  We study the dynamical entanglement of two identical atoms interacting with a
quantum field. As a simplified model for this physical system we consider two
harmonic oscillators linearly coupled to a massless scalar field in the dressed
coordinates and states approach and enclose the whole system inside a spherical
cavity of radius R. Through a quantity called concurrence, the entanglement
evolution for the two-atom system will be discussed, for a range of initial
states composed of a superposition of atomic states. Our results reveals how
the concurrence of the two atoms behaves through the time evolution, for
arbitrary cavity size and for arbitrary coupling constant, weak, intermediate
or strong. All our computations are exact and only the final step is numerical.
These numerical solutions give us fascinating results for the concurrence, such
as quasi-random fluctuations, with a resemblance of periodicity. Another
interesting result we found is when the system is initially maximally entangled
(disentangled), after the time t = 2R, the system becomes again strongly
entangled (disentangled) particularly during the first oscillations, later this
phenomenon could be wrecked depending on the initial condition. We also show
the concurrence after a too long time elapsed with a good precision.
