From spontaneous to explicit symmetry breaking in a finite-sized system: Bosonic bound states of an impurity

TL;DR

This paper investigates how a single impurity induces a transition from a homogeneous to a localized state in a finite bosonic system, revealing symmetry breaking and bosonic bound states through exact and mean-field analyses.

Contribution

It demonstrates the transition mechanism driven by an impurity in a finite system and compares few-body exact results with mean-field predictions, highlighting the role of symmetry breaking.

Findings

Localization around impurity observed in pair correlations

Finite-size precursors of Higgs-Anderson and Nambu-Goldstone modes identified

Agreement between exact diagonalization and mean-field improves with increased boson repulsion

Abstract

The presence of a single attractive impurity in an ultracold repulsive bosonic system can drive a transition from a homogeneous to a localized state, as we here show for a one-dimensional ring system. In the few-body limit the localization of the bosons around the impurity, as seen in the pair correlations, is accompanied by low-lying modes that resemble finite-size precursors of Higgs-Anderson and Nambu-Goldstone-like modes. Tuning the impurity-boson mass ratio allows for the exploration of the transition from a spontaneous to an explicit breaking of the continuous rotational symmetry of the Hamiltonian. We compare the minimum of the Higgs-Anderson-like mode as a marker of the onset of localization in the few-body limit to mean-field predictions of binding. We find improved agreement between the few-body exact diagonalization results and mean-field predictions of binding with increasing boson-boson repulsion.