  We present a perturbative study of the response of cold atoms in an optical
lattice to a weak time- and space-asymmetric periodic driving signal. In the
noninteracting limit, and for a finite set of resonant frequencies, we show how
a coherent, long lasting ratchet current results from the interference between
first and second order processes. In those cases, a suitable three-level model
can account for the entire dynamics, yielding surprisingly good agreement with
numerically exact results for weak and moderately strong driving.
