Density matrix superoperator for periodic quantum systems and its application to quantum cascade laser structures

In this work we present a generalization of the Liouvillian superoperator for periodic quantum systems that can be formulated through partitioned Hamiltonians. We formulate a compact algebraic form of the superoperator that allows efficient numerical implementation along with the possibility of further generalization and the inclusion of the system’s boundary effects (i.e. device contacts). We apply this formalism to Quantum Cascade Laser structure where we compare the second nearest and the nearest on approximation, and present the laser dynamics that is independent from the number of states considered.