Single channel Josephson effect in a high transmission atomic contact

The Josephson effect in scanning tunneling microscopy (STM) is an excellent tool to probe the properties of a superconductor on a local scale. We use atomic manipulation in a low temperature STM to create mesoscopic single channel contacts and study the Josephson effect at arbitrary transmissions. We observe significant deviations from the Ambegaokar-Baratoff formula relating the critical current to the order parameter starting from transmissions of tau > 0.1. Using the full current-phase relation, we model the Josephson effect in the dynamical Coulomb blockade regime, where the charging energy of the junction capacitance cannot be neglected, and find excellent agreement with the experimental data. Projecting the current-phase relation onto the charge transfer operator shows that at high transmission, non-linear behaviour arises and multiple Cooper pair tunneling may occur. Our model includes these deviations, which become non-negligible in Josephson-STM, for example, when scanning across single adatoms.