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Abstract

Mössbauer spectroscopy is well established across the natural sciences. The exceptionally narrow linewidths of Mössbauer nuclei also make them a promising platform for x-ray quantum optics. Several fundamental quantum-optical phenomena, including electromagnetically induced transparency and superradiance, have already been demonstrated. Yet for decades, the same narrow linewidth restricted experiments at synchrotrons to the low-excitation regime, with on average less than one resonant photon per pulse. This limitation changed with the advent of X-ray free-electron lasers (XFELs), which deliver orders of magnitude more photons than synchrotrons. As a result, pulses containing multiple resonant photons occur frequently, enabling experiments previously not possible. In this thesis, we present several first-of-their-kind XFEL-experiments conducted within our collaborations. We demonstrate the x-ray excitation of the 45 Sc nuclear clock transition, introduce and apply a single-shot analysis to Mössbauer time-domain data, and investigate unexpected signals observed in nuclear resonant scattering with XFELs. Additionally, we simulate the de-excitation dynamics of a nuclear ensemble. Besides establishing a suitable simulation scheme, we focus on non-linear effects arising from dipole-dipole couplings and non-linear modifications of propagation effects. Together, these results show how the unprecedented intensities of XFELs open a new era for Mössbauer science, advancing both experiment and theory.