Perturbation treatment of mixing in Josephson junctions

We consider a current biased, resistively shunted josephson junction irradiated at two frequencies. The perturbation technique introduced by Aslamasov and Larkin is used in the calculations. Both signals are treated as perturbations. The second order calculation yields the size of the mixing steps at . As in the case of a single frequency we show that subharmonic mixing steps are absent. The amplitude of the voltage oscillation at the difference and sum frequencies is shown to be non-zero at all voltages. We calculate the microwave resistance for one frequency ω2to third order in the perturbation. There are negative resistance regions near (as well as near ). Near V, the negative resistance region appears for bias voltage V just above , while near V the region appears for V just below . This means that when an incident frequency mixes with a cavity mode the mixing step at will be inverted compared to the cavity step itself.