  The role of retardation in the entanglement dynamics of two distant atoms
interacting with a multi-mode 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 sub-wavelength 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 sub-wavelength 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.
