  We investigate the ground state properties of an ultracold atom system
consisting of many-body polarons, quasiparticles formed by impurity atoms in
optical lattices immersing 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 being in a self-bound
superfluid phase with its particle density distribution manifesting a
self-concentrated structure. While in a relatively deep optical lattice, the
attractive interaction can drive the system forming the Mott-insulator phase
even though the global filling factor is not 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 attractive interaction. Detailed
estimation on relevant experimental parameters shows that these rich physics
can be readily observed in current experimental setups.
