  We study the non-equilibrium dynamics of a pair of qubits made of two-level
atoms separated in space with distance $r$ and interacting with one common
electromagnetic field but not directly with each other. Our calculation makes a
weak coupling assumption but no Born or Markov approximation. We write the
evolution equations of the reduced density matrix of the two-qubit system after
integrating out the electromagnetic field modes. We study two classes of states
in detail: Class A is a one parameter family of states which are the
superposition of the highest energy and lowest energy states, and Class B
states which are the linear combinations of the symmetric and the antisymmetric
Bell states. Our results for an initial Bell state are similar to those
obtained before for the same model derived under the Born-Markov approximation.
However, in the Class A states the behavior is qualitatively different: under
the non-Markovian evolution we do not see sudden death of quantum entanglement
and subsequent revivals, except when the qubits are sufficiently far apart. We
provide explanations for such differences of behavior both between these two
classes of states and between the predictions from the Markov and non-Markovian
dynamics. We also study the decoherence of this two-qubit system.
