Emergent Mott insulators at noninteger fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground-state properties of an ultracold-atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersed in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system to be in a self-bound superfluid phase, with its particle density distribution manifesting a self-concentrated structure. However, in a relatively deep optical lattice, the attractive interaction can drive the system, leading to the Mott-insulator phase even though the global filling factor is not an integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott insulators, with their effective density manifesting a devil's-staircase structure with respect to the strength of the attractive interaction. A detailed estimation of the relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups.