Ion induced density bubble in a strongly correlated one dimensional gas

TL;DR

This paper investigates how a single ion embedded in a strongly correlated one-dimensional Tonks-Girardeau gas creates a localized density bubble, revealing new insights into impurity effects in quantum gases.

Contribution

It models the ion as a static deformation and uses quantum defect theory to analyze the density profile, introducing a pseudopotential approach for simplicity.

Findings

A density bubble of about a micron forms around the ion.

The ionic impurity can be effectively modeled with a pseudopotential.

Exact results demonstrate the impurity's impact on the gas density.

Abstract

We consider a harmonically trapped Tonks-Girardeau gas of impenetrable bosons in the presence of a single embedded ion, which is assumed to be tightly confined in a RF trap. In an ultracold ion-atom collision the ion's charge induces an electric dipole moment in the atoms which leads to an attractive $r^{-4}$ potential asymptotically. We treat the ion as a static deformation of the harmonic trap potential and model its short range interaction with the gas in the framework of quantum defect theory. The molecular bound states of the ionic potential are not populated due to the lack of any possible relaxation process in the Tonks-Girardeau regime. Armed with this knowledge we calculate the density profile of the gas in the presence of a central ionic impurity and show that a density \textit{bubble} of the order of a micron occurs around the ion for typical experimental parameters. From these exact results we show that an ionic impurity in a Tonks gas can be described using a pseudopotential, allowing for significantly easier treatment.