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Due to their conceptual appeal and computational convenience, two-levelsystems (TLS) and their generalisations are often used to investigate nonlinearbehavior in quantum optics, and to assess the applicability of theoreticalmethods. Here the focus is on second harmonic generation (SHG) and, as systemof interest, on the Dicke model, which consists of several TLSs inside anoptical cavity. The main aspect addressed is the scope of non-equilibriumGreen's function (NEGF) to describe the effect of disorder andelectron-electron (e-e) interactions on the SHG signal. For benchmarkingpurposes, exact diagonalization (ED) results are also presented and discussed.SHG spectra obtained with NEGF and ED are found to be in very good mutualagreement in most situations. Furthermore, inhomogeneity in the TLS and e-einteractions reduce the strength of SHG, and the reduction is stronger withinhomogeneity than with interactions. This trend is consistently noted acrossdifferent (small to large) system sizes. Finally, a modified NEGF approach isproposed to account for cavity leakage, where the quantum photon fields arecoupled to a bath of classical oscillators. As to be expected, within thismixed quantum-classical scheme a decrease in the intensity of the fluorescentspectra takes place depending on the entity of cavity leakage.

Time resolved optical response of the Dicke's model via the nonequilibrium Green's function approach