SYNCHRONIZATION OF FLUXON MOTION ON SHAPIRO STEPS IN JOSEPHSON-JUNCTIONS

We demonstrate that shuttling fluxons can exist on Shapiro steps in open ended long Josephson junctions driven by a large amplitude, high frequency, electric field if the junction is described by the overlap geometry. If a small amplitude, low frequency, magnetic field is applied to the system we further demonstrate that the frequency of the shuttling fluxon may phase-lock to a subharmonic of the frequency of the magnetic field. Analytical expressions for the range of phase-locking in bias current are evaluated and excellent agreement is found when these are compared to the results of direct numerical simulations of the perturbed sine-Gordon equation, modeling the junction.