  We show that Rydberg states in an ultra-cold gas can be excited with strongly
preferred nearest-neighbor distance if densities are well below saturation. The
scheme makes use of an echo sequence in which the first half of a laser pulse
excites Rydberg states while the second half returns atoms to the ground state,
as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002].
Near to the end of the echo sequence, almost any remaining Rydberg atom is
separated from its next-neighbor Rydberg atom by a distance slightly larger
than the instantaneous blockade radius half-way through the pulse. These
correlations lead to large deviations of the atom counting statistics from a
Poissonian distribution. Our results are based on the exact quantum evolution
of samples with small numbers of atoms. We finally demonstrate the utility of
the omega-expansion for the approximate description of correlation dynamics
through an echo sequence.
