r - a  [nm] (a) (c) N cav P e (b) (d) n  = 0.04 - n  = 0.2 - The frequencies of the probe field, the cavity, and the atom in free space are equal, i.e. ω$_{p}$ = ω$_{c}$ = ω$_{0}$ . The input probe power is P$_{in}$ = 1 pW (left panel) and 5 (right panel) pW, corresponding to the mean number ¯ n = 0 . 04 and 0.2, respectively, of intracavity photons in the absence of the atom. The order m of the cavity resonance mode is an even number. For the parameters of this figure, we find the atom-cavity coupling coefficient G ( r, z ) | r = a,z =0 = 5 . 33 γ$_{0}$ , the cavity damping rate κ = 7 . 02 γ$_{0}$ , and the atomic decay rate γ ( r ) | r = a = 1 . 73 γ$_{0}$ , with γ$_{0}$ = 5 . 25 MHz being the natural linewidth of the D$_{2}$ -line transition of atomic cesium. It is clear that the strong-coupling condition 2 | G | > κ, γ is satisfied when the atom is close to the fiber and to an antinode of the cavity standing-wave field. The figure shows that 13 FIG. 2: Mean photon number N$_{cav}$ and atomic excited-state population P$_{e}$ as functions of the atom- to-surface distance r − a . The solid and dashed lines represent the results of the calculations from the exact steady-state solutions to the density-matrix equations (26) and from the approximate solutions (33) and (34), respectively. The fiber radius is a = 200 nm. The FBG cavity length is L = 10 cm. The FBG mirror reflectivity is | R | 2 = 0 . 9. The input probe power is P$_{in}$ = 1 pW (left panel) and 5 pW (right panel). The parameters for the two-level atom correspond to the D$_{2}$ -line transition 6 S$_{1}$$_{/}$$_{2}$F = 4 M = 4 ↔ 6 P$_{3}$$_{/}$$_{2}$F ′ = 5 M ′ = 5 of atomic cesium, with the wavelength λ$_{0}$ = 852 nm and the natural linewidth γ$_{0}$ = 5 . 25 MHz. The frequencies of the probe field, the cavity, and the atom in free space are equal, i.e. ω$_{p}$ = ω$_{c}$ = ω$_{0}$ . The order m of the cavity resonance mode is an even number. The axial position z of the atom corresponds to an antinode of the cavity standing-wave field. The van der Waals coefficients are C$_{3}$$_{g}$ = 1 . 56 kHz µ m 3 and C$_{3}$$_{e}$ = 3 . 09 kHz µ m $^{3}$.