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Quasiparticle spectra of supersolid lattice gases at near-resonant Rydberg-dressing

One of the major challenges in realizing a strongly interacting lattice gas using Rydberg states is the occurrence of avalanche loss processes. As these are directly proportional to the total Rydberg fraction, the commonly suggested solution is using far off-resonantly excited Rydberg states. We instead propose the realization of a correlated bosonic lattice gas at near-resonant excitation, where the total Rydberg fraction in the bulk is low due to the strong, interaction-driven effective detuning. Using real-space dynamical mean-field theory we show that its reduced effect at the boundary of a system can easily be compensated by considering a tailored beam-waist of the driving Rabi-laser. In this geometry we discuss the spectral properties at the crossover between the supersolid and the superfluid state and present the momentum resolved spectral properties of the supersolid bulk. The latter results are obtained within an extended quasiparticle method which also yields a correction of the mean-field phase transition.