Correlations of Rydberg excitations in optically-driven atomic ensembles

I will discuss resonant optical excitation of Rydberg states of atoms in the presence of relaxations.
Atoms in high-lying Rydberg states strongly interact with each other via long-range potentials.
These interactions translate into the level shifts of multiple Rydberg excitations which are therefore
strongly suppressed. Collection of atoms within a certain "blockade" volume can then accommodate
at most a single Rydberg excitation. Perhaps counterintuitively, dephasing of atomic polarization
increases the steady-state excitation probability of such a Rydberg "superatom". Larger atomic
ensembles can accommodate more Rydberg excitations which effectively repel each other.
The Rydberg superatoms behave as soft spheres resulting in highly sub-Poissonian probability
distribution of the number of excitations. In the finite size one- and two-dimensional systems,
the boundary effects mediate quasi-crystallization of Rydberg excitations, while the density-density
correlations exhibit damped spatial oscillations. Similarly to a single superatom, dephasing and
larger atom density lead to stronger density-density correlations of Rydberg excitations.