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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=566011
• 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.

当我们试图在非常小的尺度上理解世界时（例如，比人类头发宽度小10，000倍）或超低温（例如，当温度接近零下273摄氏度时，经典（牛顿）物理学达到了极限，我们需要一种非常不同的自然描述，即量子力学。在过去的20年里，超冷原子实验为物理学家提供了前所未有的机会，以一种非常可控的方式观察量子物理学的奇异世界。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，原子可以暴露于附加的空间限制（从而降低系统的维度），沿着有可能调整原子彼此相互作用的方式。这相当于在实验室里创造了一个量身定制的量子系统供物理学家研究。这样的系统被称为量子多体系统，因为它们必须由量子力学描述，并且由许多粒子组成。冷原子系统本质上是有趣的，因为它们允许理论和实验之间的共生，相互激励的动态;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种属性，称为“自旋”。自旋是内部自由度（即，与原子的空间性质无关），没有牛顿的类似物。自旋导致原子被归类为费米子或玻色子。费米子是反社会的，这意味着它们不喜欢合作。另一方面，玻色子更倾向于一致行动。我们熟悉的激光器是一个很好的例子，说明玻色子（在这种情况下，光子）的集体性质导致相干光束，这对于费米子来说是不可能实现的，因为它们的不合作行为。我的项目是通过对低维超冷原子气体的物理性质的理论研究来研究量子多体问题。费米子或玻色子的低维气体可能具有与它们的三维（3D）对应物非常不同的性质。被称为玻色-爱因斯坦凝聚（BEC）的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玻色气体可能具有BEC（一种新的物质状态，其中所有原子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的维度，从而需要新的配方的多体问题，这是不敏感的系统的维数。量子计算、超导和2D石墨烯物理的许多范例都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，携带电流的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的深入理解。因此，我对低维量子系统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。