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.

关于我们的世界，我们知道哪些基本事实？首先，人类很长一段时间都相信空间是平的。一个很好的近似值是：如果你画一个三角形，那么内角之和是180度。后来我们发现，地球实际上是弯曲的。如果你在地球表面画一个非常大的三角形，它的内角之和将大于180度。数学家称之为正曲率。他们还意识到，存在一种更有趣的几何形状，这种几何形状被称为负弯曲，三角形的内角之和可以小于180度，甚至为零！这个空间被称为双曲空间，它有许多无法用我们的直觉来理解的特征，但数学家们喜欢它，因为它的美丽，物理学家们在过去的几十年里意识到，我们物理世界的许多性质可能秘密地与双曲空间有关。另一个这样的真理，虽然你可能不经常想到它，是电子的存在---那些亚原子带电粒子，负责固体中的电子电流，并填充原子的电子壳层。电子有一个内在的属性，称为它们的自旋量子数，它有两个值，通常称为“上”或“下”，或“+1/2”和“-1/2”。（由于后者，我们说电子的自旋为1/2。）电流和我们周围的所有化学元素的性质都是由于电子可以以这两种状态出现。物理学家长期以来一直在寻找自旋为3/2的类电子粒子，这种粒子有四种状态，称为“+3/2”，“+1/2”，“-1/2”和“-3/2”，但没有发现具有这种性质的基本粒子。本研究项目将研究如果世界是负弯曲的，或者如果电子自旋为3/2，会发生什么。当然，我们这样做是为了满足我们的好奇心，但这样的分析结果也会影响我们对基本物理定律的理解，并可能有技术应用。在过去的几年里，有两个实验性的突破激发了这个项目。一个是实现一个双曲晶格超导谐振器，这是一个七边形平铺，只存在于负弯曲的空间。在这样的晶格上运动的粒子认为它们是在双曲空间中。另一个是拓扑半金属材料的合成，其中携带电荷的粒子像自旋为3/2的电子一样。这两种设置都被称为“量子模拟”，因为它们创建了一个人工世界，以便通过实验研究其属性。具体来说，我们将分析双曲空间如何改变许多粒子的物理特性，并从理论上帮助创建两个实验平台进行研究：电路和超冷量子气体。我们将研究自旋为3/2的粒子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。