Nowadays experiments with Josephson circuits that behave as artificial atoms rival and even surpass their atomic physics counterparts. Nevertheless, these circuits exploit only partially the richness of the Josephson effect, as they overlook the existence of an internal, spin-like degree freedom, inherent to all Josephson structures. We spotlight this pseudospin with experiments on the simplest Josephson weak-link: a one-atom contact between two superconductors. The pseudospin represents here the two possible states of a Cooper pair localized around the contact. We will describe in particular experiments in which the atomic contact is coupled to a microwave resonator and show the coherent manipulation of the quantum state of the pseudospin, illustrated by Rabi oscillations and Ramsey fringes, as done for atoms and qubits.