Perturbative analysis of coherent quantum ratchets in cold atom systems

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.