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Recent experiments have illustrated that long range two-body interactions canbe induced by laser coupling atoms to highly excited Rydberg states. Stimulatedby this achievement, we study supersolidity of lattice bosons in anexperimentally relevant situation. In our setup, we consider two-componentatoms on a square lattice, where one species is weakly dressed to anelectronically high-lying (Rydberg) state, generating a tunable, soft-coreshape long-range interaction. Interactions between atoms of the second speciesand between the two species are characterized by local inter- and intra-speciesinteractions. Using a dynamical mean-field calculation, we find thatinterspecies onsite interactions can stabilize a pronounced region ofsupersolid phases. This is characterized by two distinctive types ofsupersolids, where the bare species forms supersolid phases that are immersedin strongly correlated quantum phases, i.e. a crystalline solid or supersolidof the dressed atoms. We show that the interspecies interaction leads to aroton-like instability in the bare species and therefore is crucially importantto the supersolid formation. We provide a detailed calculation of theinteraction potential to show how our results can be explored under currentexperimental conditions.

Supersolidity of lattice Bosons immersed in strongly correlated Rydberg dressed atoms