Spontaneous-decay dynamics in atomically doped carbon nanotubes

Abstract

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.

van der Waals coupling in atomically doped carbon nanotubes

“…(43), the transition frequencyω A decreases with increasing the transverse local photonic DOS ξ ⊥ (r A , ω), i.e. when the atom approaches the CN surface [10], thereby bringing the unperturbed atomic levels together, or even making them degenerated if ξ ⊥ (r A , ω) is large enough (see a typical example in Fig. 2).…”

“…This tensor was derived and analysed in Ref. [10]. Assuming further that the atomic subsystem is sufficiently localized in space, so that the long-wavelength approximation applies, one can expand the field operatorsÂ(r) andφ(r) in the Hamiltonian (6) around the atomic center of mass position r A and only keep the leading non-vanishing terms of the expansions.…”

“…[15,16] and adapted for an atom near a CN in Refs. [9,10]. In this approach, the Fourier-images of electric and magnetic fields are considered as quantum mechanical observables of corresponding electric and magnetic field operators.…”

“…A theoretical analysis recently done [8,9,10] of spontaneous decay dynamics of excited atomic states near CNs has brought out fasci- * Corresponding author. E-mail address: bondarev@tut.by nating peculiarities of the vacuum-field interactions in atomically doped CNs.…”

Spontaneous emission of light from atoms: the model

“…where 7 p i = −i∂ i , α is the fine-structure constant, and A i (t, x) denotes the vector-potential operator, in the radiation gauge, with the free time-evolution already implemented 8 . This is a standard interaction…”