Entanglement between internal and external degrees of freedom of a driven trapped atom

We study the dynamics of a Lambda-shaped trapped atom that is driven by two lasers to conditions approaching electromagnetically induced transparency. Solving numerically the full quantum master equation describing the coupled system of electronic and vibrational degrees of freedom, we investigate the dynamics of the entanglement and the quantum mutual information during the cooling process. Far from the Lamb-Dicke limit, an intricate behaviour of these quantities is found, as well as the emergence of a mixed entangled non-equilibrium stationary state.