Entanglement properties of a strongly driven resonant Jaynes-Cummings system

We describe the unitary dynamics and the entanglement properties of a system where a cavity field mode is resonantly coupled to one or two two-level atoms that are strongly driven in the cavity by a coherent field. The cavity field and one atom prepared in pure states always entangle, except when atoms are maximally polarized. The entanglement is maximum for atoms in the upper or lower state and for interaction times in the strong coupling regime. Two atoms, though correlated via the cavity field, do not entangle if the field is not accessible to measurements as in the microwave domain. However, in the optical regime, a null measurement of the cavity field can conditionally prepare an atom pair in a maximally entangled state.