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The defence will be in English.
Abstract: Quantum impurity models are of paramount importance in condensed matter physics, as they make it possible to describe the emergent properties of a large collection of particles interacting with a single quantum system. Recent progress in experimental techniques have been leveraged to emulate such models in the lab. In particular, recent advances in the field of circuit-quantum electrodynamics (circuit-QED) have made it possible to experimentally reach the quantum impurity regime where a single defect, like a qubit or a weak link, is ultra-strongly coupled to many modes of an electromagnetic environment. In such systems, owing to the strong non-linearity of the impurity, effective interactions start to develop between the initially independent modes of the environment, including processes that do not conserve the number of excitations – microwave photons in that context. The inelastic scattering of these latter off the impurity is archetypical of such non-conserving processes and has been indirectly observed through the microwave spectroscopy of superconducting circuits in very recent experiments. In this thesis, we go beyond spectroscopy and report the direct experimental observation of the photons that are produced during these inelastic scattering processes. More specifically, taking advantage of state-of-the-art amplification near the quantum limit, the fluorescence signal associated to the spontaneous down-conversion of microwave photons was directly measured. Additionally, we show that this down-conversion of microwave photons is directly linked to the dissipation of the system, hence confirming the scenario envisioned in spectroscopic studies preceeding this work. This photon-conversion process also allows us to explore the effects of quasiparticles (also known as broken Cooper pairs) on the excited states of the system. We report the observation of commensurable charging effects on a three-photon state that we can spectroscopically resolve through its coupling to a single-photon state. Beyond the motivations inherited from the study of quantum impurity models, these results contribute to the booming field of many-body quantum optics and offer a direct signature of the ultra-strong light-matter coupling. They are also of particular interest in the understanding of the coherence properties of high-impedance qubits, such as the Fluxonium or the 0 − π qubit, that rely on multi-mode structures.
