  We propose to use ultracold fermionic atoms in one-dimensional optical
lattices to quantum simulate the electronic transport in quantum cascade laser
(QCL) structures. The competition between the coherent tunneling among (and
within) the wells and the dissipative decay at the basis of lasing is
discussed. In order to validate the proposed simulation scheme, we
quantitatively address such competition in a simplified one-dimensional model.
We show the existence of optimal relationships between the model parameters,
maximizing the particle current, the population inversion (or their product),
and the stimulated emission rate. This substantiates the concept of emulating
the QCL operation mechanisms in cold-atom optical lattice simulators, laying
the groundwork for addressing open questions, such as the impact of
electron-electron scattering and the origin of transport-induced noise, in the
design of new-generation QCLs.
