Eur. Phys. J. D (2012) 66: 311
https://doi.org/10.1140/epjd/e2012-30380-1

Regular Article

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

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

^a e-mail: shxiang97@163.com

Received: 18 June 2012
Received in final form: 10 October 2012
Published online: 11 December 2012

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.