Modelling the Nonlinear High-Frequency Response of a Short Josephson Junction under Two-Frequency Irradiation

TL;DR

This study investigates the nonlinear high-frequency response of a short Josephson Junction under simultaneous two-frequency irradiation, revealing complex impedance behaviors and features dependent on frequency ratios and signal amplitudes.

Contribution

It introduces a detailed analysis of the nonlinear response of a Josephson Junction to dual high-frequency signals, highlighting new impedance features and behaviors not predicted by single-frequency models.

Findings

Impedance at probe frequency remains generally consistent across different pump frequencies.

Negative real parts of impedance observed under certain conditions.

Distinct fine structures in impedance steps for specific frequency ratios and amplitudes.

Abstract

The nonlinear response of a short Josephson Junction (JJ), being irradiated simultaneously with two high-frequency signals, has been studied in the framework of the nonlinear Resistively-Shunted Junction (RSJ) Model. One of the signals, hereafter referred to as "probe signal", has a small amplitude $I_{pr}<I_c$ ($I_c$ is the critical current of the JJ) and frequency $f_{pr}$, and is used to monitor the response of the junction to the other high-power signal with amplitude $I_{pm}$ and frequency $f_{pm}$, hereafter referred to as "pump signal". Varying the frequency ratio $f_{pm}/f_{pr}$ from 0.5 to 100, and the current amplitude of the probe signal from 0.01 to 0.9 of $I_c$, we found that the dependence of the junction impedance at the frequency $f_{pr}$, $Z_s^{f_{pr}}$, versus $I_{pm}$ preserves its general features, independent of $f_{pm}/f_{pr}$ and $I_{pr}/I_c$ values. At the same time, some particular features, like negative values of $Re(Z_s^{f_{pr}})$ and "fine" structure of the steps in $Z_s^{f_{pr}}(I_{pm})$ are observed for $f_{pm}/f_{pr}<1$ and for particular values of $I_{pr}/I_c$. In general, the behavior of $Z_s^{f_{pr}}(I_{pm})$ is rather different from that predicted by the nonlinear RSJ model for a short JJ in the regime of single-frequency irradiation, when one and the same signal plays the roles of the pump and the probe signals simultaneously. Possible applications of the model are briefly discussed.