  The strong interaction between Rydberg atoms can be used to control the
strength and character of the interatomic interaction in ultracold gases by
weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals
for the realization of various complex phases and applications in quantum
simulation exist. Also a simple model has been already developed that describes
the basic idea of Rydberg dressing in a two-atom basis. However, an
experimental realization has been elusive so far. We present a model describing
the ground state of a Bose-Einstein condensate dressed with a Rydberg level
based on the Rydberg blockade. This approach provides an intuitive
understanding of the transition from pure twobody interaction to a regime of
collective interactions. Furthermore it enables us to calculate the deformation
of a three-dimensional sample under realistic experimental conditions in
mean-field approximation. We compare full three-dimensional numerical
calculations of the ground state to an analytic expression obtained within
Thomas-Fermi approximation. Finally we discuss limitations and problems arising
in an experimental realization of Rydberg dressing based on our experimental
results. Our work enables the reader to straight forwardly estimate the
experimental feasibility of Rydberg dressing in realistic three-dimensional
atomic samples.
