  We discuss the dynamical behavior of the entanglement between the internal
and the external degrees of freedom of a trapped atom in
electromagnetically-induced transparency (EIT) laser cooling. It is shown that
essential features of the intricate entanglement dynamics observed in full
numerical simulations of the underlying quantum master equation can be
understood in terms of a two-state model on the basis of Landau-Zener
splittings in the atom-laser field Hamiltonian. An extension of this model to
an effective non-Hermitian Hamiltonian is constructed which describes the decay
of entanglement by spontaneous emission processes. We also discuss schemes for
the control of entanglement and demonstrate that a permanent entanglement can
be imprinted on trapped atoms through a rapid switch off of the driving fields.
Finally, we point out fundamental distinctions between the entanglement created
in EIT cooling and in the cooling scheme based on velocity-selective coherent
population trapping.
