Introduction

Unlike atoms, self assembled QDs are not identical to each other but present a small size inhomogeneity and are randomly distributed in the sample. This results in a finite dispersion in the coupling to the cavity modes and in the emission frequency. The aim of this Chapter is to analyze the effect of such differences in the SS under incoherent continuous pump. In particular, we show how one can take advantage of them to understand and engineer the emission of the structure, its lasing properties, or the generation of entangled states. For this purpose, we study the case of two QDs (extensible to two excitons in a single QD), each one represented as a two-level system (2LS), and coupled to a cavity mode, as was done by Gywat et al. (2006) or Perea & (2005). In this Chapter, we again neglect internal degrees of freedom, such as carrier spin or photon polarization, what can be achieved, for instance, by working with charged QDs.

The Chapter is organized as follows. In Section 6.2, we turn to the case where the dots are in a cavity and close to resonance with one of its modes. A new master equation is derived for two different pumping configurations. In Section 6.2.1, the potentiality of the system for entangling two equal QDs is discussed and analyzed through its tangle and entropy. In Section 6.2.2, we propose an application of this entanglement mechanism in a transport experiment with three QDs. In Section 6.2.3, the one-photon lasing properties are analyzed through the photon population and the second-order coherence.

In Section 6.3, we consider again a cavity mode strongly coupled to a single QD, but that is large enough to host two excitons (a biexciton state). This case can be described with a similar Hamiltonian than that of two QDs, but including the biexciton energy, that we present. We study the two-photon lasing properties of the system and the spectrum of emission.

Finally, in Section 6.4, we present some future lines of research and in Section 6.5, the main conclusions of the Chapter.