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 fr amework of the nonlinear Resistively-Shunted Junction (RSJ) Model. One of t he 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 si gnal with amplitude I-c, and frequency f(pm), hereafter referred to as "pum p 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 th at the dependence of the junction impedance at the frequency f(pr), Z(s)(fp r), 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 negat ive values of Re(Z(s)(fpr)) and "fine" structure of the steps in Z(s)(fpr) (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)(fpr) (I-pm) is rather different from t hat predicted by the nonlinear RSJ model for a short JJ in the regime of si ngle-frequency irradiation, when one and the same signal plays the roles of the pump and the probe signals simultaneously. Possible applications of th e model are briefly discussed.