Introduction

In absence of nonlinearity or saturation of some sort, the quantum case is equivalent to the classical one (see, for instance, the work by Rudin & Reinecke (1999)). In particular, the PL spectrum exhibits a Rabi doublet at resonance, which can be equally well accounted for by a purely classical model, as was shown by Zhu et al. (1990). There is therefore a strong incentive to evidence nonlinear deviations and attribute them to quantum effects. Numerous proposals and experiments can be found in the literature on the topic: such as those by Srinivasan & (2007), Press et al. (2007), Kroner et al. (2008), Fink et al. (2008), Schneebeli et al. (2008), Steiner et al. (2008), etc...

With QDs in microcavities, mainly two types of strong nonlinearities are expected, both associated to the active material, i.e., the excitons. The first one comes from Coulomb repulsion of the charged particles, and is the one investigated in Secs. 5.2 and 5.3, in the case where it is comparable to the coupling strength or decaying rate. In Sec. 5.2, we first study isolated excitons with interactions, in an anharmonic oscillator model (AO), in order to understand the implications of interactions alone. In Sec. 5.3, we add such interactions to the linear model (LM) and investigate their effect on the strong coupling (SC) physics and spectra. In this part, we have in mind large dots (or microcavity polaritons), where excitons still behave as weakly interacting bosons. In this context, Pauli exclusion (the second nonlinearity we refer to) can be taken into account phenomenologically by a phase-space filling effect that screens the exciton-photon interaction, as has been done before by Hanamura (1970), Schmitt-Rink et al. (1985) or Imamoglu (1998). This results in loss of strong-coupling and we therefore focus on the intermediate regime in these two first sections, where such renormalization of the coupling strength can be neglected. We prefer to take into account Pauli exclusion, and the saturation it induces, separately in Sec. 5.4. It arises from the fermionic character of the particles that compose the exciton (electrons and holes) as has been pointed out by Combescot &-Matibet (2004) among others. The most suitable and fundamental model to study fermionic saturation is the Jaynes-Cummings model (JCM) that we introduced in the Introduction and in Sec. 2.3. It consists in the coupling of an harmonic oscillator (AO) and a two-level system (2LS). With this separate analysis of the nonlinearities in dissipative and incoherently pumped light-matter systems, we can conclude in Sec. 5.6 which feature in the spectra of emission can be attributed to which effect.

As in the previous ones, in this Chapter, we neglect the spin-degree of freedom, in particular the sign-dependent interaction between same and opposite-spins excitons, respectively. This allows us to focus on nonlinear deviations and neglecting more complicated correlations effects of the multi-excitons complexes such as formations of bound pairs or molecules that would give rise to bipolaritons, as was shown by Ivanov et al. (1998), Ivanov et al. (2004) or Gotoh et al. (2005). Experimentally, this could be realized by using a circularly polarized pump.