  Cold atoms in optical lattices have emerged as an ideal system to investigate
the ratchet effect, as demonstrated by several recent experiments. In this work
we analyze theoretically two aspects of ac driven transport in cold atoms
ratchets. We first address the issue of whether, and to which extent, an ac
driven ratchet for cold atoms can operate as a motor. We thus study
theoretically a dissipative motor for cold atoms, as obtained by adding a load
to a 1D non-adiabatically driven rocking ratchet. We demonstrate that a current
can be generated also in the presence of a load, e.g. the ratchet device can
operate as a motor. Correspondingly, we determine the stall force for the
motor, which characterizes the range of loads over which the device can operate
as a motor, and the differential mobility, which characterizes the response to
a change in the magnitude of the load. Second, we compare our results for the
transport in an ac driven ratchet device with the transport in a dc driven
system. We observe a peculiar phenomenon: the bi-harmonic ac force stabilizes
the dynamics, allowing the generation of uniform directed motion over a range
of momentum much larger than what is possible with a dc bias. We explain such a
stabilization of the dynamics by observing that a non-adiabatic ac drive
broadens the effective cooling momentum range, and forces the atom trajectories
to cover such a region. Thus the system can dissipate energy and maintain a
steady-state energy balance. Our results show that in the case of a
finite-range velocity-dependent friction, a ratchet device may offer the
possibility of controlling the particle motion over a broader range of momentum
with respect to a purely biased system, although this is at the cost of a
reduced coherency.
