Impurities immersed in hard-core Bose gases offer exciting opportunities to explore polaron and bipolaron physics. We investigate the ground-state properties of a single and a pair of impurities throughout the superfluid and insulating (charge density wave) phases of the bosonic environment. In the superfluid phase, the impurity exhibits polaron-like behavior, forming a dressed quasiparticle. In contrast, in the insulating phase, the impurity regains its particle-like character, moving through a potential landscape shaped by the charge density wave order. Moreover, we show that two impurities can form a bound state even in the absence of an explicit impurity-impurity coupling. We establish the stability of this bound state within both the superfluid and insulating phases. Our results offer valuable insights for ongoing lattice polaron experiments with ultracold gases.

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• Charge density waves
• Polarons
• Rydberg gases
• Bose-Hubbard model