Polarons in Ultracold Atomic Gases

耦合到量子系统的杂质动力学代表了一个概念简单，但高度非平凡的物理系统。例如，电子穿过离子晶格会局部扭曲晶格（由于库仑排斥）。杂质加上局部畸变的组合系统通常称为极化子。极化子在许多方面表现得像一个孤立的粒子，并且具有明确的能量和质量，这与孤立的杂质有很大的不同。极化子在包括超导体、近藤系统和巨磁阻材料在内的各种凝聚态物质系统中发挥着重要作用。此外，在理论层面上，极化子本身就很有趣。举个例子，费曼路径积分的第一个重要应用就是计算极化子的质量。尽管从Frohlich和Feynmann的早期工作开始，人们已经进行了多年的研究，但极化子的许多方面仍然没有被理解。因此，在过去的五年中，大量利用超冷原子气体聚焦极化子的实验工作已经开展。与固态材料相比，超冷系统具有许多明显的优势。特别是，对于超冷原子，可以实现被认为描述固态极化子的最小模型的清洁实现。此外，由于高度的可调性（例如使用费什巴赫共振），可以用超冷气体探索极化子物理的新体制。这个博士项目将研究超冷气体混合物中的极化子。最近的研究表明，当原子物种之间的耦合较弱时，系统可以用所谓的Frohlich hamilton来描述[例如，参见New Journal of Physics， 19,103035, 2017]。弗罗里希哈密顿量是凝聚态物理中的一个典型模型，它描述了粒子和声子之间的耦合。它是描述标准超导体的起点。然而，当气体之间的耦合不弱时，Frohlich模型就不再提供对系统的准确描述。在这个项目中，我们将使用另一个起点-耦合系统的完整微观哈密顿量。极化子的许多基本关系（比如它们的质量和能量）都是在Frohlich模型的背景下表述的。因此，我们的第一个任务将是在更一般的上下文中表达这些。接下来，我们将我们将把格罗斯-皮塔耶夫斯基平均场理论应用到这个系统中。这个平均场理论抓住了Frohlich模型中没有的非线性。然而，格罗斯-皮塔耶夫斯基，因为它是一个平均场理论，并没有提供一个完整的极化子的量子性质的说明。为了捕捉这种量子效应，并评估其重要性，我们将采用所谓的截断维格纳展开。虽然最近利用超冷气体的实验工作显示出与弱耦合状态下的理论非常一致，但在强耦合状态下存在主要的突出难题。例如，在强耦合状态下的极化子的实验测量质量[例如，参见PRA 85, 023623(2012)]显示出与迄今为止的理论结果有很大的分歧。这个博士项目的一个主要目标就是解决这个难题。

The dynamics of an impurity coupled to a quantum system represents a conceptually simple, yet highly non-trivial physical system. For instance, an electron moving through an ionic lattice will locally distort the lattice (due to Coulomb repulsion). The combined system of the impurity plus the local distortion is conventionally referred to as a polaron. The polaron acts like an isolated particle in many ways, and has a well-defined energy and mass that can differ considerably from that of the isolated impurity.Polarons play essential roles in a variety of Condensed Matter systems including superconductors, Kondo systems, and colossal magnetoresitance materials. Additionally, at the theoretical level, polarons are interesting intheir own right. Ror instance, one of the first non-trivial application of Feynman's path integral focused on computing the mass of a polaron.Despite years of investigation dating back to the early work of Frohlich and Feynmann, many aspects of polarons are still not understood. For this reason, in the past five years, a large amount of experimental work employing gases of ultra-cold atoms focusing on polarons has been carried out. The ultra-cold systems offer a number of distinct advantages over their solid-state material counterparts. In particular, with ultra-cold atoms, clean realisations of minimal models, thought to describe solid-state polarons, can be achieved. Additionally, due to the high degree of tunability (using, for instance, Feshbach resonances) novel regimes of polaron physics can be explored with ultra cold gases.This PhD project will investigate polarons in mixtures of ultra-cold gases. It has recently been shown that when the coupling between the atomic species is weak, the system can be described by the so-called Frohlich Hamiltonian [see, for instance, New Journal of Physics, 19, 103035, 2017]. The Frohlich Hamiltonian is a canonical model in condensed matter physics, which describes the coupling between particles and phonons. It is thestarting point for describing standard superconductors. However, when the coupling between the gases is not weak, the Frohlich model ceases to provide an accurate description of the system.In this project, we will use an alternative starting point - the full microscopic Hamiltonian of the coupled system. Many of the basic relations for polarons (like their mass and energy) are phrased in the context of the Frohlich model. Therefore, our first task will be to phrase these in a more general context. Next, we will we will employ the so-called Gross-Pitaevskii mean-field theory to this system. This mean-field theory captures the non-linearities that are absent in the Frohlich model. However, the Gross-Pitaevskii, as it is a mean-field theory, does not provide a full account of the quantum nature of the polaron. To capture such quantum effects, and to assess their importance, we will employ the so-called truncated Wigner expansion.While recent experimental work utilising ultra-cold gases has shown excellent agreement with theory in the weak-coupling regime, there are major outstanding puzzles in the strong-coupling regime For instance, the experimentally measured mass of the polaron in the strong-coupled regime [see, for instance, PRA 85, 023623 (2012)] shows substantial disagreement with theoretical results to date. A major goal of this PhD project is to solve this puzzle.