  We describe a mechanism for a controlled generation of a pure Bell state with
correlated atoms that involve two or zero excitations. The mechanism inhibits
transitions into singly excited collective states of a two-atom system by
shifting them from their unperturbed energies. The shift is accomplished by the
dipole-dipole interaction between the atoms. The creation of the Bell state is
found to be dependent on the relaxation of the atomic excitation. When the
relaxation is not present or can be ignored, the state of the system evolves
harmonically between a separable to the maximally entangled state. We follow
the temporal evolution of the state and find that the concurrence can be
different from zero only in the presence of the dipole-dipole interaction.
Furthermore, in the limit of a large dipole-dipole interaction, the concurrence
reduces to that predicted for an X-state of the system. A general inequality is
found which shows that the concurrence of an X-state system is a lower bound
for the concurrence of the two-atom system. With the relaxation present, the
general state of the system is a mixed state that under a strong dipole-dipole
interaction reduces the system to an X-state form. We find that mixed states
admit of lower level of entanglement, and the entanglement may occur over a
finite range of time. A simple analytical expression is obtained for the
steady-state concurrence which shows that there is a threshold value for the
dipole-dipole interaction relative to the Rabi frequency of the driving field
above which the atoms can be entangled over the entire time of the evolution.
