  We propose a scheme to implement the quantum teleportation protocol with
single atoms trapped in cavities. The scheme is based on the adiabatic passage
and the polarization measurement. We show that it is possible to teleport the
internal state of an atom trapped in a cavity to an atom trapped in another
cavity with the success probability of 1/2 and the fidelity of 1. The scheme is
resistant to a number of considerable imperfections such as the violation of
the Lamb-Dicke condition, weak atom-cavity coupling, spontaneous emission, and
detection inefficiency.
