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

旋量玻色-爱因斯坦凝聚中非阿贝尔涡旋和拓扑过程的受控产生和动力学

基本信息

批准号：
EP/V03832X/1
负责人：
Magnus Borgh
金额：
$ 48.26万
依托单位：
University of East Anglia
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2021
资助国家：
英国
起止时间：
2021 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FV03832X%2F1
关键词：
Controlled Creation Dynamics non Abelian

项目摘要

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.

流体中的漩涡在日常生活中很常见，当我们搅拌一杯茶或放干浴缸时就会出现。在没有粘性的超流体中，涡旋呈现出由量子力学产生的性质，并且表现出与我们所习惯的非常不同的行为。也许自相矛盾的是，结果是涡旋的基本性质变得对超流体中粒子如何相互作用的细节相对不敏感。相反，旋涡的基本特征一般是从使用拓扑学的物理状态的内部对称性来理解的，拓扑学是研究物体在扭曲或变形时保持不变的数学领域。因此，拓扑学所产生的现象在物理学的各个领域都是普遍存在的，并引起了人们的广泛关注，2016年诺贝尔物理学奖就是其中之一。在这里，我们将运用理论方法研究旋量玻色-爱因斯坦凝聚体（BEC）中的特殊涡旋。这是一种超流体状态的物质，出现在某些原子气体中，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，因为这样出现的涡旋可能是所谓的非阿贝尔涡旋。涡旋是按照所谓的拓扑荷来分类的。一种电荷可以加到另一种电荷上，但这种加法并不总是遵循熟悉的算术规则。对于非阿贝尔涡旋，顺序很重要：A + B与B + A不同。这导致了高度违反直觉的漩涡相互作用，例如，如果两个漩涡碰撞，它们必须形成一个新的漩涡，即使它们分开，也会继续连接它们。这不仅仅是一种好奇心：用同样的数学描述的类似物体也可以出现在液晶或宇宙学理论中。因此，实验的一个中心目标是在高度可及的旋量BEC中受控地产生非阿贝尔涡旋，这也就不足为奇了，它可以作为更广泛重要的物理学的仿真器。存在用于在BEC中受控地产生涡流的若干技术。然而，这些不能直接用于创建显示非阿贝尔属性的旋涡。我们将提出具体的协议，创造这样的旋涡和旋涡合奏。我们还将使用计算机模拟，确定这些漩涡一旦被允许进化后的样子。然后，我们可以提供解释实验所需的可观察特征。为了使这项工作取得成功，我们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合作。我们将通过模拟拓扑缺陷（如涡流）决定物理特性的动态场景来推动计算极限。例如，同一旋量BEC的两个不同相之间的界面类似于超流氦-3中的类似边界。我们将确定当界面碰撞时会产生什么样的旋涡。重要的是，这代表了实验室规模的模拟过程，类似于早期宇宙理论中提出的过程。非阿贝尔缺陷起什么作用？旋量玻色-爱因斯坦凝聚能告诉我们关于这些过程的什么？当超流体从一种状态到另一种状态经历相变时，也会产生缺陷（一个熟悉的例子是水冻结成冰）。这样的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非阿贝尔涡旋，如果是的话，这意味着只有阿贝尔涡旋的系统中的相变有什么不同。在实验室里模拟宇宙学现象的诱人前景再次激励了我们。