Non-linear microwave impedance of short and long Josephson Junctions

TL;DR

This paper investigates the non-linear microwave impedance of short and long Josephson junctions under various excitation conditions, revealing fluxon dynamics, interference effects, and phase locking phenomena relevant to high-temperature superconductor devices.

Contribution

It provides a comprehensive calculation of the non-linear microwave impedance of Josephson junctions, including fluxon entry effects, interference phenomena, and phase locking under combined ac and dc biases.

Findings

Resistance exhibits step-like features at fluxon entry.

Fluxon interference leads to unique impedance effects.

Phase locking causes periodic impedance variations with dc bias.

Abstract

The non-linear dependence on applied $ac$ field ($b_{\omega}$) or current ($% i_{\omega}$) of the microwave (ac) impedance $R_{\omega}+iX_{\omega}$ of both short and long Josephson junctions is calculated under a variety of excitation conditions. The dependence on the junction width is studied, for both field symmetric (current anti-symmetric) and field anti-symmetric (current symmetric) excitation configurations.The resistance shows step-like features every time a fluxon (soliton) enters the junction, with a corresponding phase slip seen in the reactance. For finite widths the interference of fluxons leads to some interesting effects which are described. Many of these calculated results are observed in microwave impedance measurements on intrinsic and fabricated Josephson junctions in the high temperature superconductors, and new effects are suggested. When a $% dc$ field ($b_{dc}$) or current ($i_{dc}$) is applied, interesting phase locking effects are observed in the ac impedance $Z_{\omega}$. In particular an almost periodic dependence on the dc bias is seen similar to that observed in microwave experiments at very low dc field bias. These results are generic to all systems with a $\cos (\phi)$ potential in the overdamped limit and subjected to an ac drive.