Entanglement of a qubit coupled to a resonator in the adiabatic regime

We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strength, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.