  We developed a time-dependent density-matrix model to study photon-assisted
(PA) electron transport in quantum cascade lasers. The Markovian equation of
motion for the density matrix in the presence of an optical field is solved for
an arbitrary field amplitude. Level-broadening terms emerge from microscopic
Hamiltonians and supplant the need for empirical parameters that are often
employed in related approaches. We show that, in quantum cascade lasers with
diagonal design, photon resonances have a pronounced impact on electron
dynamics around and above the lasing threshold, an effect that stems from the
large spatial separation between the upper and lower lasing states. With the
inclusion of PA tunneling, the calculated current density and output power are
in good agreement with experiment.
