During the first half of project FERMIcQED, the team has executed a two-pronged strategy, which consists in developing and characterizing hybrid Josephson junctions of high-quality on the one hand, and building cQED architectures that are compatible with low-dimensional conductors on the other. A novel nanofabrication technique was first developed, which allows for the production of hybrid Josephson junction devices based on encapsulated carbon nanotubes. Multiple devices were fabricated and measured at cryogenic temperatures. Quantum transport experiments demonstrated gate-dependent supercurrents, as large as 8 nA, and spectroscopic signatures of the Andreev bound states. These measurements led to the discovery of new physics, with the observation of quantum phase transitions in a four-fold degenerate superconducting quantum dot. In parallel, cQED architectures were developed and characterized at microwave frequencies. A quantum control experiment was first performed using a tunnel junction-based transmon qubit that displayed large coherence times, thus demonstrating that the experimental setup is ready for more exotic qubits. Carbon nanotube-based junctions were then integrated in these architectures, in order to detect the Andreev bound states with photons. To do so, we developed a novel two-tone spectroscopy technique that is based on the AC Josephson effect and that can operate at millimeter-wave frequencies. Finally, a carbon nanotube-based bosonic qubit could be implemented. Radio-frequency measurements were performed and demonstrated a gate-tunable qubit spectrum, consistent with Andreev physics. This work culminated with the quantum control of this newly developed qubit, with modest though promising coherent times of ~ 40 ns. In parallel, theoretical works were performed in order to investigate the hybridization of the Andreev bound sates in double quantum dot geometries and the resulting non-reciprocal Josephson effect.
