  We investigate the polaronic properties of a single impurity immersed in a
weakly interacting bosonic environment confined within a one-dimensional
double-well potential using an exact diagonalization approach. We find that an
increase of the impurity-bath coupling results in a vanishing residue,
signifying the occurrence of the polaron orthogonality catastrophe. Asymptotic
configurations of the systems' ground state wave function in the strongly
interacting regime are obtained by means of a Schmidt decomposition, which in
turn accounts for the observed orthogonality catastrophe of the polaron. We
exemplify that depending on the repulsion of the Bose gas, three distinct
residue behaviors appear with respect to the impurity-bath coupling. These
residue regimes are characterized by two critical values of the bosonic
repulsion and originate from the interplay between the intra- and the interband
excitations of the impurity. Moreover, they can be clearly distinguished in the
corresponding species reduced density matrices with the latter revealing a
phase separation on either the one- or the two-body level. The impact of the
interspecies mass-imbalance on the impurity's excitation processes is
appreciated yielding an interaction shift of the residue regions. Our results
explicate the interplay of intra- and interband excitation processes for the
polaron generation in multiwell traps and for designing specific polaron
entangled states motivating their exposure in current experiments.
