Polarons in Ultracold Atomic Gases

杂质耦合到量子系统的动力学代表了一个概念上简单但非常不平凡的物理系统。例如，一个穿过离子晶格的电子会使晶格局部扭曲(由于库仑排斥)。杂质加上局域失真的组合系统通常被称为极化子。极化子在许多方面就像一个孤立的粒子，具有明确的能量和质量，可能与孤立杂质的能量和质量有很大的不同。极化子在各种凝聚态系统中扮演着重要的角色，包括超导体、近藤系统和巨磁电阻材料。此外，在理论层面上，极化子本身也很有趣。例如，费曼路径积分的第一个非平凡应用之一，专注于计算极化子的质量。尽管多年的研究可以追溯到Frohlich和Feynmann的早期工作，但极化子的许多方面仍然不被理解。为此，在过去的五年中，利用聚焦于极化子的超冷原子气体进行了大量的实验工作。与固态材料相比，超冷系统提供了许多明显的优势。特别是，利用超冷原子，可以干净地实现最小模型，这种模型被认为是描述固态极化子的。此外，由于极化子的高度可调谐性(例如，使用费什巴赫共振)，可以用超冷气体探索新的极化子物理区域。这个博士项目将研究超冷气体混合物中的极化子。最近已经证明，当原子物种之间的耦合很弱时，该系统可以用所谓的弗洛利希哈密顿量来描述[例如，见《新物理学杂志》，19,103035,2017年]。Frohlich哈密顿量是凝聚态物理中的一个正则模型，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模型不能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-耦合系统的全微观哈密顿量。极化子的许多基本关系(如它们的质量和能量)都是在Frohlich模型的背景下表述的。因此，我们的首要任务将是在更广泛的背景下表述这些问题。接下来，我们将我们将所谓的格罗斯-皮塔夫斯基平均场理论应用到这个系统中。这一平均场理论捕捉到了Frohlich模型中所没有的非线性。然而，由于格罗斯-皮塔夫斯基是平均场理论，它并不能完全解释极化子的量子性质。为了捕捉这种量子效应，并评估它们的重要性，我们将使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在弱耦合区域与理论显示出很好的一致性，但在强耦合区域有一些主要的悬而未决的难题，例如，在强耦合区域实验测量的极化子的质量[参见，例如，PRA85,023623(2012年)]表明到目前为止与理论结果有很大的不同。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.