ac Josephson Effect in a Single Quantum Channel

Abstract

We have calculated all the components of the current in a short one-dimensional channel between two superconductors for arbitrary voltages and transparencies $D$ of the channel. We demonstrate that in the ballistic limit ( $D\simeq 1$) the crossover between the quasistationary evolution of the Josephson phase difference $\varphi$ at small voltages and transport by multiple Andreev reflections at larger voltages can be described as the Landau-Zener transition induced by finite reflection in the channel. For perfect transmission and vanishing energy relaxation rates the stationary current-phase relation is never recovered, and $I\left(\varphi \right){=I}_c\mid \sin \varphi /2\mid \mathrm{sgn}V$ for arbitrary small voltages.