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Abstract

In this thesis, a theoretical framework for x-ray cavity QED with Mössbauer nuclei is developed. First, it is shown how Jaynes-Cummings-like few-mode models for open resonators can be derived from first principles, which has been an open question in the quantum optics literature. The resulting ab initio few-mode theory is applied to the x-ray cavity case, generalizing a previous phenomenological model. In addition, a second orthogonal approach is developed to enable the numerically efficient treatment of complex cavity geometries. It is shown that one can thereby directly derive a nuclear ensemble Master equation using Green's functions to encode the cavity environment. This approach provides an ab initio quantum theory for the system, which resolves previous discrepancies and allows to semi-analytically calculate cavity-modified nuclear level schemes without the need for a fitting procedure. On the basis of the two developed theories, multi-mode effects resulting from large losses in leaky resonators are investigated. A general criterion is introduced to identify and classify such multi-mode effects, which demonstrates that they are responsible for previously observed signatures in x-ray cavity experiments and can be harnessed to artificially tune nuclear quantum systems. Further interesting cusp features in nuclear Fano interference trajectories of x-ray cavities with overlapping modes are reported. Finally, the gained insights are employed to investigate nonlinear excitation dynamics of Mössbauer nuclei in the presence of strong x-ray driving fields. The feasibility of inverting nuclear ensembles at upcoming facilities and the possibility of using focused pulses in combination with x-ray cavities for intensity boosting is analyzed.