  In this work we demonstrate how the directed motion of atomic Bose-Einstein
condensates in a toroidal trap can be controlled by applying a zero-mean
oscillatory driving field. We show that due to the self-trapping effect in
momentum space, the oscillatory amplitude of the current can be significantly
suppressed and a nearly constant directed current can be obtained preserving
the initial current values, by decreasing the driving amplitude, even when the
atomic interactions are relatively small. We also reveal numerically the
mean-field chaos can serve as an indicator of a quantum phase transition
between the vanishing current regime and nonvanishing current regime. Our
results are corroborated by an effective three-mode model, which provides an
excellent account of the ratchet dynamics of the system.
