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We consider a trapped atomic ensemble of interacting bosons in the presenceof a single trapped ion in a quasi one dimensional geometry. Our study iscarried out by means of the newly developed multilayer-multiconfigurationtime-dependent Hartree method for bosons, a numerical exact approach tosimulate quantum many-body dynamics. In particular, we are interested in thescenario by which the ion is so strongly trapped that its motion can beeffectively neglected. This enables us to focus on the atomic ensemble only.With the development of a model potential for the atom-ion interaction, we areable to numerically obtain the exact many-body ground state of the atomicensemble in the presence of an ion. We analyse the influence of the atom numberand the atom-atom interaction on the ground state properties. Interestingly,for weakly interacting atoms, we find that the ion impedes the transition fromthe ideal gas behaviour to the Thomas-Fermi limit. Furthermore, we show thatthis effect can be exploited to infer the presence of the ion both in themomentum distribution of the atomic cloud and by observing the interferencefringes occurring during an expansion of the quantum gas. In the stronginteracting regime, the ion modifies the fragmentation process in dependence ofthe atom number parity which allows a clear identification of the latter inexpansion experiments. Hence, we propose in both regimes experimentally viablestrategies to assess the impact of the ion on the many-body state of the atomicgas. This study serves as the first building block for systematicallyinvestigate many-body physics of such hybrid system.

Ground state properties of ultracold trapped bosons with an immersed ionic impurity