  We show how Cooper-pair-assisted transport, which describes the stimulated
transport of electrons in the presence of Cooper-pairs, can be engineered and
controlled with cold atoms, in regimes that are difficult to access for
condensed matter systems. Our model is a channel connecting two cold atomic
gases, and the mechanism to generate such a transport relies on the coupling of
the channel to a molecular BEC, with diatomic molecules of fermionic atoms. Our
results are obtained using a Floquet-Redfield master equation that accounts for
an exact treatment of the interaction between atoms in the channel. We explore,
in particular, the impact of the coupling to the BEC and the interaction
between atoms in the junction on its transport properties, revealing
non-trivial dependence of the produced particle current. We also study the
effects of finite temperatures of the reservoirs and the robustness of the
current against additional dissipation acting on the junction. Our work is
experimentally relevant and has potential applications to dissipation
engineering of transport with cold atoms, studies of thermoelectric effects,
quantum heat engines, or Floquet Majorana fermions.
