affect significantly the guided cavity field even in the overdamped regime. Note that the shapes of the curves in Figs. 8 and 9 are very similar to those in Figs. 3 and 4, respectively. The substantial difference between the magnitudes of the mean photon number N$_{cav}$ in the case of Figs. 8–10 and the case of Figs. 3–5 results from the substantial difference in the cavity length L . Meanwhile, the shapes of the curves in Fig. 10(a) are very different from the shapes of the curves in Fig. 5(a). Indeed, the curves in Fig. 10(a) do not show the vacuum Rabi splitting. Such a splitting can be observed only under the condition of strong coupling. V. SUMMARY We have studied the effect of an atom on a quantum guided field in a weakly driven FBG cavity. We have calculated the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We have shown that, due to the confine- ment of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number as well as the photon statistics even though the cavity finesse is moderate, the cavity is long, and the probe field is weak. Due to the effect of the van der Waals potential, the vacuum Rabi splitting can become asymmetric with respect to the positions and heights of the peaks. The photon statistics of the quantum guided cavity field can be super- or sub-Poissonian depending on the position of the atom and the detuning of the probe field. [1] For reviews on cavity quantum electrodynamics see, for example, in Cavity Quantum Electro- dynamics , edited by P. R. Berman (Academic, New York, 1994); Spontaneous Emission and Laser Oscillations in Microcavities , edited by H. Yokoyama and K. Ujihara (CRC, New York, 1995). [2] G. Rempe, Appl. Phys. B 60 , 233 (1995). [3] A. C. Doherty, A. S. Parkins, S. M. Tan, and D. F. Walls, Phys. Rev. A 56 , 833 (1997). [4] H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, Opt. Lett. 21 , 1393 (1996). [5] C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, Phys. Rev. Lett. 80 , 4157 (1998). 20