# Unraveling the Structure of Ultracold Mesoscopic Molecular Ions

## TL;DR

This paper provides a detailed many-body analysis of mesoscopic molecular ions in a one-dimensional Bose-Einstein condensate, revealing their structure, phase diagram, and dynamical behavior through advanced computational methods.

## Contribution

It introduces a microscopic many-body approach to characterize mesoscopic molecular ions, including their phase diagram, structure, and dynamics, highlighting quantum correlations.

## Key findings

- Determined the maximum number of atoms bound to the ion.
- Revealed strong interaction-induced localization of the ion.
- Predicted the ion's dynamical response to perturbations.

## Abstract

We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can build-up when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures of ultracold bosonic species for solving the underlying many-body Schr\"odinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.