  We study the behavior of a Bose-Einstein condensate in which atoms are weakly
coupled to a highly excited Rydberg state. Since the latter have very strong
van der Waals interactions, this coupling induces effective, nonlocal
interactions between the dressed ground state atoms, which, opposed to dipolar
interactions, are isotropically repulsive. Yet, one finds partial attraction in
momentum space, giving rise to a roton-maxon excitation spectrum and a
transition to a supersolid state in three-dimensional condensates. A detailed
analysis of decoherence and loss mechanisms suggests that these phenomena are
observable with current experimental capabilities.
