Attosecond physics o ers new insights into ultrafast quantum phenomena involving electron dynamics on the fastest measurable timescales. The rapid progress in this field enables us to re-visit one of the most fundamental strong-field phenomena: field-induced tunnel ionization 1-3 . In this work, we employ high-harmonic generation to probe the electron wavefunction during field-induced tunnelling through a potential barrier. By using a combination of strong and weak driving laser fields, we modulate the atomic potential barrier on optical subcycle timescales. This induces a temporal interferometer between attosecond bursts originating from consecutive laser half-cycles. Our study provides direct insight into the basic properties of field-induced tunnelling, following the evolution of the electronic wavefunction within a temporal window of approximately 200 attoseconds.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

High harmonic spectroscopy has the potential to combine attosecond temporal with sub-Angstrom spatial resolution of the early nuclear and multielectron dynamics in molecules. It involves strong field ionization of the molecule by the IR laser field followed by time-delayed recombination of the removed electron with the molecular ion. The time-delay is controlled on the attosecond time scale by the oscillation of the IR field and is mapped into the harmonic number, providing a movie of molecular dynamics between ionization and recombination. One of the challenges in the analysis of high harmonic signal stems from the fact that the complex dynamics of both ionization and recombination with their multiple observables are entangled in the harmonic signal. Disentangling this information requires multidimensional approach, capable of mapping ionization and recombination dynamics into different independent parameters. We suggest multidimensional high harmonic spectroscopy as a tool for characterizing of ionization and recombination processes separately allowing for simultaneous detection of both the ionization delays and sub-cycle ionization rates. Our method extends the capability of the two dimensional (2D) set-up suggested recently by Shafir et al on reconstructing ionization delays, while keeping the reconstruction procedure as simple as in the original proposal. The scheme is based on the optimization of the high harmonic signal in orthogonally polarized strong fundamental and relatively weak multicolour control fields.

High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena.

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Multidimensional high harmonic spectroscopy is a cutting-edge technique for studying the effect of the intense low-frequency laser fields on atoms and molecules. The high energy photons, emitted by a particle as a result of the interaction with the strong laser field, carry the information about the processes in atoms and molecules, which lead to the emission. Multidimensional character of the technique allows to extract parameters of the molecular and atomic ionization dynamics, that were inaccessible before in the same experiment, such as sub-cycle ionization rates, ionization and recombination times.The Thesis presents in detail theoretical analysis of the multidimensional high harmonic generation process within semi-classical approach. Several generating field configurations are considered. The developed theoretical apparatus is then applied to describe multidimensional high harmonic spectroscopy experiments in helium. Initial analysis of the applicability of the technique for the study of multielectron dynamics in carbon dioxide is also performed.The problems, solutions to which are presented in the Thesis, are:• theoretical description of high harmonic generation in multicolor fields• analysis of the gating techniques for the extraction of the parameters of electron trajectories in high harmonic generation in He• proposition of an alternative reconstruction procedure of electron trajectory parameters, that allows one to access to all of them simultaneouslyThe main results of our work are:• Based on theoretical analysis of multidimensional high harmonic generation, we showed, that optimization of the two-dimensional harmonic 3 signal is achieved at each step of the process: ionization, propagation, dynamics in the ion and recombination• We demonstrated, that multidimensional high harmonic spectroscopy is a very sensitive tool allowing one to extract parameters of electron trajectories, such as complex ionization time and complex electron momentum, from the observed harmonic signal• We developed and applied theory to the analysis of two-color high harmonic generation experiments of He atom• We performed initial analysis of two-color HHG experiments in carbon dioxide, which was necessary for further investigation and reconstruction I thank Bettina Becker, the most helpful person in the institute or in the whole world, who made the bureaucratic problems very easy. There was no question she didn't answer and no problem she didn't solve quickly and efficiently.

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