, the force which contains the highest amount of electron-nuclear correlations that can be retained in the quantum-classical limit of the electron-nuclear system. We re-evaluate the classical limit of the nuclear Schrödinger equation from the perspective of the exact factorization, and address the long-standing question of the validity of the popular quantum-classical surface hopping approach in laserdriven cases. In particular, our access to the exact classical force allows for an elaborate evaluation of the various and completely different potential energy surfaces frequently applied in surface hopping calculations. The highlight of this work consists in a generalization of the exact factorization and its application to the laser-driven molecular wave function in the Floquet picture, where the molecule and the laser form an united quantum system exhibiting its own Hilbert space. This particular factorization enables us to establish an analytic connection between the exact nuclear force and Floquet potential energy surfaces. Complementing above topics, we combine different well-known and proven methods to give a systematic study of molecular dissociation mechanisms for the complicated electric fields provided by modern attosecond laser technology.:Contents Introduction 1 The exact factorization of time-dependent wave functions 1.1 Concern and state of the art 1.2 The exact factorization of the electron-nuclear wave function 1.3 The generalized exact factorization 1.4 The exact factorization for coupled harmonic oscillators 1.5 The exact factorization for a single particle with spin 1.6 The exact factorization of the laser-driven electron-nuclear wave function in the Floquet picture 1.7 Summary and conclusion 2 Quantum-classical molecular dynamics from an exact factorization perspective 2.1 Concern and state of the art 2.2 The exact nuclear TDSE 2.3 The Wigner-Moyal equation for the nuclear TDSE and its classical limit 2.4 The Bohmian formulation of the nuclear TDSE and its classical limit 2.5 Comparative calculations 2.5.1 Scenario 1: stationary states 2.5.2 Scenario 2: laser-driven dynamics 2.6 Summary and conclusion 3 Surface hopping in laser-driven molecular dynamics 3.1 Concern and state of the art 3.2 Surface hopping 3.3 Quantum-classical dynamics on the EPES 3.4 The benchmark model and its potential energy surfaces 3.5 Surface hopping in laser-driven molecular dynamics 3.6 Summary and conclusion 4 Beyond the limit of the Floquet picture: molecular dissociation in few-cycle laser pulses 4.1 Concern and state of the art 4.2 Theoretical few-cycle pulses 4.3 Calculation of dissociation probabilities 4.4 Dissociation in few-cycle pulses 4.4.1 Dissociation in half-cycle pulses 4.4.2 Dissociation in few-cycle pulses 4.5 Dissociation in realistic attosecond pulses 4.6 Summary and conclusion Outlook Appendices A List of abbreviations B Numerical details C Calculating electronic observables within quantum-classical molecular dynamics D Ionization in few-cycle pulses E Modeling an optical attosecond pulse Bibliography