  We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic
ensembles interacting with a classical electromagnetic field in the regime of
Rydberg blockade, where the time dynamics of the average number of Rydberg
excitations in mesoscopic ensembles displays collapses and revivals typical of
this model. As the frequency of Rabi oscillations between collective states of
Rydberg blockaded ensembles depends on the number of interacting atoms, for
randomly loaded optical dipole traps we predict collapses and revivals of Rabi
oscillations. We have studied the effects of finite interaction strengths and
finite laser line width on the visibility of the revivals. We have shown that
observation of collapses and revivals of Rabi oscillations can be used as a
signature of Rydberg blockade without the need to measure the exact number of
Rydberg atoms.
