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Qubit Entanglement from a Bipartite Atomic System in a Carbon Nanotube

I.V. Bondarev and B. Vlahovic
North Carolina Central University, US

Keywords:
carbon nanotubes, atomic doping, optical properties, entanglement

Abstract:
The development of materials that may host quantum coherent states is a critical research problem for the nearest future. Important would be to demonstrate quantum information transfer between two quantum bits arbitrarily separated in the material. This would involve entangling operations, followed by the nearest neighbor interaction over short distances and quantum information transfer over longer distances.
 
Recent successful experiments on the encapsulation of single atoms into single-walled carbon nano-tubes (CNs)[1], as well as the progress in the growth techniques of centimeter-long small-diameter single-walled CNs[2], stimulate the study of dynamical quantum processes in atomically doped CN systems. We have recently demonstrated[3] that the nanotube increases dramatically the density of photonic states in its vicinity due to the presence of additional surface photonic modes coupled with CN electronic quasiparticle excitations. As a consequence, the atomic spontaneous decay dynamics is strictly non-exponential close to the CN and, under certain conditions, exhibits Rabi oscillations. The latter are the principal signature of the strong coupling of an excited atomic state to vacuum surface photonic modes in the CN. Such an atomic state is nothing but a ‘quasi-1D cavity polariton’ similar to that observed for quantum dots in semiconductor planar-photonic-crystal nanocavities[4], which were recently suggested to be a possible way to produce the excitonic qubit entanglement by coupling the two quantum dots within a controlled photon environment in the planar nanocavity[5].
 
Here, we show that, being strongly coupled to the (resonator-like) cylindrical nanotube environment, the two atomic quasi-1D polaritons can be easily entangled as well, thus challenging a novel alternative approach towards quantum information transfer over long distances – centimeter-long distances, in fact, since centimeter-long small-diameter single-walled CNs are currently available technologically[2]. We analyze the robustness of the effect predicted by calculating the qubit entanglement for different atomic transition energies and relative atomic positions inside different CNs.
 
[1] G.-H.Jeong et al, Phys. Rev. B68,075410(2003); H.Shimoda et al, Phys. Rev. Lett.88,015502(2002).
[2] L.X.Zheng et al, Proceedings of the NSTI Nanotechnology Conference (May 8–12, 2005, Anaheim, California, USA), vol. 3, p. 126, 2005; J.Lu et al, ibid., vol. 3, p. 132, 2005.
[3] I.V.Bondarev and Ph.Lambin, in: Trends in Nanotubes Reasearch (NovaScience, New York, 2005); also: Phys. Rev. Lett.89,115504(2002), Phys. Rev. B70,035407(2004), Phys. Rev. B72,035451(2005).
[4] J.P.Reithmaier et al, Nature 432, 197 (2004); T.Yoshie et al, ibid., 432, 200 (2004).
[5] S.Hughes, Phys. Rev. Lett. 94, 227402 (2005).

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