Spectral properties of a three body atom-ion hybrid system

We consider a hybrid atom-ion system consisting of a pair of bosons interacting with a single ion in a quasi-one-dimensional trapping geometry. Building upon a model potential for the atom-ion interaction developed in earlier theoretical works, we investigate the behaviour of the low-energy eigenstates for varying contact interaction strength $g$ among the atoms. In particular, we contrast the two cases of a static and a mobile ion. Our study is carried out by means of the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons, a numerically-exact $\textit{ab initio}$ method for the efficient simulation of entangled mixtures. We find that repulsive atom interactions induce locally-distinct modifications of the atomic probability distribution unique to each eigenstate. Whilst the atoms on average separate from each other with increasing $g$, they do not necessarily separate from the ion. The mobility of the ion leads in general to greater separations among the atoms as well as between the atoms and the ion. Notably, we observe an exchange between the kinetic energy of the atoms and the atom-ion interaction energy for all eigenstates, which is both interaction- and mobility-induced. For the ground state, we provide an intuitive description by constructing an effective Hamiltonian for each species, which aptly captures the response of the atoms to the ion's mobility. Furthermore, the effective picture predicts enhanced localisation of the ion, in agreement with our results from exact numerical simulations.