Intra- and interband excitations induced residue decay of the Bose polaron in a one-dimensional double-well

TL;DR

This study explores how intra- and interband excitations influence the decay of the Bose polaron residue in a one-dimensional double-well, revealing regimes of orthogonality catastrophe and phase separation driven by impurity-bath interactions.

Contribution

It provides a detailed analysis of residue behaviors and ground state configurations in a double-well system, highlighting the roles of intra- and interband excitations and mass imbalance.

Findings

Residue vanishes with increased impurity-bath coupling indicating orthogonality catastrophe.

Three distinct residue regimes depend on bosonic repulsion and impurity interactions.

Phase separation observed in reduced density matrices correlates with residue behavior.

Abstract

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.