Solid State Quantum Simulation: From Hyperbolic Space to Emergent Spin-3/2 Fermions

固态量子模拟：从双曲空间到涌现自旋 3/2 费米子

• 批准号: RGPIN-2021-02534
• 负责人: Boettcher, Igor
• 金额: $ 2.4万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762415
• 关键词: Solid; State; Quantum; Simulation; Hyperbolic

What are the basic truths we know about our world? For one, humankind believed for a long time that space is flat. And to a good approximation, it is: If you draw a triangle, the sum of the interior angles is 180 degrees. Later we discovered that our Earth is actually curved. If you were to draw a very large triangle on Earth's surface, its sum of interior angles would be larger than 180 degrees. Mathematicians call this a positive curvature. They also realized that a much more intriguing geometry exists, one that is called negatively curved, where the sum of interior angles in a triangle can be less than 180 degrees, even zero! This space, called hyperbolic space, has many features that evade our intuition, but Mathematicians love it because of its beauty, and Physicists realized over the last decades that many properties of our physical world may secretly be related to hyperbolic space. Another such truth, although you might not think about it often, is the existence of electrons --- those subatomic charged particles that are responsible for electronic current in solids and that populate the electronic shell of atoms. Electrons have an intrinsic property, called their spin quantum number, which takes two values, commonly called "up" or "down", or "+1/2" and "-1/2". (Because of the latter, we say that the electron has spin 1/2.) The properties of electrical currents and all chemical elements around us result from the fact that the electron can appear in these two states. Physicists have long searched for electron-like particles with spin 3/2, which have four states, called "+3/2", "+1/2", "-1/2", and "-3/2", but no fundamental particle with this property was found. This research project will investigate what would happen if the world would be negatively curved or if electrons had spin 3/2. We do this to satisfy our curiosity, of course, but the outcome of such an analysis will also affect our understanding of the fundamental Laws of Physics and could have technological applications. The last few years have seen two experimental breakthroughs that motivate this project. One is the realization of a hyperbolic lattice with superconducting resonators, which is a heptagonal tiling that only exists in negatively curved space. Particles moving on such a lattice think they are in hyperbolic space. The other is the synthesization of topological semimetal materials, where the charge carrying particles act like electrons with spin 3/2. Both settings are called "quantum simulations", because they create an artifical world in order to experimentally study its properties. Specifically, we will analyse how the physics of many particles is altered by hyperbolic space and we will theoretically help to create two more experimental platforms for their investigation: electrical circuits and ultracold quantum gases. We will investigate how the interactions between spin-3/2 particles alter the properties of solids and how this can be measured in experiment.

我们对世界的基本真理是什么？首先，人类长期以来一直认为空间是平坦的。并且是一个良好的近似值，这是：如果绘制三角形，则内部角度的总和为180度。后来我们发现我们的地球实际上是弯曲的。如果您要在地球表面绘制一个非常大的三角形，则其内部角度总和将大于180度。数学家称其为积极的曲率。他们还意识到存在一个更有趣的几何形状，即呈负弯曲的几何形状，其中三角形中的内角之和可能小于180度，甚至零！这个称为双曲线空间的空间具有许多逃避我们直觉的特征，但是数学家由于其美丽而喜欢它，并且物理学家在过去几十年中意识到，我们物理世界的许多特性可能与双曲线空间有关。另一个这样的事实，尽管您可能不经常考虑，但存在电子的存在 - 那些负责固体中电子电流并填充原子电子壳的亚原子带电颗粒。电子具有固有属性，称为其自旋量子数，该量子数量通常称为“向上”或“向下”或“ +1/2”和“ -1/2”。 （由于后者，我们说电子具有旋转1/2。）电流的特性和我们周围的所有化学元素是由于电子可以出现在这两个状态中的事实而造成的。物理学家长期以来一直在搜索具有自旋3/2的电子样颗粒，这些颗粒具有四个状态，称为“ +3/2”，“ +1/2”，“ -1/2”和“ -3/2”，但没有发现具有该特性的基本粒子。该研究项目将调查如果世界将是负弯曲或电子3/2旋转的情况，将会发生什么。当然，我们这样做是为了满足我们的好奇心，但是这种分析的结果也会影响我们对物理基本定律的理解，并可能具有技术应用。在过去的几年中，有两个实验性突破激发了该项目。一种是实现具有超导谐振器的双曲线晶格，这是一个仅存在于负弯曲的空间中的七型瓷砖。在这样的晶格上移动的颗粒认为它们在双曲线空间中。另一个是拓扑半学材料的合成，其中携带颗粒的电荷像带有3/2的电子一样。这两种设置都称为“量子模拟”，因为它们创建了一个人工世界，以实验研究其特性。具体而言，我们将分析多双曲空间的许多颗粒的物理学如何改变，理论上将帮助创建两个实验平台以进行研究：电路和超低量子气体。我们将研究Spin-3/2颗粒之间的相互作用如何改变固体的性质以及如何在实验中测量它。