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

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.