Effective approach to impurity dynamics in one-dimensional trapped Bose gases

TL;DR

This paper studies how an impurity atom behaves over time in a one-dimensional trapped Bose gas after interaction strength changes, highlighting the importance of inhomogeneity and proposing an effective model.

Contribution

It introduces an effective single-particle Hamiltonian accounting for inhomogeneity effects via renormalized mass and spring constant, validated through advanced numerical methods.

Findings

Effective mass is smaller than the impurity mass.

Inhomogeneity significantly influences impurity dynamics.

The proposed model accurately describes the impurity evolution.

Abstract

We investigate a temporal evolution of an impurity atom in a one-dimensional trapped Bose gas following a sudden change of the boson-impurity interaction strength. Our focus is on the effects of inhomogeneity due to the harmonic confinement. These effects can be described by an effective one-body model where both the mass and the spring constant are renormalized. This is in contrast to the classic renormalization, which addresses only the mass. We propose an effective single-particle Hamiltonian and apply the multilayer multiconfiguration time-dependent Hartree method for bosons to explore its validity. Numerical results suggest that the effective mass is smaller than the impurity mass, which means that it cannot straightforwardly be extracted from translationally invariant models.