  We describe forms of adiabatic transport that arise for dressed-state atoms
in optical lattices. Focussing on the limit of weak tunnel-coupling between
nearest-neighbour lattice sites, we explain how adiabatic variation of optical
dressing allows control of atomic motion between lattice sites: allowing
adiabatic particle transport in a direction that depends on the internal state,
and force measurements via spectroscopic preparation and readout. For uniformly
filled bands these systems display topologically quantised particle transport.
