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On the basis of the two developed theories, multi-mode effects resulting from large losses in leaky resonators are investigated. 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. It is shown that one can thereby directly derive a nuclear ensemble Master equation using Green's functions to encode the cavity environment. In addition, a second orthogonal approach is developed to enable the numerically efficient treatment of complex cavity geometries. The resulting ab initio few-mode theory is applied to the x-ray cavity case, generalizing a previous phenomenological model. 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. In this thesis, a theoretical framework for x-ray cavity QED with Mössbauer nuclei is developed. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic–plasmonic modes. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. Feist, “Few-mode field quantization of arbitrary electromagnetic spectral densities,” Phys.

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We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes.

The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high-dimensional continuum. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant photodetection model. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models.

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Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. Our results allow one to derive rigorous models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. We also consider gauge conditions with explicit time-dependence, enabling us to unambiguously introduce phenomenologically time-dependent light-matter interactions in any gauge.

We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges. Here, we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially-dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize.