  We revisit the decoherence of the atomic state in the resonant
Jaynes-Cummings model with the field initially being in a coherent state. We
show that the purity of the atom exhibits oscillating Gaussian dependence on
the time with a width independent of the initial atomic state. It is also shown
that when the atom and the coherent state match each other in phase, the atomic
decoherence is Gaussian time dependence.
