  It is well established that an entanglement encoded in the Bell states of a
two-qubit system with correlated spins exhibits completely different evolution
properties than that encoded in states with the anti-correlated spins. A
complete and abrupt loss of the entanglement, called the entanglement sudden
death, can be found to occur for the spin correlated states, but the
entanglement evolves without any discontinuity or decays asymptotically for the
spin anti-correlated states. We consider the evolution of an initial
entanglement encoded in the spin anti-correlated states and demonstrate that
the asymptotic behavior predicted before occurs only in the weak coupling limit
or equivalently when the rotating-wave approximation (RWA) is made on the
interaction Hamiltonian of the qubits with the field. If we do not restrict
ourselves to the RWA, we find that the entanglement undergoes a discontinuity,
the sudden death phenomenon. We illustrate this behavior by employing an
efficient scheme for entanglement evolution between two cold-trapped atoms
located inside a single-mode cavity. Although only a single excitation is
initially present in the system, we find that the two-photon excited state,
which plays the key role for the discontinuity in the behavior of the
entanglement, gains a population over a short time of the evolution. When the
RWA is made on the interaction, the two-photon excited state remains
unpopulated for all times and the discontinuity is absent. We attribute this
phenomenon to the principle of complementarity between the evolution time and
energy, and the presence of the counter-rotating terms in the interaction
Hamiltonian.
