  The spontaneous decay of an excited state of an emitter placed in the
vicinity of a metallic single-wall carbon nanotube (SWNT) was examined
theoretically. The emitter-SWNT coupling strongly depends on the position of
the emitter relative to the SWNT, the length of the SWNT, the dipole transition
frequency and the orientation of the emitter. In the high-frequency regime,
dips in the spectrum of the spontaneous decay rate exist at the resonance
frequencies in the spectrum of the SWNT conductivity. In the
intermediate-frequency regime, the SWNT conductivity is very low, and the
spontaneous decay rate is practically unaffected by the SWNT. In the
low-frequency regime, the spectrum of the spontaneous decay rate contains
resonances at the antennas resonance frequencies for surface-wave propagation
in the SWNT. Enhancement of both the total and radiative spontaneous decay
rates by several orders in magnitude is predicted at these resonance
frequencies. The strong emitter-field coupling is achieved, in spite of the low
Q factor of the antenna resonances, due to the very high magnitude of the
electromagnetic field in the near-field zone. The vacuum Rabi oscillations of
the population of the excited emitter state are exhibited when the emitter is
coupled to an antenna resonance of the SWNT.
