Single-Channel Josephson Effect in a High-Transmission Atomic Contact

The Josephson effect in scanning tunneling microscopy is an excellent tool to probe the properties of the superconducting order parameter on a local scale through the Ambegaokar-Baratoff (AB) relation. Using single atomic contacts created by means of atom manipulation, we demonstrate that in the extreme case of a single transport channel through the atomic junction, modifications of the current-phase relation lead to significant deviations from the linear AB formula. Using the full current-phase relation for arbitrary transmission, we model the Josephson effect in the dynamical-Coulomb-blockade regime because the charging energy of the junction capacitance cannot be neglected. We find excellent agreement with the experimental data. Projecting the current-phase relation onto the charge-transfer operator shows that at high transmission multi-Cooper-pair tunneling processes may occur.