  Recent experiments have shown that (quasi-)crystalline phases of
Rydberg-dressed quantum many-body systems in optical lattices (OL) are within
reach. Rydberg systems naturally possess strong long-range interactions due to
the large polarizability of Rydberg atoms. Thus a wide range of quantum phases
have been predicted, such as a devil's staircase of lattice incommensurate
density wave phases as well as more exotic lattice supersolid order for bosonic
systems, as considered in our work. Guided by results in the "frozen" gas
limit, we study the ground state phase diagram at finite hopping amplitudes and
in the vicinity of resonant Rydberg driving, while fully including the
long-range tail of the van der Waals interaction. Simulations within real-space
bosonic dynamical mean-field theory (RB-DMFT) yield an extension of the devil's
staircase into the supersolid regime where the competition of condensation and
interaction leads to a sequence of crystalline phases.
