Coherent motion of vortices driven by alternating currents in an annular Josephson ratchet ladder

Vortex dynamics have been investigated numerically in a double-ring annular ladder composed of Josephson ratchet network along the circular direction. One repeat unit of the periodic ratchet potential consists of two adjacent plaquettes of different sizes, where the critical currents of their rung junctions are also assigned with different values. Each vortex generated between the two rings by a transverse magnetic field oscillates through several plaquettes or rotates along the ladder, depending on the magnitude of direct and alternating currents applied to the radial direction. Because of the broken spatial symmetry in the potential landscape, onsets of the vortex motion and widths of the Shapiro steps in the current-voltage characteristics show polarity-dependent behavior. The directional motion of vortices, already known in rectangular Josephson ratchet networks driven by alternating currents, has also been confirmed to appear as directional rotation in this annular ratchet ladder. A notable feature is that such dynamics can occur with a system’s commensurate condition that makes a Shapiro step at zero direct current, which leads to coherent rotational motion of vortices. Here, we report that for each magnetic flux applied to the system there is a finite range of alternating currents that allow vortices to move coherently.