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The spontaneous decay of an excited state of an emitter placed in thevicinity of a metallic single-wall carbon nanotube (SWNT) was examinedtheoretically. The emitter-SWNT coupling strongly depends on the position ofthe emitter relative to the SWNT, the length of the SWNT, the dipole transitionfrequency and the orientation of the emitter. In the high-frequency regime,dips in the spectrum of the spontaneous decay rate exist at the resonancefrequencies in the spectrum of the SWNT conductivity. In theintermediate-frequency regime, the SWNT conductivity is very low, and thespontaneous decay rate is practically unaffected by the SWNT. In thelow-frequency regime, the spectrum of the spontaneous decay rate containsresonances at the antennas resonance frequencies for surface-wave propagationin the SWNT. Enhancement of both the total and radiative spontaneous decayrates by several orders in magnitude is predicted at these resonancefrequencies. The strong emitter-field coupling is achieved, in spite of the lowQ factor of the antenna resonances, due to the very high magnitude of theelectromagnetic field in the near-field zone. The vacuum Rabi oscillations ofthe population of the excited emitter state are exhibited when the emitter iscoupled to an antenna resonance of the SWNT.

Spontaneous decay of an emitter's excited state near a finite-length metallic carbon nanotube