The dynamics of a cloud of ultra-cold two-level atoms is studied at
off-resonant laser driving to a Rydberg state. We find that resonant excitation
channels lead to strongly peaked spatial correlations associated with the
buildup of asymmetric excitation structures. These aggregates can extend over
the entire ensemble volume, but are in general not localized relative to the
system boundaries. The characteristic distances between neighboring excitations
depend on the laser detuning and on the interaction potential. These properties
lead to characteristic features in the spatial excitation density, the Mandel
Q parameter, and the total number of excitations. As an application an
implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is
discussed. The gate not only exploits the Rydberg blockade, but also utilizes
the special features of an asymmetric geometric arrangement of the three atoms.
We show that continuous-wave off-resonant laser driving is sufficient to create
the required spatial arrangement of atoms out of a homogeneous cloud.Comment: 8 pages, 7 figure
