Conclusions

In this Chapter, I have shown some SS properties of two QDs in a microcavity under incoherent continuous pump, considering them as two-level systems. Most of the results are obtained numerically, due to the complexity of the system.

In Sec. 6.2, I discussed a model where the QDs are pumped either in an independent or in a common fashion. I have shown that the general case is a mixture of the two kinds of pumping which is determined mainly by geometrical factors but can be increased one way or the other, for instance by applying an external electric field. In the case where the dots are essentially excited through the common pumping, quantum interferences in the dots alter significantly the dynamics and yield singularities or abrupt features in the steady state populations. For suitable sets of parameters, which include different couplings between cavity and dots, the system can be brought to a regime where the singlet state, $\ket{\mathrm{S}}=(\ket{E1}-\ket{E2})/\sqrt2$ , is predominantly occupied. This provides good values of the tangle, despite the incoherent and continuous nature of the pumping (Fig. 6.6).

Encouraged by these positive results, we proposed a quantum transport experiment for preparing and measuring in the SS a charge-entangled state of two noninteracting QDs. Each QD is coherently coupled to a third one, playing the role of the cavity in the previous scheme. The coherent trapping mechanism that creates the entanglement can be switched on and off by means of a gate potential. This allows both state preparation and entanglement detection by simply measuring the total current (Fig. 6.10).

In the case where the dots in the cavity are essentially pumped independently, the presence of a largely detuned or weakly coupled dot changes qualitatively the dynamics of a near resonant, strongly coupled dot. In view of its lasing properties, the system therefore acquires a low stimulated emission threshold resulting in efficient cavity population with Poissonian distribution, even when both dots are detuned from the cavity mode (Fig. 6.13). This is qualitatively different from a model with isolated dots which emission would scale with their number, especially at nonzero detuning.

In Sec. 6.3, we finally studied two-photon lasing considering a single QD in a microcavity but that can contain a biexcitonic state and therefore can be described by a similar Hamiltonian and master equation than the two small dots in the cavity. The biexcitonic binding energy allows for a two photon resonance while largely suppressing the one photon processes. We studied the feasibility of a two-photon correlated emission under an incoherent pump and decay and obtained positive results, directly measurable through the properties of the emitted light (Fig. 6.20 and 6.24). For this system, some analytical expressions have been derived at a Hamiltonian perturbative level, such as the effective coupling and Stark shifts, Eq. (6.28).