Ultracold hybrid ion-atom gases represent an exciting frontier for quantum simulation offering a new set of functionalities and control. Here, we study a mobile ion immersed in a Bose-Einstein condensate and show that the long-range nature of the ion-atom interaction gives rise to an intricate interplay between few- and many-body physics. This leads to the existence of several polaronic and molecular states due to the binding of an increasing number of bosons to the ion, which is well beyond what can be described by a short-range pseudopotential. We use a complementary set of techniques including a variational ansatz and field theory to describe this rich physics and calculate the full spectral response of the ion. It follows from thermodynamic arguments that the ion-atom interaction leads to a mesoscopic dressing cloud of the polarons, and a simplified model demonstrates that the spectral weight of the molecules scale with increasing powers of the density. We finally calculate the quantum dynamics of the ion after a quench experiment.

中文翻译：

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玻色-爱因斯坦凝聚中的带电极化子和分子

超冷混合离子原子气体代表了量子模拟的一个激动人心的前沿领域，提供了一组新的功能和控制。在这里，我们研究了浸入玻色-爱因斯坦凝聚态的移动离子，并表明离子-原子相互作用的长程性质导致了少体物理和多体物理之间复杂的相互作用。由于越来越多的玻色子与离子的结合，这导致了几种极化子和分子状态的存在，这远远超出了短程赝势所能描述的范围。我们使用一套互补的技术，包括变分分析和场论来描述这一丰富的物理学并计算离子的全光谱响应。根据热力学论证，离子 - 原子相互作用导致极化子的细观敷料云，一个简化的模型表明分子的光谱权重随着密度功率的增加而变化。我们最终在猝灭实验后计算了离子的量子动力学。