Experiments performed on unipolar conduction-band lasers in a resonant tunneling structure suggest that such a quantum cascade laser (QCL) may operate in the coherent regime. This paper develops a model for coherent QCL operation that is based on transitions between quasibound states created by the coherent resonances. The dynamics of the device is determined from the time evolution of a two-dimensional wave packet; the coordinates denote the electron and the quantized field. The computations performed show that the coherence not only enhances resonant tunneling but also amplifies the number of created photons considerably. In order to understand the QCL operation, the problem of a free electron in a quantum field is solved exactly and a phenomenological model for photon emission in the QCL process is developed. Using these, the dynamics of the quantum field and the tunneled electron are followed in detail. © 1996 The American Physical Society.

• Received 18 October 1995

DOI:https://doi.org/10.1103/PhysRevB.53.15789