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Differential Equations and Dynamical Systems

, Volume 27, Issue 4, pp 585–600 | Cite as

Entanglement Dynamics of a Three-level Atom in a Momentum Eigenstate Interacting with Non-linear Effect

  • N. H. Abd El-Wahab
  • Ahmed SalahEmail author
  • A. S. Abdel Rady
  • Abdel-Nasser A. Osman
Original Research

Abstract

We consider a general Hamiltonian for a system which consists of a three level lambda configuration atom interacting with a one-mode cavity field. Besides the intensity-dependent coupling the model includes multi-photon process as well as a non-linear Kerr-Like medium effect. Furthermore, the atom and the field are assumed to be coupled with modulated coupling parameter which depends explicitly on time. The atom is initially prepared in a superposition state and field in a coherent state. Under a rotating wave approximation where fast oscillations are ignored, an exact solution for the wave function in Schrödinger equation is obtained. The momentum increment, the momentum diffusion and the field entropy are calculated. The results shown that in existence of the time dependent coupling parameter leads to a time delaying in the interaction which is twice the delay time for the independent case. The general conclusions reached are illustrated by numerical results.

Keywords

Three-level atom The effective time-dependent coupling parameter Entropy Entanglement 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2016

Authors and Affiliations

  • N. H. Abd El-Wahab
    • 1
  • Ahmed Salah
    • 2
    Email author
  • A. S. Abdel Rady
    • 3
  • Abdel-Nasser A. Osman
    • 3
  1. 1.Mathematics Department, Faculty of ScienceMinia UniversityMiniaEgypt
  2. 2.Mathematics and Theoretical Physics Department, Nuclear Research CenterAtomic Energy AuthorityCairoEgypt
  3. 3.Mathematics Department, Faculty of ScienceSouth Valley UniversityQenaEgypt

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