P /g x ) 0 ( g ) 2 ( 10 0 n a κ /g=0.2 γ */g  10 −1 10 2 10 1 10 0 10 −1 10 −2 0.5 R/g 10 1 1.0 0.0 1.5 2.0 0 40 30 20 10 10 1 10 2 10 0 10 −1 10 −2 δ /g=0 γ /g=0 * =2 =10 =20 =40 P /g x 10 2 10 1 10 0 10 −1 10 −2 0.0 0.8 1.0 n $_{x}$0.6 0.4 0.2 (a) (b) (c) (d) 0 20 40 P /g x 0.1 1 R/g κ$_{=0.2g}$ 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 R/g 10 1 1.0 0.0 1.5 2.0 10 1 10 2 10 0 10 −1 10 −2 P /g x 10 2 10 1 10 0 10 −1 10 −2 0.0 0.8 1.0 n $_{x}$0.6 0.4 0.2 (a) (b) (c) (d) δ /g=0 =1 =2 =5 =10 δ /g 0 14 12 10 8 6 4 2 10 −3 10 −2 γ /g=0 * Figure 5: (Color online). Numerically calculated (a) cavity population, (b) statistics of the emitted field as a function of pump power, and (c) atomic population for different atom-cavity detunings. (d) Effective atom-cavity coupling as a function of the detuning (solid line), as compared to the cavity damping rate (dashed line). Parameters are: κ = 0 . 2 g and γ ∗ = 0. Figure 4: (Color online). Numerically calculated (a) cavity population, (b) statistics of the emitted field, and (c) atomic population as a function of pump power, for different pure dephasing rates. (d) Effective atom-cavity coupling as a function of the pure dephasing rate (solid line), as compared to the cavity damping rate (dashed line). Parameters are: κ = 0 . 2 g and δ = 0. The inset shows the effective atom-cavity coupling as a function of P$_{x}$ , for δ = 0, γ ∗ = 0. 25