  We investigate both theoretically and experimentally the effect of thermal
motion of laser cooled atoms on the coherence of Rabi oscillations induced by
an inhomogeneous driving field. The experimental results are in excellent
agreement with the derived analytical expressions. For freely falling atoms
with negligible collisions, as those used in our experiment, we find that the
amplitude of the Rabi oscillations decays with time $t$ as $\exp[-(t/\tau)^4]$,
where the coherence time $\tau$ drops with increasing temperature and field
gradient. We discuss the consequences of these results regarding the fidelity
of Rabi rotations of atomic qubits. We also show that the process is equivalent
to the loss of coherence of atoms undergoing a Ramsey sequence in the presence
of static magnetic field gradients - a common situation in many applications.
In addition, our results are relevant for determining the resolution when
utilizing atoms as field probes. Using numerical calculations, our model can be
easily extended to situations in which the atoms are confined by a potential or
to situations where collisions are important.
