  We study the response of a Bose-Einstein condensate to an unbiased periodic
driving potential. By controlling the space and time symmetries of the driving
we show how a directed current can be induced, producing a coherent quantum
ratchet. Weak driving induces a regular behavior that is strongly governed by
the interparticle interaction. Breaking both space and time symmetries is
required to produce current flow. For strong driving the behavior becomes
chaotic. The resulting effective irreversibility renders the space asymmetry
sufficient to produce the ratchet effect, although the system is completely
coherent.
