  We present two schemes for driving Raman transitions between the ground state
hyperfine manifolds of a single atom trapped within a high-finesse optical
cavity. In both schemes, the Raman coupling is generated by standing-wave
fields inside the cavity, thus circumventing the optical access limitations
that free-space Raman schemes must face in a cavity system. These cavity-based
Raman schemes can be used to coherently manipulate both the internal and the
motional degrees of freedom of the atom, and thus provide powerful tools for
studying cavity quantum electrodynamics. We give a detailed theoretical
analysis of each scheme, both for a three-level atom and for a multi-level
cesium atom. In addition, we show how these Raman schemes can be used to cool
the axial motion of the atom to the quantum ground state, and we perform
computer simulations of the cooling process.
