Dynamical formation of two-fold fragmented many-body state induced by an impurity in a double-well

TL;DR

This paper investigates how a single impurity in a double-well bosonic system dynamically forms a two-fold fragmented many-body state, influenced by impurity-bath interactions and intra/inter-band excitations, revealing complex quantum phase behaviors.

Contribution

It provides a detailed analysis of the dynamical formation and destruction of fragmented states due to impurity interactions in a double-well trap, highlighting the role of intra- and inter-band excitations.

Findings

Weak impurity-bath interactions lead to two-fold fragmentation.

Strong impurity-bath coupling destroys fragmentation.

Weakly interacting baths suppress excitations, resulting in less fragmentation.

Abstract

We unravel the correlated quantum quench dynamics of a single impurity immersed in a bosonic environment confined in an one-dimensional double-well potential. A particular emphasis is placed on the structure of the time-evolved many-body wave function by relying on a Schmidt decomposition whose coefficients directly quantify the number of configurations that are macroscopically populated. For a non-interacting bosonic bath and weak postquench impurity-bath interactions, we observe the dynamical formation of a two-fold fragmented many-body state which is related to intra-band excitation processes of the impurity and manifests as a two-body phase separation (clustering) between the two species for repulsive (attractive) interactions. Increasing the postquench impurity-bath coupling strength leads to the destruction of the two-fold fragmentation since the impurity undergoes additional inter-band excitation dynamics. By contrast, a weakly interacting bath suppresses excitations of the bath particles and consequently the system attains a weakly fragmented many-body state. Our results explicate the interplay of intra- and inter-band impurity excitations for the dynamical generation of fragmented many-body states in multi-well traps and for designing specific entangled impurity states.