P /g x ) 0 ( g ) 2 ( 10 0 n a κ /g=0.2 10 −1 10 2 10 1 10 0 10 −1 10 −2 0.5 10 1 1.0 1.5 2.0 P /g x 10 10 1 10 0 10 −1 10 −2 0.0 0.8 1.0 n $_{x}$0.6 0.4 0.2 (a) (b) (c) (d) γ */g R/g 0 30 20 10 0.5 0.2 0.3 0.4 0.1 0.0 δ /g=2 =0.2 =2 =20 =40 γ /g=0 * Figure 6: (Color online) Numerically calculated (a) cavity population, (b) statistics of the emitted field as a function of pump power, (c) atomic population, for different pure dephasing rates. (d) Effective atom-cavity coupling as a function of the pure dephasing rate (solid line), as compared to the cavity damping rate (dashed line). Parameters are: κ = 0 . 2 g and δ = 2 g . (a)  (b)  P$_{x }$ P$_{x }$ Figure 7: Proposal to achieve a single atom-like laser using a QD doped with a single electron. A quasi-resonant pumping of the QD using a phonon-assisted optical transition is used to excite a trion. Due to this particular pumping protocol, the emitter has only two possible states: (a) no exciton in the QD; (b) a single exciton in the QD. 26