The possibility that quantum mechanical computers might be able to efficiently solve problems that are intractable for classical computers has led to an explosive growth of interest in the field of Quantum Logic and Computing. Of particular interest to our group are topics related to the implementation of quantum logic operations with well understood atomic physics and quantum optics systems. At Georgia Tech, a joint experimental/theoretical effort is underway to explore a new implementation scheme for a quantum computer based on trapped atoms and cavity QED systems. We are performing theoretical research into the relevant atomic physics and quantum optics in support of the joint effort.