van der Waals coupling in atomically doped carbon nanotubes

We have investigated atom-nanotube van der Waals (vdW) coupling in atomically doped carbon nanotubes (CNs). Our approach is based on the perturbation theory for degenerated atomic levels, thus accounting for both weak and strong atom-vacuum-field coupling. The vdW energy is described by an integral equation represented in terms of the local photonic density of states. By solving it numerically, we demonstrate the inapplicability of standard weak-coupling-based vdW interaction models in a close vicinity of the CN surface where the local photonic DOS effectively increases, giving rise to an atom-field coupling enhancement. An inside encapsulation of atoms into the CN has been shown to be energetically more favorable than their outside adsorption by the CN surface. If the atom is fixed outside the CN, the modulus of the vdW energy increases with the CN radius provided that the weak atom-field coupling regime is realized (i.e., far enough from the CN). For inside atomic position, the modulus of the vdW energy decreases with the CN radius, representing a general effect of the effective interaction area reduction with lowering the CN curvature.

Figure 1

(Color online) The geometry of the problem.

Figure 2

(Color online) Schematic of the energy levels in the problem of the ground-state atom vdW interaction with the CN. On the left are the unperturbed atomic levels given by the Hamiltonian (22), on the right are the levels of the coupled “atom-nanotube” system given by the total Hamiltonians (20, 21, 22, 23). The relevant virtial transition of the system is shown by the vertical dashed arrows.

Figure 3

(Color online) Dimensionless unperturbed energy levels [given by the Hamiltonians (21, 22)] and total ground-state energy [given by Eqs. (42, 43, 44, 45, 46)] as functions of the atomic position for the two-level atom outside the (9,0) CN. See Eq. (43) for $x_A$.

Figure 4

(Color online) Transverse local photonic DOSs (a) and ground-state vdW energies (b) as functions of the atomic position for the two-level atom outside the (9,0) CN. The “bare” atomic transition frequencies are indicated by dashed lines in (a).

Figure 5

(Color online) Longitudinal local photonic DOSs (a) and ground-state vdW energies (b) as functions of the atomic position for the two-level atom nearby the (10,10) CN. The “bare” atomic transition frequencies are indicated by dashed lines in (a).

Figure 6

Ground-state van der Waals energy of the two-level atom positioned at a fixed atom-surface distance [equal to the radius of the (9,0) CN] inside and outside “zigzag” $(m,0)$ CNs of different radii, as a function of the nanotube index $m$.