In the vicinity of the fiber surface, the atom experiences the effect of the van der Waals potential on the internal state energy and on the center-of-mass motion. Let V$_{g}$ and V$_{e}$ be the van der Waals potentials for the ground state | g 〉 and the excited state | e 〉 , respectively. In the presence of the fiber, the atomic transition frequency is shifted from the bare frequency ω$_{0}$ and is given by where V$_{eg}$ = V$_{e}$ − V$_{g}$ . The Hamiltonians of the atom and the guided cavity field in the case of no coupling between them are given by respectively. Here p and M are the momentum and the mass of the atom, respectively. When we sum up the Hamiltonians (12), (17), (21), and (22), we obtain the total Hamiltonian H = H$_{A}$ + H$_{F}$ + H$_{AF}$ + H$_{P}$ for the combined atom-field system. We decompose H into two parts, H$_{0}$ = ¯ hω$_{p}$ ( a $^{†}$a + σ$_{z}$/ 2) and H$_{I}$ = H − H$_{0}$ . In the interaction picture, the combined atom-field system is described by the Hamiltonian H$_{int}$ = e iH 0 t/ ¯ $^{h}$H$_{I}$ e − iH 0 t/ ¯ $^{h}$, whose explicit expression is and Here Δ$_{a}$ = ω$_{p}$ − ω$_{a}$ is the detuning of the probe field frequency ω$_{p}$ from the surface-shifted atomic transition frequency ω$_{a}$ . The Hamiltonian (23) is almost same as that for a weakly driven microcavity [12]. The difference between the two models is that the presence of the van der Waals potential in the case of the nanofiber-based cavity affects the transition frequency and the center-of-mass motion of the atom. For the treatments in the remaining part of this paper, we assume that the translational motion of the atom can be neglected. This situation can be realized in the cases where the atom is trapped, the atom is slow (the atomic ensemble is kept at a low temperature), or the two-level atom is replaced by a heavy particle like a quantum dot. We note that trapping of neutral cesium atoms in a one-dimensional optical lattice above the surface of a 8 H$_{int}$ = p 2 2 M − 1 2 ¯ h Δ$_{a}$ σ$_{z}$ − ¯ h Δ$_{c}$ a $^{†}$a − i ¯ hG ( aσ † − a $^{†}$σ ) − i ¯ hη ( a − a $^{†}$) + V$_{e}$ + V$_{g}$ 2 . (23) H$_{F}$ = ¯ hω$_{c}$a $^{†}$a, (22) H$_{A}$ = p 2 2 M + 1 2 ¯ hω$_{a}$σ$_{z}$ + V$_{e}$ + V$_{g}$ 2 (21) ω$_{a}$ ( r ) = ω$_{0}$ + V$_{eg}$ ( r ) / ¯ h, (20)