(a) (b) (c) N cav P e g cav (2) π −π π/2 −π/2 0 β$_{c}$  z FIG. 4: Mean photon number N$_{cav}$ , second-order photon correlation function g (2) $_{cav}$, and atomic excited-state population P$_{e}$ as functions of the axial position z of the atom along the fiber. The distance from the atom to the fiber surface is r − a = 200 nm. Other parameters are as for Fig. 3. to the fact that the absorption of a photon of a weak field by a ground-state atom (or a weakly excited one) can reduce the photon-number spread. Figure 4(c) shows that the axial position dependence of P$_{e}$ is complicated [see Eq. (34)]. Indeed, P$_{e}$ has shallow minima at the antinodes and deep minima at the nodes of the guided cavity field. We plot in Fig. 5 the mean photon number N$_{cav}$ , the second-order photon correla- tion function g (2) $_{cav}$, and the atomic excited-state population P$_{e}$ as functions of the detuning Δ$_{c}$ of the probe field from the cavity resonance in the case where the cavity is at exact resonance with the atom in free space, i.e. ω$_{c}$ = ω$_{0}$ . Figure 5(a) shows that the spec- trum of N$_{cav}$ has a vacuum Rabi splitting. The positions of the two peaks are close to Δ$_{vdW}$ / 2 ± √ G 2 + κγ/ 4 + Δ 2 $_{vdW}$/ 4, where Δ$_{vdW}$ = V$_{eg}$/ ¯ h is the frequency shift caused by the van der Waals potential. Due to the effect of the van der Waals potential, the two peaks are not symmetric in height and position. The peak on the negative side of the detuning Δ$_{c}$ is lower and farther away from the center than the other peak. Comparison between the solid lines (for r − a = 200 nm), the dashed lines (for r − a = 100 nm), and the dotted lines (for r − a = 50 nm) shows that the smaller the distance r − a , the stronger the asymmetry of the peaks. The reason is that the depth of the van der Waals potential increases with decreasing distance r − a . Figure 5(b) shows that g (2) cav > 1, that is, the photon statistics is super-Poissonian, in a broad frequency region where the corresponding atomic excitation P$_{e}$ is significant [see Fig. 5(c)]. The dashed and dotted lines in Figs. 5(b) indicate that 16