Abstract : The Josephson effect appears when a weak-link establishes phase coherence between two superconductors. A unifying theory of this effect emerged in the 90's within the framework of mesoscopic physics. Based on two cornerstone concepts, conduction channels and Andreev reflection, it predicts the current-phase relation for the most basic weak-link: a single conduction channel of arbitrary transmission.
This thesis illustrates this mesoscopic point of view with experiments on superconducting atomic size contacts. In particular, we have focused on the supercurrent peak around zero voltage, put into evidence the ac Josephson currents in a contact under constant bias voltage (Shapiro resonances and photon assisted multiple Andreev reflections), and performed direct measurements of the current-phase relation.