0 5 10 0.5 1 1.5 P e 0 5 10 1 2 P e gt 0 20 40 0.5 1 R 0 20 40 0.05 0.1 R ! $^{*}$/g (a)  (b)  (c)  (d)  − 1 0 1 0 2 4 6 8 10 n a I − 1 0 1 0 1 2 3 n a I (a) (b) Figure 3: Evolution of the steady state cavity population n$_{a}$ with respect to population inversion I We took κ = 0 . 2 g . (a) R = g (good cavity regime); (b) R = 0 . 1 g (bad cavity regime). Figure 2: (Color online). Evolution of the atomic population as a function of time for resonant (a) and (b) detuned (with δ = 10 g ) case. Dotted line: the atom and the cavity are not coupled. Solid black curve: γ ∗ = 0. Dashed red curve: γ ∗ = 20 g . Corresponding behavior of the effective atom cavity coupling, R , as a function of pure dephasing is shown for both (b) resonant and (d) detuned cases. The black arrow indicates the case where γ ∗ = 0 [corresponding to the red curves in (a) and (c)], while the red dashed arrow is for the case γ ∗ = 20 g . [corresponding to the red curves in (a) and (c)]. The other parameters of the model for these calculations are: γ = 0 . 01 g , κ = 5 g . 24