  Using matter waves that are trapped in a deep optical lattice,
dissipationless directed transport is demonstrated to occur if the single-band
quantum dynamics is periodically tilted on one half of the lattice by a
monochromatic field. Most importantly, the directed transport can exist for
almost all system parameters, even after averaged over a broad range of
single-band initial states. The directed transport is theoretically explained
within ac-scattering theory. Total reflection phenomena associated with the
matter waves travelling from a tilting-free region to a tilted region are
emphasized. The results are of relevance to ultracold physics and solid-state
physics, and may lead to powerful means of selective, coherent, and directed
transport of cold particles in optical lattices.
