Spectrally Resolved Extreme Ultraviolet Lensless Imaging With High Order Harmonic Generation Sources

High harmonic generation (HHG) serves as a transformative gateway to the quantum dynamics of electrons, offering a unique perspective on the ultrafast processes that govern chemical and physical transformations at the atomic scale. By focusing intense laser pulses into a noble gas, we can coerce the gas's electrons into a nonlinear dance—where they absorb multiple photons, tunnel through their atomic potentials, and re-emit this energy as they snap back to lower energy states, producing bursts of extreme ultraviolet (EUV) and soft X-ray radiation. Combining HHG with lensless imaging paves the way for revolutionary technological advancements in imaging and diagnostics, probing dynamics previously veiled by the limits of temporal resolution. The focus of the second chapter is the application of HHG in coherent diffractive imaging (CDI), where the coherence and extreme ultraviolet wavelengths of HHG sources allow for imaging with high spatial resolution and chemical sensitivity. CDI, a lensless imaging technique, circumvents the resolution limits imposed by lens-based systems, exploiting the phase retrieval from diffraction patterns to reconstruct images of nanostructures and biological specimens. The unique properties of HHG-enhanced CDI lie in its ability to spectrally reconstruct the image of the object, providing a powerful tool for understanding the 3D structure of the object and its chemical composition. This chapter paves the way towards spectrally resolved ptychography. In the third chapter, we propose the concept of spatial entropy minimization as a computational design principle for both mono- and polychromatic focusing optics. We show that spatial entropy minimization yields conventional ZPs for monochromatic radiation. For polychromatic radiation, we observe a previously unexplored class of diffractive optical elements (DOEs), allowing for balanced spectral efficiency. We apply the proposed approach to the design of a binary ZP, tailored to multispectral focusing of extreme ultraviolet (EUV) radiation from a high-harmonic table top source. The polychromatic focusing properties of these ZPs are experimentally confirmed using ptychography. This work provides a new route towards polychromatic wavefront engineering at EUV and soft-X-ray wavelengths. The fourth chapter focus on the technical challenges and solutions associated with measuring and manipulating the wavefronts of high-order harmonic beams. Here we present a wavefront sensing solution based on multiplexed ptychography, with which we show spectrally-resolved, high-resolution beam reconstructions.using these high fidelity quantitative wavefront measurements, we investigate aberration transfer mechanisms in the high harmonic generation process, where we present and explain harmonic-order dependent astigmatism inheritance from the fundamental wavefront. This ptychographic wavefront sensing concept thus enables detailed studies of the high-harmonic generation process, such as spatiotemporal effects in attosecond pulse formation. The final chapter consolidates the chromatic aberrations inherent in the HHG process, highlighting their impact on the focusability and quality of generated beams across different harmonic orders. By systematically varying the generation conditions and employing sophisticated wavefront characterization techniques, we uncover the wavelength-dependent focusing properties of HHG beams. The insights gained from these studies are crucial for optimizing the generation and application of high harmonics in various scientific and technological arenas

Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we theoretically study a related but different system with reduced symmetry - twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal stacked bilayer graphene sheets, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field $D$. We construct a phase diagram as a function of twist angle and $D$, incorporating interactions via a Hartree-Fock approximation. At half filling, ferromagnetic insulators are stabilized, typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the metallic state are argued to lead to spin triplet superconductivity from pairing between electrons in opposite valleys. Response of these states to a magnetic field applied either perpendicular or parallel to the graphene sheets is obtained, and found to compare favorably with a recent experiment. We highlight a novel orbital effect arising from in-plane fields that can exceed the Zeeman effect and plays an important role in interpreting experiments.Comment: main 15 pages, appendix 11 page

Dynamics of Frenkel excitons in pigment-protein complexes and hybrid systems

A Quantum Master Equation approach is applied to describe the exciton dynamics of the FMO complex, focusing on the effects of vibrations. Further, an excitonic model is applied to the description of the LH2 antenna complex to unravel the origin of the unusual B800 absorption band splitting and to connect this to observed exciton relaxation rates. In the second part a DFTB approach yielding a discrete representation of the electronic quantum mechanical charge density in terms of atom-centered Mulliken charges is used for the description of molecules nearby a metal nanosphere.In der vorliegenden Arbeit wurde der Zugang der Quanten-Master-Gleichung genutzt, um die Dynamik im FMO-Komplex zu untersuchen. Weiterhin wurde ein exzitonisches Modell für den LH2-Antennenkomplex der Bakterienform Alc. vinosum, entwickelt, um eine Erklärung der ungewöhnlichen Form der B800 Absorptionsbande und deren Beziehung zu den beobachteten Exziton-Relaxationsraten zu finden. Im zweiten Teil der Arbeit wurde ein DFTB-Zugang, der eine diskrete Darstellung quantenmechanischer elektronischer Ladungsdichten erlaubt, zur Beschreibung von Hybridsystemen genutzt