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Three-step approach to Fokker-Planck equation for an interacting open waveguide system and localizable entanglement dynamics

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Abstract

We consider a system of three coupled single-mode waveguides each locally interacting with its own Gaussian environment and present a general solution for this coupled system initially in any Gaussian state using the symplectic operations. We investigate the dynamics of two-mode localizable entanglement contained in the evolved state when the system is initially in three-mode bisymmetric Gaussian state in contact with the independent decoherence. We show that such an entanglement exhibits a damped oscillation in a regime of weak waveguide-waveguide coupling and small mean photon numbers of the bath. Remarkably, we find that the entanglement can reappear after the long-time death and arrives at a steady-state oscillation, whose maximum depends strongly on both the squeezing of the bath and the coupling strength between these waveguides. Finally, we generalize the approach to a common squeezed environment case.

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Authors and Affiliations

  1. Department of Physics and Information Engineering, Huaihua University, 418008 Huaihua, Hunan, P.R. China

    S.H. Xiang, D.H. Lu & K.H. Song

Authors
  1. S.H. Xiang
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  2. D.H. Lu
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  3. K.H. Song
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Correspondence to S.H. Xiang.

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Xiang, S., Lu, D. & Song, K. Three-step approach to Fokker-Planck equation for an interacting open waveguide system and localizable entanglement dynamics. Eur. Phys. J. D 66, 311 (2012). https://doi.org/10.1140/epjd/e2012-30380-1

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