Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons

TL;DR

This paper provides an exact analysis of an impurity particle's motion in a 1D gas of hard-core bosons, revealing a polaron-like state and solving for all mass ratios and interaction strengths.

Contribution

It introduces a comprehensive exact solution for impurity dynamics in a 1D hard-core boson system for all mass ratios and interaction strengths, extending previous special cases.

Findings

Impurity forms a polaron-like composite with a gray soliton.

Exact solutions obtained for all impurity-boson mass ratios.

The method employs second quantization and a Lee-Low-Pines transformation.

Abstract

The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.