  We study the response of ultracold atoms to a weak force in the presence of a
temporally strongly modulated optical lattice potential. It is experimentally
demonstrated that the strong ac-driving allows for a tailoring of the mobility
of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically
either along or against the direction of the applied force. Our results are in
agreement with a theoretical analysis of the Floquet spectrum of a model
system, thus revealing the existence of diabatic Floquet bands in the atom's
band spectra and highlighting their role in the non-equilibrium transport of
the atoms.
