Conclusions

In this Chapter, I have presented a unified formalism for the zero-dimensional light-matter interaction between bosons (the linear model), both in the WC and SC regimes, for the two cases of SE of an initial state, and emission in the SS maintained by an incoherent continuous pumping. The general theory provided here is suitable to describe not only the traditional cavity quantum electrodynamics (direct SE of the excited atom in a cavity), but also the more recent semiconductor version with quantum dots in microcavities.

I have emphasized how a proper consideration of the incoherent pumping scheme is needed to describe the effective quantum state realized in the system, and how this bears consequences on the spectral lineshapes, in particular on the ability to resolve a Rabi doublet when the splitting to broadening ratio is small.

The main results of this Chapter are to be found in Eqs. (3.37)-(3.40) that provide the analytical expression for the emission spectra of a system whose specificities--such as whether it corresponds to SE or the SS established by an incoherent continuous pumping--are provided by a single parameter . These formulas, valid for an arbitrary detuning between the bare modes, reduce to more self-contained expressions at resonance, namely Eq. (3.59) for SE and Eq. (3.65) for SS. The resonance case allows an unambiguous definition of SC, depending on whether the complex Rabi frequency, Eq. (3.12), is pure imaginary (WC) or real (SC), which means that the dynamics is ruled by bare or dressed modes, respectively. However, with nonnegligible decoherence, there is no one-to-one mapping of the eigenenergies of the system with the lines observed in the luminescence spectrum. All cases can arise: one or two peaks can be observed at resonance both in WC and SC. For that reason, an understanding of the general picture is required to be able to position a particular experiment in the space of parameters, as was done in Figs. 3.17, rather than to rely on a qualitative effect of anticrossing at resonance. Fig. 3.10 shows how loosely related are the observed line-splitting in the PL spectrum and the actual energy splitting of the polariton modes.