Density operator of a system pumped with polaritons: a Jaynes-Cummings-like approach

We investigate the effects of considering two different incoherent excitation mechanisms on microcavity quantum dot systems modeled using the Jaynes-Cummings Hamiltonian. When the system is incoherently pumped with polaritons it is able to sustain a large number of photons inside the cavity with Poisson-like statistics in the stationary limit, and it also leads to a separable exciton-photon state. We also investigate the effects of both types of pumpings (excitonic and polaritonic) in the emission spectrum of the cavity. We show that the polaritonic pumping considered here is unable to modify the dynamical regimes of the system at variance with the excitonic pumping. Finally, we obtain a closed form expression for the negativity of the density matrices that the quantum master equation considered here generates.