Entanglement generation by a dispersive vacuum

We study how the entanglement between two atoms can be created or modified even when they do not interact but when each of them interacts dispersively, i.e., weak and far from the resonance, with a single mode of the field. In particular, we study two cases: First we consider each atom to be initially in a pure state and secondly we assume that they start in a Werner state. Analytically we find that both atoms can, periodically, reach maximum entanglement if each of them starts in any state belonging to the Bloch sphere equator, independent of the initial Fock state of the mode. Thus, in particular, we find that a dispersive vacuum mode can generate entanglement between two two-level atoms. In the second case, when the field mode is initially in a coherent or thermal state we find that, in the high energy limit, in general there is no entanglement between the two atoms. However, at well defined moments, the initial entanglement appears and disappears suddenly, becoming a narrow entanglement-beats structure.