Effect of retardation on the dynamics of entanglement between atoms

Qurrat-ul-Ain Gulfam, Zbigniew Ficek, and Jörg Evers
Phys. Rev. A 86, 022325 – Published 22 August 2012

Abstract

The role of retardation in the entanglement dynamics of two distant atoms interacting with a multimode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms, and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long-time dynamics for both the multi- and subwavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi- but also at subwavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the Jaynes-Cummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.

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  • Received 22 May 2012

DOI:https://doi.org/10.1103/PhysRevA.86.022325

©2012 American Physical Society

Authors & Affiliations

Qurrat-ul-Ain Gulfam1,*, Zbigniew Ficek2,†, and Jörg Evers1,‡

  • 1Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Deutschland
  • 2The National Centre for Mathematics and Physics, KACST, P.O. Box 6086, Riyadh 11442, Saudi Arabia

  • *qurrat-ul-ain@mpi-hd.mpg.de
  • zficek@kacst.edu.sa
  • joerg.evers@mpi-hd.mpg.de

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Issue

Vol. 86, Iss. 2 — August 2012

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