  We theoretically study the occurrence of quantum jumps in the resonance
fluorescence of a trapped atom. Here, the atom is laser cooled in a
configuration of level such that the occurrence of a quantum jump is associated
to a change of the vibrational center-of-mass motion by one phonon. The
statistics of the occurrence of the dark fluorescence period is studied as a
function of the physical parameters and the corresponding features in the
spectrum of resonance fluorescence are identified. We discuss the information
which can be extracted on the atomic motion from the observation of a quantum
jump in the considered setup.
