Nonlinear impedance of a microwave-driven Josephson junction with noise

The nonlinear impedance of a point Josephson junction is calculated under v arious conditions for the resistively shunted junction model in the presenc e of noise. The calculation proceeds by solving the Langevin equation for t he mechanical problem of a Brownian particle in a tilted cosine potential i n the presence of a strong ac force ignoring inertial effects. The exact so lution of the infinite hierarchy of equations For the moments (expectation values of the Fourier components of the phase angle), which describe the dy namics of the junction, is expressed in terms of a matrix continued fractio n. This solution allows one to evaluate the nonlinear response of the junct ion (nonlinear microwave impedance, for example) to an ac microwave current of arbitrary amplitude. Strong nonlinear effects in the resistance and the reactance are observed for large ac currents as is demonstrated by plottin g the nonlinear response characteristics as a function of the model paramet ers. For weak ac currents and low noise strengths, our results agree closel y with previously available linear response and nonlinear response noiseles s solutions, respectively. Applications of the model to the interpretation of recent experimental data found in the literature for the nonlinear behav ior of microwave impedance of superconducting weak links are discussed.