(a) (b) (c) N cav P e g cav (2) π −π π/2 −π/2 0 β$_{c}$  z (a) (b) (c) N cav P e g cav (2) Δ$_{c }$ [MHz] FIG. 9: Same as Fig. 4 except for the cavity length L = 1 mm. FIG. 10: Same as Fig. 5 except for the cavity length L = 1 mm. tion G 2 ≫ max( κγ/ 4 , | Δ$_{c}$ || Δ$_{a}$ | , | Δ$_{c}$ | γ/ 2 , | Δ$_{a}$ | κ/ 2) is satisfied. In the case where Δ$_{c}$ , Δ$_{a}$ ∼ = 0, the above condition reduces to G 2 ≫ κγ/ 4. The strong-coupling condition 2 G ≫ κ, γ is not required. We plot in Figs. 8–10 the results of the numerical calculations for the case where the FBG cavity length is L = 1 mm. Such a length is two orders smaller than the length used for the calculations of the previous figures. For the parameters of Figs. 8–10, we find the atom-cavity coupling coefficient G ( r, z ) | r = a,z =0 = 53 . 3 γ$_{0}$ , the cavity damping rate κ = 702 γ$_{0}$ , and the atomic decay rate γ ( r ) | r = a = 1 . 73 γ$_{0}$ . Since the cavity length L is small, the atom-cavity coupling coefficient G and the cavity damping rate κ are large. It is clear that the strong-coupling condition 2 G ≫ κ, γ is not satisfied. The reason is that κ increases with decreasing L faster than G does. Figures 8–10 show that the atom can still 19