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 behavior of the low-energy eigenstates for varying contact interaction strength $g$ among the atoms. In particular, we contrast the two cases of a static ion and a mobile ion. Our study is carried out by means of the multilayer multiconfiguration time-dependent Hartree method for bosons, a numerically exact 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. While 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 localization of the ion, in agreement with our results from exact numerical simulations.

中文翻译：

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三体原子-离子杂化系统的光谱性质

我们考虑了一个混合原子离子系统，该系统由一对玻色子与一个单一的离子在准一维俘获几何结构中相互作用。建立在较早的理论工作中开发的原子-离子相互作用的模型潜能的基础上，我们研究了低能本征态在不同接触相互作用强度下的行为$G$在原子之间。特别地，我们对比了静态离子和移动离子这两种情况。我们的研究是通过玻色子的多层多配置时变Hartree方法进行的，该方法是一种数值精确的从头算方法，可以有效地模拟纠缠混合物。我们发现，排斥原子相互作用会引起每个本征态唯一的原子概率分布的局部不同的修改。平均而言，原子彼此之间的间隔随着增加而增加$G$，它们不一定与离子分离。离子的迁移率通常导致原子之间以及原子与离子之间的更大分离。值得注意的是，我们观察到所有本征态的原子动能和原子-离子相互作用能之间的交换，这既是相互作用的，也是迁移率的诱导。对于基态，我们通过为每个物种构造有效的哈密顿量来提供直观描述，该哈密顿量能恰当地捕获原子对离子迁移率的响应。此外，与我们从精确数值模拟得出的结果一致，有效图片预测了离子的增强定位。