Dissipative phase transition and duality of the Josephson junction

More than a century after its discovery, superconductivity is used today in many applications. One of those is in superconducting electronics, of which the Josephson junction is a basic building block. This element has enabled the realisation of electronic circuits in the quantum regime, and it has helped redefining the Volt in the SI system around quantum effects. Nowadays, a lot of time and efforts are spent in order to improve Josephson junction based circuits to realise state of the art Quantum-bits for quantum computing. One may think that those highly sensitive experiments involving Josephson junctions and conventional superconductivity imply an exquisite understanding of the component and its behaviour. We show in this thesis work that this is not entirely the case, and we explore two types of superconducting quantum circuits that are in need of clarification. The first one concerns the Josephson junction itself, and a subtle issue regarding its interaction with its electromagnetic environment. Indeed, it has been predicted nearly 40 years ago that a Josephson junction would become insulating when connected to a resistance larger than Rq=h/4e²≈6.45 kΩ. We find no traces of such insulating state in our experiments which measure the admittance of a Josephson junction connected in parallel to a resistance R>Rq. The second circuit we explore is the supposedly dual circuit to the Josephson junction, the quantum phase slip junction, which consists of a nanowire made of a highly inductive superconductor. In those nanowires 2π phase slips of the superconducting phase should produce the dual effects of the Cooper-pair tunneling in Josephson junctions. The control of such an effect would then permit the realisation of a new class of superconducting quantum devices. We measured microwaves resonators patterned in a thin film of a highly inductive superconductor. We find no clear signal revealing the presence of quantum phase slips in our devices. However, we find a clear signature of two-level system low frequency noise, and we explore its implication in this kind of devices.