Static properties of positive ions in atomic Bose-Einstein condensates

TL;DR

This paper investigates the static properties of positive ions in atomic Bose-Einstein condensates, analyzing atom excess numbers through thermodynamics and Gross-Pitaevskii equation solutions, revealing multiple solution states and discontinuous transitions.

Contribution

It introduces a combined thermodynamic and Gross-Pitaevskii approach to study ion-induced atom excess and uncovers multiple solution states with density-dependent merging phenomena.

Findings

Excess atom number proportional to scattering length ratio at low densities

Multiple solutions to the Gross-Pitaevskii equation exist for given densities

Discontinuous changes in system state occur with increasing density

Abstract

The excess number of atoms around an ion immersed in a Bose-Einstein condensate is determined as a function of the condensate density far from the ion. We use thermodynamic arguments to demonstrate that in the limit of low densities the excess number of atoms is proportional to the ratio of the atom-ion and atom-atom scattering lengths. For denser systems we calculate the excess number from solutions of the Gross-Pitaevskii equation using a model potential that has a $1/r^{4}$ attraction coming from the polarization of the neutral atoms and a hard core repulsion at short distances. We show that there exist in general many solutions to the Gross-Pitaevskii equation for a given condensate density, the maximum number of solutions being related to the number of bound states of the Schr\"odinger equation for the same potential. With increasing density, pairs of these solutions merge and disappear, implying a discontinuous change of the state of the system.