Polarons in Ultracold Atomic Gases

耦合到量子系统的杂质的动力学代表了一个概念上简单但高度非平凡的物理系统。例如，电子移动通过离子晶格将局部扭曲晶格（由于库仑排斥）。杂质加上局域畸变的组合系统通常被称为极化子。极化子在许多方面都像孤立粒子一样，具有明确的能量和质量，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发挥着重要作用，包括超导体、近藤系统和巨磁阻材料。此外，在理论水平上，极化子本身也很有趣。Ror实例，费曼路径积分的第一个重要应用之一，集中于计算极化子的质量。尽管可以追溯到Frohlich和Feynmann的早期工作，多年的研究，极化子的许多方面仍然没有被理解。为此，在过去的五年中，已经进行了大量的实验工作，使用超冷原子气体聚焦极化子。超冷系统提供了许多明显的优势，超过其固态材料的同行。特别是，用超冷原子，可以实现被认为是描述固态极化子的最小模型的清晰实现。此外，由于高度的可调谐性（例如，使用Feshbach共振），可以用超冷气体探索极化子物理的新机制。这个博士项目将研究超冷气体混合物中的极化子。最近已经表明，当原子种类之间的耦合较弱时，系统可以由所谓的Frohlich Hamilton描述[参见，例如，New Journal of Physics，19，103035，2017]。Frohlich哈密顿量是凝聚态物理学中的一个正则模型，它描述了粒子和声子之间的耦合。它是描述标准超导体的出发点。然而，当气体之间的耦合并不弱时，Frohlich模型不再提供系统的准确描述。在这个项目中，我们将使用另一个出发点-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）都是在弗罗利希模型的背景下表述的。因此，我们的第一项任务将是在一个更一般的背景下表述这些问题。接下来，我们将把所谓的Gross-Pitaevskii平均场理论应用于这个系统。这种平均场理论捕捉到了弗罗利希模型中不存在的非线性。然而，由于Gross-Pitaevskii是一个平均场理论，它并没有提供极化子量子性质的完整解释。为了捕捉这种量子效应，并评估它们的重要性，我们将采用所谓的截断维格纳展开。虽然最近的实验工作利用超冷气体已经显示出与理论在弱耦合区的良好一致性，但在强耦合区存在主要的突出难题。例如，实验测量的极化子在强耦合区的质量[见，例如，PRA 85，023623（2012）]显示了与迄今为止的理论结果的实质性分歧。这个博士项目的一个主要目标是解决这个难题。

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.