  We propose a method to implement cavity QED and quantum information
processing in high-Q cavities with a single trapped but non-localized atom. The
system is beyond the Lamb-Dick limit due to the atomic thermal motion. Our
method is based on adiabatic passages, which make the relevant dynamics
insensitive to the randomness of the atom position with an appropriate
interaction configuration. The validity of this method is demonstrated from
both approximate analytical calculations and exact numerical simulations. We
also discuss various applications of this method based on the current
experimental technology.
