Theory of Degenerate Two-Dimensional Quantum Gases

简并二维量子气体理论

• 批准号: RGPIN-2014-03662
• 负责人: vanZyl, Brandon
• 金额: $ 1.82万
• 依托单位: St. Francis Xavier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633346
• 关键词: Theory; Degenerate; Two; Dimensional; Quantum

When we try to understand the world at very small length scales (e.g., 10,000 times smaller than the width of a human hair) or ultra-cold temperatures (e.g., nearly 273 degrees below zero Celsius), classical (Newtonian) physics reaches its limits, and we require a very different description of nature, known as quantum mechanics. Over the last two decades, experiments on ultra-cold atoms have allowed physicists an unprecedented opportunity to observe the bizarre world of quantum physics in a very controlled fashion. Typically, a gas of about 10,000-100,000 atoms (each atom is very small indeed) is cooled to ultra-cold temperatures, and trapped in a localized region of space. The atoms may then be exposed to additional spatial confinement (thereby lowering the dimensionality of the system), along with the possibility of tuning the way in which the atoms interact with each other. This amounts to having created in the laboratory, a tailor-made quantum system for physicists to study. Such systems are called quantum many-body systems, since they must be described by quantum mechanics, and consist of many particles. Cold atomic systems are inherently interesting, because they allow for a symbiotic, mutually inspiring dynamic between theory and experiment; that is, experiments help to verify theory, and theory provides the impetus for additional experiments.A quantum mechanical description of matter requires that we introduce another property to each atom, known as "spin". Spin is an internal degree of freedom (i.e., has nothing to do with the spatial properties of the atom) with no Newtonian analogue. The spin results in the atoms being classified as either fermions or bosons. Fermions are rather anti-social, meaning that they do not like to behave cooperatively. Bosons, on the other hand, prefer to behave in unison. The familiar laser is an excellent example of where the collective properties of bosons (in this case, photons) result in a coherent beam of light, which is not realizable for fermions owing to their uncooperative behaviour.My project is to investigate the quantum many-body problem through a theoretical investigation of the physical properties of low-dimensional ultra-cold atomic gases. Low-dimensional gases of fermions or bosons may have very different properties from their three-dimensional (3D) counterparts. The phenomenon known as Bose-Einstein condensation (BEC) is an archetypical example of where dimensionality has a profound influence on the collective properties of the quantum gas. In particular, a uniform 3D gas of bosons may have a BEC (a new state of matter in which all of the atoms may be described effectively as a single object), whereas a uniform 1D Bose gas is not permitted to have a BEC. Moreover, many of the theoretical tools used to address 3D systems are not applicable to lower dimensions, thereby requiring new formulations of the many-body problem which are not sensitive to the dimensionality of the system.Many of the paradigms for quantum computation, superconductivity and the physics of 2D sheets of graphene, rely on some of the special properties of low-dimensional quantum systems. In addition, the demand for electronic devices to be made smaller and smaller (i.e., the current carrying electrons must move in very small, restricted geometries) implies that new designs need to be considered, which necessitates a deep understanding of low-dimensional quantum systems. Therefore, my theoretical research in low-dimensional quantum systems will have an impact on the development of new technologies, new industries, and help stimulate future experimental and theoretical studies.

当我们试图以非常小的长度尺度（例如，比人类头发宽度小 10,000 倍）或超冷温度（例如，零摄氏度以下近 273 度）来理解世界时，经典（牛顿）物理学就达到了极限，我们需要一种非常不同的自然描述，称为量子力学。在过去的二十年中，超冷原子实验为物理学家提供了前所未有的机会，以一种非常受控的方式观察量子物理的奇异世界。通常，大约 10,000-100,000 个原子（每个原子实际上非常小）的气体被冷却到超冷温度，并被困在空间的局部区域中。然后，原子可能会受到额外的空间限制（从而降低系统的维数），并有可能调整原子彼此相互作用的方式。这相当于在实验室中创建了一个专门为物理学家研究的量子系统。这样的系统被称为量子多体系统，因为它们必须用量子力学来描述，并且由许多粒子组成。冷原子系统本质上很有趣，因为它们允许理论和实验之间存在共生、相互启发的动态；也就是说，实验有助于验证理论，理论为额外的实验提供动力。物质的量子力学描述要求我们为每个原子引入另一个属性，称为“自旋”。自旋是一种内部自由度（即与原子的空间特性无关），没有牛顿的类似物。自旋导致原子被分类为费米子或玻色子。费米子相当反社会，这意味着它们不喜欢合作。另一方面，玻色子更喜欢表现一致。熟悉的激光是一个很好的例子，说明玻色子（在本例中为光子）的集体特性产生相干光束，但由于费米子的不合作行为，这是无法实现的。我的项目是研究量子多-通过对低维超冷原子气体的物理性质的理论研究来解决身体问题。费米子或玻色子的低维气体可能与三维 (3D) 气体具有非常不同的特性。玻色-爱因斯坦凝聚（BEC）现象是维度对量子气体的集体性质产生深远影响的典型例子。特别是，均匀的 3D 玻色子气体可能具有 BEC（一种新的物质状态，其中所有原子都可以有效地描述为单个物体），而均匀的 1D 玻色气体不允许具有 BEC。此外，许多用于解决 3D 系统的理论工具不适用于较低维度，因此需要对系统维度不敏感的多体问题的新表述。量子计算、超导和量子计算的许多范式二维石墨烯片的物理学依赖于低维量子系统的一些特殊性质。此外，对电子设备越来越小的需求（即载流电子必须在非常小的、受限的几何形状中移动）意味着需要考虑新的设计，这需要对低维量子系统有深入的了解。因此，我在低维量子系统方面的理论研究将对新技术、新产业的发展产生影响，并有助于激发未来的实验和理论研究。