  The realization of a directed current for a quantum particle in a flashing
asymmetric potential is studied. It is found that a positive current, i.e. in
the direction expected for a conventional diffusive ratchet, can be attained at
short times in the limit where the potential is weak and quantum diffusion
dominates, while current reversal is obtained for stronger potentials. A single
parameter, the ratio between the kicking frequency and the optical lattice
potential strength, determines both the degree to which quantum effects
dominate, and the possibility of obtaining a ratchet current. The effect should
be readily observable in experiments.
