Simulating Quantum Cascade Lasers: The Challenge to Quantum Theory

Quantum cascade lasers provide a variety of challenges to theory, which are outlined in this review: (i) The choice of basis states is discussed, where energy eigenstates are badly defined if the full periodic structure is considered. (ii) The tunneling through barriers requires a treatment of quantum coherences, which sets particular demands on the formulation of the quantum kinetic equations. Here the advantages and disadvantages of different approaches such as rate equations, Monte-Carlo simulations, different density matrix approaches, and Green’s functions methods are addressed. (iii) The evaluation of gain is detailed, where broadening is of utmost importance. (iv) An overview regarding the electrical instabilities of the extended structure due to domain formation is given, which strongly affect the overall performance.