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The role of retardation in the entanglement dynamics of two distant atomsinteracting with a multi-mode field of a ring cavity is discussed. Theretardation is associated with a finite time required for light to travelbetween the atoms located at a finite distance and between the atoms and thecavity boundaries. We explore features in the concurrence indicative ofretardation and show how these features evolve depending on the initial stateof the system, distance between the atoms and the number of modes to which theatoms are coupled. In particular, we consider the short-time and the long timedynamics for both the multi- and sub-wavelength distances between the atoms. Itis found that the retardation effects can qualitatively modify the entanglementdynamics of the atoms not only at multi- but also at sub-wavelength distances.We follow the temporal evolution of the concurrence and find that at shorttimes of the evolution the retardation induces periodic sudden changes ofentanglement. To analyze where the entanglement lies in the space spanned bythe state vectors of the system, we introduce the collective Dicke states ofthe atomic system that explicitly account for the sudden changes as a periodicexcitation of the atomic system to the maximally entangled symmetric state. Atlong times, the retardation gives rise to periodic beats in the concurrencethat resemble the phenomenon of collapses and revivals in the Jaynes-Cummingsmodel. In addition, we identify parameter values and initial conditions atwhich the atoms remain separable or are entangled without retardation duringthe entire evolution time, but exhibit the phenomena of sudden birth and suddendeath of entanglement when the retardation is included.

Effect of retardation on the dynamics of entanglement between atoms