  We report a strictly non-exponential spontaneous decay dynamics of an excited
two-level atom placed inside or at different distances outside a carbon
nanotube (CN). This is the result of strong non-Markovian memory effects
arising from the rapid variation of the photonic density of states with
frequency near the CN. The system exhibits vacuum-field Rabi oscillations, a
principal signature of strong atom-vacuum-field coupling, when the atom is
close enough to the nanotube surface and the atomic transition frequency is in
the vicinity of the resonance of the photonic density of states. Caused by
decreasing the atom-field coupling strength, the non-exponential decay dynamics
gives place to the exponential one if the atom moves away from the CN surface.
Thus, atom-field coupling and the character of the spontaneous decay dynamics,
respectively, may be controlled by changing the distance between the atom and
CN surface by means of a proper preparation of atomically doped CNs. This opens
routes for new challenging nanophotonics applications of atomically doped CN
systems as various sources of coherent light emitted by dopant atoms.
