Josephson junction parameters for alternating current wave form synthesis

Abstract

The paper discusses the dynamics of different types of overdamped Josephson junctions biased by a sinusoidal microwave current. The results clarify the theoretical background for optimizing the single junction and the junction array parameters for their use as alternating current (ac) wave form synthesizers. The determined phase lock areas demonstrate the degree of overlap for Shapiro steps [S. Shapiro, Phys. Rev. Lett. 11, 80 (1963)] of different orders as a function of the normalized frequency μ=2πfωc−1, where f is the microwave frequency and ωc is the Josephson junction characteristic frequency. For μ⩽0.7, which is a typical operation range for superconductor-insulator-superconductor Josephson junctions in the conventional direct current (dc) voltage standard at the bias frequency range from 10to100GHz, the Shapiro steps overlap completely. For μ⩾1.4 [typical for superconductor-normal-superconductor junctions at the same frequency range], the steps do not overlap. This allows for ac voltage synthesis by means of binary arrays and pulse-driven systems. For 0.7⩽μ⩽1.4 there is a range of partially overlapping Shapiro steps, which allows a rapid switching of the Josephson dc voltages for ac synthesis by microwave power modulation. Experimentally we have achieved this range through properly designed superconductor-insulator-normal-insulator-superconductor junctions.