Bloch oscillations in small-capacitance Josephson junctions.

Abstract

An analytic study of ac-bias-current effects on the Bloch oscillations in small Josephson junctions at the ${\mathit{E}}_{\mathit{c}}$\ensuremath{\gg}${\mathit{E}}_{\mathit{J}}$ limit (${\mathit{E}}_{\mathit{c}}$ is the charging energy and ${\mathit{E}}_{\mathit{J}}$ is the Josephson energy) is presented. By solving the quasicharge differential equation proposed by Likharev et al., solutions for the quasicharge q(t), as well as the I-V curves, are analyzed. It is shown that due to the sudden jump of the Bloch-oscillation period at some value of the dc current I, resistive steps of anomalous differential resistance emerge in the I-V curve. A general relation between the position of the resistive step on the I-V curve and the applied frequency f is derived. The connections and the differences between our formula and the weak-damping-limit formula I=(m/n)2ef are discussed. The results are compared with recent experiments.