frequencies because of exciton-exciton interaction, it was initially thought that such a device would suffer from blinking [21]. In fact, it can be intuitively argued that if the excitonic transition of the QD is resonant with the cavity mode, the QD decouples from the cavity as soon as it contains two excitons, thus leading to the device switch off. Although, experimental evidence has shown that single QDs-based lasers do not suffer from blinking, and their lasing transitions display different statistical behaviors ranging from partial antibunching to Poissonian [35, 41]. In this context, the evolution of the statistics of the cavity light field with respect to the pump power has not the same physical meaning as in the two-level atom case, which has been the subject of the present work, as it was also underlined in [41]. As a matter of fact, because of pure dephasing, phonon-assisted processes, or power broadening (as it was evidenced above), increasing pump power leads to a broadening of the higher order excitonic transitions, that can also contribute to cavity feeding. In the limiting case where all the transitions are efficiently coupled to the cavity, the statistics of the cavity field will simply map the Poissonian statistics related to the number of excitons in the QD. As a consequence, the role played by the cavity is drastically different from the single atom case: it does not act as a photon trap, delaying the emission of the field until a Poissonian statistics has built in the mode, but rather as a common relaxation channel for all the transitions of the QD. Thus, the crossover from the antibunched to the Poissonian field just reflects the excitation and the broadening of the multiexcitonic transitions. Note that the observation of such a transition does not require the good cavity regime, which explains why lasing was also observed in Refs. [35, 40], where the QD and the cavity mode were only weakly coupled. We propose an alternative strategy to realize a single atom-like laser with a QD coupled to a cavity mode, namely, to use a QD doped with a single electron embedded in a high- Q /low- V microcavity in the good cavity regime (see schematic picture in Fig. 7). Such a device, including tuning parameters to control the charge state of the QD and the QD- cavity detuning, is within reach of current technology [45, 46]. One can selectively inject an additional exciton in the QD through a quasi-resonant optical pumping, using a transition assisted by the creation of a phonon (either optical or acoustic). If the energy levels in the QD are energetically well separated, the injection of an additional exciton is forbidden because of Pauli blocking. This experimental approach will permit to realize the device proposed in the present manuscript, namely a compact and solid-state based system that 18