Fig. 1: Pictorial representation of the three identified regimes of the ionic bipolaron consisting of two ions—cyan spheres labeled with “+” surrounded by a gray larger sphere representing the typical range R^⋆—and a density of weakly interacting condensed bosons.

The inset in each regime displays the atoms' distribution in the neighborhood of the ions. a Illustrates the weakly-interacting regime (i), where the local density modulation is small, thus permitting a quasi-particle description. b Displays the regime (ii) with strong interaction having a hard core part. In this case, close to the ions the bath density vanishes. c Illustrates the regime (iii) in which the atom-ion interaction supports a two-body bound state (depicted by the wiggly red lines) participating in the formation of a many-body bound state. In this scenario, the bath density around the ion is strongly modified as many bosons are trapped in the vicinity of the ions.