N$_{cav}$ and P$_{e}$ substantially depend on the atom-to-surface distance r − a . We observe that the radial profile of N$_{cav}$ has a minimum and the radial profile of P$_{e}$ has a maximum. The minimum of N$_{cav}$ is closer to the surface than the maximum of P$_{e}$ is. When r − a is large, N$_{cav}$ decreases and P$_{e}$ increases with decreasing r − a . Such behaviors are due to the radial dependence of the atom-cavity coupling coefficient G . In contrast, when r − a is small, N$_{cav}$ increases and P$_{e}$ decreases with decreasing r − a . Such behaviors are due to the effect of the van der Waals potential on the radial dependence of the surface-shifted atomic transition frequency ω$_{a}$ . We emphasize again that the van der Waals potential is negligible in the region of large r − a but significant in the region of small r − a . Figure 2(d) shows that, although the probe field is very weak ( P$_{in}$ = 5 pW) and the mean photon number in the absence of the atom is small (¯ n = 0 . 2), the atomic excitation P$_{e}$ can reach quite large values (e.g. P$_{e}$ ∼ = 0 . 2 at r − a ∼ = 320 nm). Such substantial excitation is a result of the strong coupling between the atom and the guided cavity field. Comparison between the solid and dashed lines in Fig. 2 shows that the approximate solutions (33) and (34) almost coincide with the results of the exact calculations from the density-matrix equations (26) when ¯ n is on the order of or smaller than 0.04, that is, when the power P$_{in}$ of the probe field is on the order of or smaller than 1 pW. When the power P$_{in}$ of the probe field is on the order of or larger than 5 pW, the discrepancy between the exact and approximate solutions becomes serious. The effect of the atom on the quantum guided cavity field is significant only when the mean photon number is small. However, it is not easy to measure the transmitted field when the mean intracavity photon number is too small. Therefore, we focus on the case where the mean photon number in the absence of the atom is less than one but not too small. For this purpose, we choose the input probe power P$_{in}$ = 10 pW, which corresponds to the value ¯ n = 0 . 4 for the mean photon number in the absence of the atom. The FBG cavity length is L = 10 cm. We plot in Fig. 3 the mean photon number N$_{cav}$ , the second-order photon correlation function g (2) $_{cav}$, and the atomic excited-state population P$_{e}$ as functions of the distance r − a from the atom to the fiber surface. The frequencies of the probe field, the cavity, and the atom in free space are equal, i.e. ω$_{p}$ = ω$_{c}$ = ω$_{0}$ . Figures 3(a) and 3(c) show that N$_{cav}$ and P$_{e}$ substantially depend on the atom-to-surface distance r − a . Figure 3(b) shows that g (2) cav > 1, that is, the photon statistics is super-Poissonian. It is clear from the figure that, in the region of large r − a , where the van der Waals potential is weak, the 14