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.

当我们试图以很小的长度（例如，比人头发的宽度小10,000倍）或超冷的温度（例如，近273度低于零摄氏摄氏度）时，古典（牛顿）物理学达到了极限时，我们需要对自然的描述，称为量子力学。在过去的二十年中，对超冷原子的实验使物理学家有一个前所未有的机会，可以以非常受控的方式观察量子物理的怪异世界。通常，将约10,000-100,000个原子的气体冷却至超冷的温度，并将其捕获在局部空间区域中。然后，原子可以暴露于其他空间限制（从而降低系统的维度），并可能调整原子相互作用的方式。这相当于在实验室中创建的，这是一种量身定制的量子系统，供物理学家学习。这样的系统称为量子多体系统，因为它们必须用量子力学描述，并且由许多颗粒组成。冷原子系统本质上很有趣，因为它们允许在理论和实验之间具有共生，相互启发的动态。也就是说，实验有助于验证理论，理论为其他实验提供了动力。物质的量子机械描述要求我们向每个原子（称为“旋转”）引入另一种特性。自旋是内部自由度（即，与原子的空间特性无关），没有牛顿类似物。旋转导致原子被归类为费米子或玻色子。费米子是反社会的，这意味着他们不喜欢合作。另一方面，玻色子更喜欢一致行事。熟悉的激光是一个很好的例子，说明了玻色子的集体特性（在这种情况下为光子）导致一连串的光束，这是由于其不合作行为而无法实现的。我的项目是通过对低维超质量超高质量的物理特性进行的量子多体性问题进行调查。费米或玻色子的低维气体可能与三维（3D）对应物具有截然不同的特性。这种现象称为Bose-Einstein凝结（BEC）是一个典型的例子，表明维度对量子气的集体特性具有深远的影响。特别是，玻色子的均匀3D气体可能具有BEC（一个新的物质状态，可以有效地将所有原子描述为单个物体），而均匀的1D玻色气则不允许具有BEC。此外，许多用于解决3D系统的理论工具不适用于较低的尺寸，因此需要对系统的尺寸不敏感的多体问题的新表述。量子计算范式的范式进行了超导性，超导性的范例，并依赖于某些特殊量化的量子的量子，并依赖于某些质量量的特殊性量化量的物理学。此外，对电子设备的需求越来越小（即，当前的携带电子必须以很小的，受限的几何形状移动）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，我在低维量子系统中的理论研究将对新技术，新行业的发展产生影响，并有助于刺激未来的实验和理论研究。