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.
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