Higher order Shapiro steps in ac-driven Josephson junctions

Abstract

We demonstrate that the well known phase-locking mechanism leading to Shapiro steps in ac-driven Josephson junctions is always accompanied by a higher order phase-locking mechanism similar to that of the parametrically driven pendulum. This effect, resulting in a $π$-periodic effective potential for the phase, manifests itself clearly in the parameter regions where the usual Shapiro steps are expected to vanish.