Condensation versus long-range interaction: Competing quantum phases in bosonic optical lattice systems at near-resonant Rydberg dressing

Recent experiments have shownthat (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 has been predicted, such as a devil's staircase of lattice-incommensurate density wave phases as well as the 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 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.