Numerical Simulation of quantized voltage steps in overdamped Josephson junctions controlled by simple pulse codes

Shapiro steps crossing the zero-current axis, i.e., zero-crossing steps, in the overdamped Josephson junction driven with a simple pulse code consisting of single and multiple pulses in each repetition period are studied based on numerical simulations. In this study, it is confirmed that the quantized voltage at which the zero-crossing step appears can be controlled by the number of the additional pulses without changing current bias range. The case in which the additional pulses having small fluctuations in phase is also considered. No visible effect of the fluctuations on the current position of the Shapiro steps is observed, so that the current range with respect to the phase lock between the Josephson oscillation and the pulse code is determined by the number of pulses.