  Ionic Bose polarons are quantum entities emerging from the interaction
between an ion and a Bose-Einstein condensate (BEC), featuring long-ranged
interactions that can compete with the gas healing length. This can result in
strong interparticle correlations and enhancement of gas density around the
ion. One possible approach to describe this complex system with high accuracy
relies on numerical treatment such as the quantum Monte Carlo (QMC) techniques.
Nevertheless, it is computationally very expensive and does not easily allow to
study the system dynamics. On the other hand, a mean-field based variational
ansatz in the co-moving frame can capture a sizeable change in the gas density.
We apply it to the case of regularized ion-atom potential and find that it
qualitatively reproduces the full numerical results. In addition, we also study
the system of two pinned ions, focusing on their effective interaction induced
by the bath. This approach seems to be promising for studying transport and
nonequilibrium dynamics of charged (bi)polarons in condensed media.
