  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. This is the result of strong non-Markovian memory effects arising
from the rapid frequency variation of the photonic density of states near the
nanotube. The system exhibits vacuum-field Rabi oscillations 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.
