Effects of motion in cavity QED

We consider effects of motion in cavity quantum electrodynamics experiments where single cold atoms can now be observed inside the cavity for many Rab i cycles. We discuss the timescales involved in the problem and the need fo r good control of the atomic motion, particularly the heating due to exchan ge of excitation between the atom and the cavity, in order to realize nearl y unitary dynamics of the internal atomic states and the cavity mode which is required for several schemes of current interest such as quantum computi ng. Using a simple model we establish the ultimate effects of the external atomic degrees of freedom on the action of quantum gates. The performance o f the gate is characterized by a measure based on the entanglement fidelity and the motional excitation caused by the action of the gate is calculated . We find that schemes which rely on adiabatic passage, and are not therefo re critically dependent on laser pulse areas, are very much more robust aga inst interaction with the external degrees of freedom of atoms in the quant um gate.