  We investigate the collective aspects of Rydberg excitation in ultracold
mesoscopic systems. Strong interactions between Rydberg atoms influence the
excitation process and impose correlations between excited atoms. The
manifestations of the collective behavior of Rydberg excitation are the
many-body Rabi oscillations, spatial correlations between atoms as well as the
fluctuations of the number of excited atoms. We study these phenomena in detail
by numerically solving the many-body Schr\"edinger equation.

Quantum Physics