  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 strenght, 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.
