Weakly driven quantum coherent ratchets in cold-atom systems

We present an analytical 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