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arXiv:cond-mat/0605579 · Physical Review B

Entanglement of a pair of atomic qubits near a carbon nanotube

Igor V. Bondarev, Branislav Vlahović

Published Jan 5, 2007• 24 citations
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Abstract

We investigate the entanglement of quasi-one-dimensional atomic polariton states formed by atoms (ions) located close to or encapsulated inside carbon nanotubes and strongly coupled to the nanotube virtual photonic modes. Small-diameter metallic nanotubes are shown to result in sizable amounts of two-qubit atomic entanglement, which persists with no damping for very long times.

DOI
10.1103/physrevb.75.033402

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We investigate the entanglement of quasi-one-dimensional atomic polariton states formed by atoms (ions) located close to or encapsulated inside carbon nanotubes and strongly coupled to the nanotube virtual photonic modes. Small-diameter metallic nanotubes are shown to result in sizable amounts of two-qubit atomic entanglement, which persists with no damping for very long times.
Quantum optics phenomena, including light absorbtion and atomic states entanglement, are discussed for carbon nanotubes doped with atoms (ions). It has been shown that, similar to semiconductor microcavities and photonic band-gap materials, carbon nanotubes may qualitatively change the character of the atom-electromagnetic-field interactions, yielding strong atom-field coupling regime with the formation of quasi-one-dimensional atomic polaritons. These may be observed experimentally via the effect of the absorption line splitting (Rabi splitting) in the frequency range close to the atomic transition frequency. A scheme for entangling atomic polaritons is investigated using the photon Green function formalism for quantizing electromagnetic fields in the presence of quasi-one-dimensional absorbing and dispersing media. Small-diameter metallic nanotubes are shown to result in sizable amounts of the two-qubit atomic entanglement with no damping for sufficiently long times, thus challenging novel applications of atomically doped carbon nanotubes in quantum information science.
We study theoretically a pair of spatially separated extrinsic atomic type species (extrinsic atoms, ions, molecules, or semiconductor quantum dots) near a metallic carbon nanotube, that are coupled both directly via the inter-atomic dipole-dipole interactions and indirectly by means of the virtual exchange by resonance plasmon excitations on the nanotube surface. We analyze how the optical preparation of the system by using strong laser pulses affects the formation and evolution of the bipartite atomic entanglement. Despite a large number of possible excitation regimes and evolution pathways, we find a few generic scenarios for the bipartite entanglement evolution and formulate practical recommendations on how to optimize and control the robust bipartite atomic entanglement in hybrid carbon nanotube systems.
We report a strictly nonexponential 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 nonexponential 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.
A new model of cold atoms trap using a carbon nanotube is proposed. In this model, for the existence of a stable bound state of cold atom, we send a strong electromagnetic field through the carbon nanotube. This field generates an evanescent wave around the carbon nanotube and creates an effective attractive potential. The consideration of some possible boundary conditions leads to this non-trivial bound state solution. We compare also our result to the two most recent models concerning trapping of cold atoms by using a charged carbon nanotube and an optical fiber.