Controlled Creation and Dynamics of non-Abelian Vortices and Topological Processes in spinor Bose-Einstein condensates

在日常生活中，液体中的漩涡是很熟悉的，当我们搅拌一杯茶或排干浴缸的水时，就会出现漩涡。在没有黏性的超流体中，涡旋具有量子力学的特性，其行为与我们所熟悉的非常不同。也许矛盾的是，结果是，涡旋的基本特性对超流体中粒子如何相互作用的细节变得相对不敏感。相反，漩涡的基本特征是通过使用拓扑从物理状态的内部对称性中一般理解的，拓扑是研究物体在扭曲或扭曲时保持不变的数学领域。因此，由拓扑学产生的现象在看似不同的物理学领域中往往是普遍存在的，并引起了相当大的关注，2016年诺贝尔奖就是一个突出的例子。本文将应用理论方法研究自旋玻色-爱因斯坦凝聚体（BECs）中的特定涡旋。这是一种物质的超流体状态，出现在某些原子气体中，它被冷却到接近绝对零度，使用的技术不会冻结原子的量子力学自旋。自旋是整数值。我们对自旋等于2的原子感兴趣，因为这时出现的涡流可能是非阿贝尔的。旋涡是由所谓的拓扑电荷分类的。一个电荷可以加到另一个电荷上，但这种加法并不总是遵循我们所熟悉的算术规则。对于非阿贝尔涡旋，顺序很重要：A + B与B + A不一样。这导致了高度反直觉的涡旋相互作用，例如，如果两个涡旋碰撞，它们必须形成一个新的涡旋，即使它们分开，也要继续连接它们。这不仅仅是一种好奇心：用同样的数学方法描述的类似物体，也可以出现在液晶或宇宙学理论中。因此，实验的中心目标是在高度可接近的旋量bec中可控地创造非阿贝尔漩涡也就不足为奇了，这些旋量bec可以作为具有更广泛重要性的物理模拟器。我们项目的中心任务是为这一努力提供理论基础。有几种技术可以控制涡流的产生。然而，这些不能直接用于创建显示非阿贝尔属性的漩涡。我们将提出创建这样的涡旋和涡旋群的具体方案。我们还将使用计算机模拟，确定这些漩涡在允许它们进化后的样子。然后，我们可以提供解释实验所需的可观察到的特征。为了使这项工作取得成功，这项工作将与美国马萨诸塞州阿默斯特学院的实验项目合作伙伴密切联系。我们将通过模拟拓扑缺陷（如漩涡）决定物理的动态场景来推动计算极限。例如，同一个旋量BEC的两个不同相之间的界面类似于超流体氦-3中的类似边界。我们将确定当界面碰撞时产生什么样的涡流。重要的是，这代表了与早期宇宙理论中提出的过程类似的实验室规模模拟。非阿贝尔缺陷起什么作用？关于这些过程，spinor bec一般能告诉我们什么？当超流体通过相变，从一种状态到另一种状态（一个熟悉的例子是水冻结成冰）时，也会产生缺陷。这些过程在其他量子系统和宇宙学中也非常重要。我们将试图确定在相变中是否产生了非阿贝尔涡，如果有，这对只有阿贝尔涡的系统的相变意味着什么差异。我们再次被在实验室中模拟宇宙现象的有趣前景所激励。

Vortices in fluids are familiar from everyday life, appearing when we stir a cup of tea or drain a bath tub. In superfluids, which flow without viscosity, vortices take on properties arising from the underlying quantum mechanics and behave very differently from what we are used to. Perhaps paradoxically, the consequence is that the fundamental properties of the vortices become relatively insensitive to details of how the particles in the superfluid interact. Instead, the essential features of vortices are understood generically from internal symmetries of the physical state using topology, the field of mathematics that studies what remains unchanged about an object as it is twisted or distorted. Phenomena arising from topology are therefore often universal across seemingly disparate parts of physics and have attracted considerable attention, highlighted by the 2016 Nobel Prize.Here we will apply theoretical methods to study particular vortices in spinor Bose-Einstein condensates (BECs). This is a superfluid state of matter that appears in certain atomic gases cooled to near absolute zero using techniques that do not freeze out the atoms' quantum-mechanical spin. The spin comes at integer values. We are interested in atoms where the spin is equal to 2, for the reason that the vortices that then appear can be what is called non-Abelian. Vortices are categorised by so-called topological charges. One charge can be added to another, but this addition does not always follow the familiar rules of arithmetics. For non-Abelian vortices, the order matters: A + B is not the same as B + A. This leads to highly counter-intuitive vortex interactions, such that if two vortices collide, they must form a new vortex that continues to connect them even as they move apart. This is not a mere curiosity: analogous objects, described by the same mathematics, can appear also in liquid crystals or in cosmological theories. It is no surprise then that a central goal for experiments is the controlled creation of non-Abelian vortices in the highly accessible spinor BECs, which could act as emulators of physics of much wider importance.The central task of our project is to provide the theoretical underpinnings for this effort. Several techniques exist for controlled creation of vortices in BECs. However, these cannot be used directly to create vortices that show the non-Abelian properties. We will propose specific protocols for the creation of such vortices and vortex ensembles. We will also, using computer simulations, determine what these vortices look like once they have been allowed to evolve. We can then provide the observable signatures necessary for interpreting the experiments. For this effort to succeed, the work will be done in close contact with experimental project partners at Amherst College, Massachusetts, USA.We will push the computational limits by simulating dynamical scenarios where topological defects such as vortices determine the physics. For example, the interface between two distinct phases of the same spinor BEC is analogous to similar boundaries in superfluid helium-3. We will determine what vortices are produced when interfaces collide. Importantly, this represents a laboratory scale simulation of processes analogous to those proposed in theories of the early universe. What role do non-Abelian defects play? What can spinor BECs teach us about such processes in general? Defects are also produced when superfluids pass through phase transitions, from one state to another (a familiar example is the freezing of water into ice). Such processes are enormously important also in other quantum systems as well as in cosmology. We will seek to determine whether non-Abelian vortices are produced in the phase transition and, if so, what differences that implies to phase transitions in systems with only Abelian vortices. Again we are motivated by the intriguing prospect of simulating cosmological phenomena in the laboratory.