This thesis explores how engineered bosonic environments in superconducting circuits can be harnessed to control light-matter interaction in regimes that extend beyond conventional cavity quantum electrodynamics (QED). We develop a scalable platform based on high kinetic inductance superconducting films, enabling the realization of compact, low-disorder coupled cavity arrays (CCAs) with fine spectral control. This platform is then used to study the dynamics of a giant atom in the superstrong coupling regime, where the coupling (G_n) of the qubit to mode (n) exceeds the free spectral range of the CCA, (\Delta\Omega_n).

In the first part of the thesis, we present the design and characterization of high-impedance CCAs using NbN thin films. This approach allows the implementation of resonators with footprints as small as (50 \times 75~\mu\mathrm{m}^2) and impedances of (Z_r \sim 1.5~\mathrm{k}\Omega), supporting free spectral ranges from hundreds of MHz down to 5~MHz. We engineer arrays with up to five resonators per unit cell and realize various band structures, including uniform, dimerized (Su-Schrieffer-Heeger SSH), and multigap configurations. We quantitatively characterize the CCA disorder using topological edge modes in SSH arrays, developing a likelihood-based method to extract resonator frequency fluctuations. Measurements on over 25 SSH devices confirm frequency disorder levels of (0.22^{+0.04}{-0.03}%), while maintaining low internal losses ((\kappa\textrm{int}/2\pi \sim 100~\mathrm{kHz})) and excellent scalability.

In the second part, we explore multimode QED in the superstrong coupling regime by embedding a transmon qubit into a two-band CCA. The qubit is non-locally coupled to seven lattice sites, forming a giant atom whose interaction with the bath strongly modifies the spectrum. Harnessing interference effects between the giant atom and the bath, we reach coupling ratios (G_n/\Delta\Omega_n > 10). Using a combination of spectroscopy and time-domain measurements, we extract the atomic participation ratio (APR) for all eigenmodes and observe a clear breakdown of the single-mode Jaynes-Cummings model, revealing mode-mode interactions mediated by the qubit.

Furthermore, we investigate directionality in the dressed CCA wavefunction induced by the qubit. We experimentally demonstrate asymmetric mode localization, leading to directional emission of single-photon states. By preparing the qubit in a bandgap-localized state and transferring it into the band, we show that emission can be routed predominantly to one side of the array. This result opens new opportunities for directional quantum optics in engineered superconducting systems.

Together, these results establish high-kinetic inductance CCAs as a powerful platform for analog quantum simulation of impurity models and structured light-matter interactions, offering new pathways to control dissipation, engineer photon-mediated interactions, and probe non-Markovian dynamics in circuit QED.