Threshold Analysis for the Inverse ac Josephson Effect

The inverse ac Josephson effect involves rf-induced (Shapiro) steps that cross over the zero-current axis; the phenomenon is of interest in voltage standard applications. The standard analysis of the step height in current, which yields the well-known Bessel-function dependence on an effective ac drive amplitude, is valid only when the drive frequency is large compared with the junction plasma frequency or when the drive amplitude is large compared with the zero-voltage Josephson current. Using a first-order Krylov-Bogoliubov power-balance approach we derive an expression for the threshold value of the drive amplitude for zero-crossing steps that is not limited to the large frequency or large amplitude region. Comparison with numerical solutions of the RSJ differential equation shows excellent agreement for both fundamental and subharmonic steps. The power-balance value for the threshold converges to the Bessel-function value in the high- frequency limit.