Generalized Gross-Pitaevskii model for intersubband polariton lasing

We develop a generalized Gross-Pitaevskii approach to the driven-dissipative dynamics of intersubband polaritons in patterned planar microcavities where the cavity mode is strongly coupled to the intersubband transitions in doped quantum wells. Substantial differences with respect to the case of interband excitonic polaritons are highlighted, in particular, the non-Markovian features of the radiative decay. We show that the method is able to reproduce well the experimental observations, as validated on the linear reflection properties of the cavity. The theoretical framework is then applied in the nonlinear regime to study optical parametric oscillation processes for intersubband polaritons. Our findings open interesting perspectives in view of novel coherent laser sources operating in the mid and far infrared.