Rectifying effect in a Josephson junction ratchet array

We have studied numerically a rectifying effect in an underdamped Josephson junction ratchet array driven by dc and ac current. The array consists of both alternating potential barriers and alternating inter-capacitances along the direction of vortex flow. The guide banks of high critical currents are assigned for all the longitudinal junctions to prevent the percolative pattern of vortex motion. In some junction parameters, we see a rectifying effect which indicates a finite value of the time-averaged voltage at zero dc bias. The directional dependence of the vortex motion becomes fairly large when the junction parameters lie in an optimal range which gives rise to a Shapiro step at zero dc bias. Such a rectifying effect survives for small thermal fluctuation, but eventually disappear beyond a certain critical temperature.