Density-Matrix Model for Photon-Driven Transport in Quantum Cascade Lasers

Quantum cascade lasers (QCLs) are unipolar sources of coherent radiation emitting in the terahertz and infrared portions of the electromagnetic spectrum [1,2]. The gain medium of a QCL is a periodic stack of compound-semiconductor heterostructures. The resulting multi-quantum-well electron band structure in the growth direction has discrete energy levels, and the associated wave functions are quasibound. While lasing stems from ABSTRACT We develop 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.