• correlations
• Rydberg
• full counting statistics
• cold atoms

This Thesis aims to investigate the role of correlations arising in cold Rydberg samples as a consequence of the strong interactions between its constituents.
For this purpose, two different approaches, which allow the study of different types of correlations, are presented here. On the one hand, as a consequence of the interactions between the excitations, resonantly excited Rydberg ensembles exhibit a strong degree of anti-correlation, which becomes visible either through the blockade of the excitation, or through a slowing down of the dynamics. On the other hand, the Rydberg-Rydberg interactions in the off-resonant regime enhance the generation of new excitations, leading the system to exhibit strong correlations. Moreover, by analyzing the full counting statistics (FCS) of the excitation events we get more insight into this process. Thus, in the off-resonant case, the most notable features of these strong correlations are the bimodal shapes of histograms of the counting distributions. Furthermore, under strong dissipative conditions, the FCS analysis reveals signs of a transition between two dynamical phases. Although the afore-mentioned effects were observed in a system governed by an Ising-type Hamiltonian, correlations emerge in other systems as well. For instance, in systems described by Heisenberg XX-type Hamiltonians, the strong interactions lead the dipolar energy exchange between the excitations.