content_image/336854.jpg
<img src='content_image/336854.jpg'>

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 

