  We show theoretically that the dynamics of cold atoms in the lowest energy
band of a stationary optical lattice can be transformed and controlled by a
second, weaker, periodic potential moving at a constant speed along the axis of
the stationary lattice. The atom trajectories exhibit complex behavior, which
depends sensitively on the amplitude and speed of the propagating lattice. When
the speed and amplitude of the moving potential are low, the atoms are dragged
through the static lattice and perform drifting orbits with frequencies an
order of magnitude higher than that corresponding to the moving potential.
Increasing either the speed or amplitude of the moving lattice induces
Bloch-like oscillations within the energy band of the static lattice, which
exhibit complex resonances at critical values of the system parameters. In some
cases, a very small change in these parameters can reverse the atom's direction
of motion. In order to understand these dynamics we present an analytical
model, which describes the key features of the atom transport and also
accurately predicts the positions of the resonant features in the atom's phase
space. The abrupt controllable transitions between dynamical regimes, and the
associated set of resonances, provide a mechanism for transporting atoms
between precise locations in a lattice: as required for using cold atoms to
simulate condensed matter or as a stepping stone to quantum information
processing. The system also provides a direct quantum simulator of acoustic
waves propagating through semiconductor nanostructures in sound analogs of the
optical laser (SASER).
