English

In this thesis I described theoretically light-matter interaction in the presence of decoherence for quantum dots (QDs) in a microcavity. The main results of my work can be summarized as follows.

The luminescence from a cavity QED system has been long time supported theoretically by analytical formulas that describe the special case of the spontaneous emission (SE) of an excited state. This situation suits the physics of atomic cQED. In the case of semiconductors, however, the typical excitation scheme departs in that it is both continuous and incoherent. We have extended the atomic cQED formalism to take into account these specificities,^7.9 (we have also extended the atomic cQED formalism per se to cover the most general cases of arbitrary initial conditions and detunings). This extension essentially amounts to introduce two pumping rates, or $P_\sigma$ for the QD excitation and for the cavity mode.

Starting with the linear model (LM), I have presented a general analytical formula for the photoluminescence spectra in Eqs. (3.37)-(3.40), that contains both the SE and the steady state (SS) expressions allowing for a direct comparison. An appealing feature of the SS expression is that, in its full generality, it involves one parameter less than the most general case of SE, which is to be taken into account when it comes to fitting an experiment. The two realizations of cQED--atomic and semiconductor--meet in some limiting cases of interest but, in general, none fully includes the other.

On the experimental side, the theoretical description of the strong coupling (SC) spectral lineshapes in terms of Lorentzians at the polariton (eigen) energies, neglects the effect of dissipation--universally understood as one of the main ingredients of the cQED physics. The reference work for the 0D semiconductor case, by Andreani et al. (1999), did not focus on the lineshape but on the microscopic Hamiltonian, demonstrating the feasibility of semiconductor cQED, possibly encouraging its pursuit and leading to its successful realization. The luminescence emission was however taken directly from Carmichael et al. (1989) work, that specifically addresses the particular case of the direct SE of the excited state of the emitter (an atom in this case). This has various disadvantages for the semiconductor case, where emission is not that--direct--of the emitter, but instead that--``indirect''--of the cavity mode. It also has the limitation of neglecting decoherence brought by the excitation scheme as well as the SS state realized by the interplay of pumping and decay.

An anticrossing of the cavity and QD lines at resonance (the level repulsion) in the PL emission is generally granted as a proof of SC, due to the identification of the two splitted peaks with the polariton emission (the Rabi doublet). This association is already mistaken without pump, if dissipation is not negligible (the usual case). A system in SC can show an apparent crossing of the lines (when the ratio of broadening to coupling strenght is large) and, more surprisingly, also the other way around, namely, a system in weak coupling (WC) can display an apparent anticrossing, with always two peaks visible in the PL emission. Analyzing our extended theory, suitable for semiconductors, we have found that the effect of pumping further disconnects SC from an anticrossing of lines, even in very good systems with low dissipation where one would expect a very clear manifestation of SC and the Lorentzian approximation to hold. I gave a vivid description of this physics in terms of phase-diagrams that separate neatly the concept of doubly peaked emission and of SC (Fig. 3.9). This brought me to emphasize the importance of a quantitative account of the experimental data rather than a qualitative description, that would wrongly identify the mode splitting with the Rabi frequency. A consequence of this error is to discard SC in structures where it is only hidden and could be revealed by playing with the excitation scheme, providing, e.g., a more photonic character to the steady state. Considering one of the seminal reports of SC in 0D semiconductors, namely that by Reithmaier et al. (2004), we have found that our model indeed provides an excellent quantitative description of the experiment (Fig. 3.14), allowing us to confirm SC and to quantify it with an underlying exact theory. Our fitting should be understood with the following restrictions, that are in its favor: ) we have used as little parameters as possible (any other theoretical model would come with as many, or more, fitting parameters). ) we have made a global fit, which means that the coupling strength and decay parameters have been optimized globally but kept constant as detuning is varied.

Considering the effect of increased pumping, we face the problem of which underlying microscopic model best describes the semiconductor case, and how various possibilities compare with each other. My main target, owing to its fundamental importance, is the Jaynes-Cummings model (JCM) that couples a two-level system (2LS) to an harmonic oscillator (HO). In approaching this system, I investigated first the case of two coupled 2LSs, still admitting analytical solutions and enlightening on the effect of decoherence on the dressed states when there is saturation (Fig. 4.1). Two 2LSs are trivial in absence of pumping but become of tremendous academic interest when including a continuous, incoherent pumping. We could isolate some of the JC phenomena, otherwise difficult to analyze analytically. For instance, we could trace the origin of the JC bubbles and splittings of the spectral lines due to pumping (Fig.5.15).

The second step towards the JC physics, this time focusing on its multiplet spectral structures and how they melt in the transition from the quantum to the classical regime (Fig. 5.21), was the study of the anharmonic oscillator (AO). The AO in isolation is still essentially solvable. Our formalism allowed us to identify the degree of ``quantumness'' of the system depending on the strength of the nonlinearities and the pumping that probes them. A system is ``quantum'' when the lines that compose the spectra can be identified with individual transitions between the dressed states (grouped in manifolds of excitation). For example, the AO (interacting excitons) in SC with a cavity mode and at low pump (though enough to overcome the linear regime), presents clear quantum features: the spectral lines can be identified one by one with manifold transitions (Fig. 5.5).

Equivalently, a small pump is enough to probe JC ladder structure, and observe multiplets in the spectra, signature of quantum emitter by excellence (Fig. 5.18). With the JCM, we obtained semi-analytical results, and I have shown how the character of the pumping can affect visibility of the JC nonlinearities, in a similar way as described exactly in the limiting case of vanishing excitations. The thermal distribution of particles that forms at low pump, probes appreciably the nonlinear steps of the JC ladder even when the average number of particles is much below one. On the opposite, as pumping intensity is increased in a mistaken attempt of going farther into the nonlinear regime, the features of the quantized fields disappear and give rise to structures of much reduced complexities. In the best strongly coupled systems, the spectra evolves with increasing pumping from a vacuum Rabi doublet (the quantum linear regime), to the JC fork (quantum nonlinear regime), to a Mollow triplet (classical lasing regime), and, ultimately, to quenching of the coupling and emission (WC). The crossover was understood and tracked thanks to our spectra decomposition.

The method we use in terms of correlators allows to decompose the lineshapes into individual and identifiable transitions between the states of the system [Eq. (2.105)]. With this information I was able to identify unambiguously the polaritons in all the models I studied, and to characterize different regimes depending on the strenght of the coupling. Each spectral line is composed of a Lorentzian part, corresponding to the pure polaritonic emission, and a dispersive part, corresponding to the interference between different polariton emissions, overlapping in energy as a result of decoherence. This led us to introduce new definitions for SC in presence of incoherent pumping.

In the last part of the thesis, we have applied the developed techniques to more complex and practical systems involving three modes. I focused on a particular scheme of entanglement generation between two QDs in a cavity (or three QDs), on the one hand, and on two-photons generation in a QD with a biexcitonic state, on the other hand. In both cases, I have shown the feasibility of these devices with a realistic description that takes fully into account and even relies on the incoherent pumping.