This thesis discusses two experiments highlighting the existence of a fermionic degree of freedom in the Josephson effect: the Andreev doublet. They are both performed on the most basic Josephson element, a one-atom contact between two superconducting electrodes. In the first one, we observed the disappearance of the supercurrent, which reflects the spontaneous trapping of a quasiparticle in one of two Andreev bound states. In the second experiment we achieved the photon-absorption spectroscopy of this two-level system, using a Josephson junction as an integrated on-chip microwave emitter and detector. The observed spectra are well accounted for by a spin-boson model including the Andreev doublet and an electromagnetic mode of the environment.