Summary of contents

The rest of this text is organized as follows:

In Chapter 2, I introduce the two basic elements of all the theoretical light-matter models that are discussed in subsequent chapters: the harmonic oscillator (HO) and the two-level system (2LS). I will lay down in full details the Hamiltonians that describe their coupling and provide the definitions of the fundamental concepts as we go along. I will introduce the formalism of the density matrix and its equation of motion (the master equation), including decoherence (dissipation and incoherent continuous excitation). I will develop in its most general form the method to compute two-times correlators, namely, the quantum regression formula (QRF), and derive from it the spectra of emission of a dissipative system. Thanks to this Chapter, the whole text should be reasonably self-contained and accessible to a wide range of readers with elementary familiarity of quantum physics. I will then proceed to investigate systematically various cases, as sketched in Fig. 1.15.

**Figure 1.15:** Schematic representation of the systems studied in this text.

In Chapter 3, I address light-matter coupling of bosonic excitons (adequate for large QDs or a 2D-polariton mode), in the framework of the LM, that also describes the linear regime of vanishing excitation. I will show how this model successfully reproduces one of the first experimental realization of strong coupling with a single QD in a microcavity, by Reithmaier et al. (2004). The incoherent continuous pump, both electronic and photonic, is a key element to tune between the coupling regimes enhancing or hindering the visibility of the dressed modes (a Rabi doublet vs. singlet).

In Chapter 4, I present the case of two coupled 2LSs, interesting because it interpolates between the LM and the JCM of coupled modes with the considerable advantage of being fully solvable analytically. I dedicate one chapter to it for its fundamental interest and because it brings us one step closer to unravelling the JCM, shedding light on the more complex mechanisms that manifest at a larger scale there. New regimes of coupling appear for this model due to the interplay between pump and decay, giving rise to more exotic lineshapes (quadruplet and triplet structures that result in distorted doublets and singlets).

In Chapter 5, I describe light-matter coupling with models that take into account some excitonic nonlinearities, appearing when the excitation is sufficiently strong to probe the system out of its linear regime. Such nonlinearities typically arise from the Coulomb repulsion experienced by the excitons if their wavefunctions overlap in the QD, and/or from the fermionic nature of the underlying electrons and holes. The study of the first effect is done considering excitons as weakly interacting bosons, described by an anharmonic oscillator (AO). The starting point is the analytic results of LM in Chapter 3 and a separate analysis of the AO physics. The second effect of saturation is studied with the Jaynes-Cummings model, the most important and fundamental model of cQED. We unravel in this section a surprising complexity with fractal structures, that suggest a transition from the quantum to the classical realm. In all cases, the spectra has a multiplet structure, better resolved in the quantum regime, that can turn into broad singlets (AO) and Mollow triplets (JC) in the lasing regime, all depending on the competition with decoherence.

In Chapter 6, I go through different properties of three element systems. A natural extension of the previous chapters is the study of two QDs, or one QD that can accommodate up to two excitons (a biexciton) in a microcavity. The description of this configuration requires putting together two JC Hamiltonians, it is the simplest case of the Dicke model of superradiance (two 2LS coupled to an HO). I address their properties of emission, this time distinguishing between one- and two-photon emission and lasing. The finding of a scheme of incoherent excitation that generates entanglement between the QDs, leads us to the proposal of an equivalent transport experiment with three QDs, controlled with gate voltages.

In Chapter 7, I provide a brief overview of the main results of this thesis, drawing some general conclusions.