  We study the entanglement between the internal electronic and the external
vibrational degrees of freedom of a trapped atom which is driven by two lasers
into electromagnetically-induced transparency. It is shown that basic features
of the intricate entanglement dynamics can be traced to Landau-Zener splittings
(avoided crossings) in the spectrum of the atom-laser field Hamiltonian. We
further construct an effective Hamiltonian that describes the behavior of
entanglement under dissipation induced by spontaneous emission processes. The
proposed approach is applicable to a broad range of scenarios for the control
of entanglement between electronic and translational degrees of freedom of
trapped atoms through suitable laser fields.
