Features of the dynamics of a josephson junction biased by a sinusoidal microwave current

Abstract

Applicability of the voltage biasing approximation, which is widely used for estimating the width of Shapiro steps in the I–V characteristics of Josephson junctions biased by a sinusoidal microwave current, is considered in relation to the bias-current frequency f. For the first time, the configuration of the phase-lock area is shown to depend on the frequency parameter μ = (2πf)/ωc. It is shown that overlapping Shapiro steps, which are typical of tunnel Josephson structures with high V c and ωc, exist in the range μ ≤ 1. For μ > 1, Shapiro steps do not overlap, which is typical of overdamped Josephson structures with relatively low V c. For the practically important case of sinusoidal microwave bias, the diagrams showing the phase-lock areas are plotted for several values of parameter μ. On the basis of these diagrams, the operating principle of ac-voltage quantum standards is illustrated, the methods of their design are specified, and the requirements for the bias current are formulated.