Theory of Degenerate Two-Dimensional Quantum Gases

当我们试图以非常小的尺度(例如，比人类头发的宽度小10,000倍)或超低温(例如，近零下273摄氏度)来理解世界时，经典(牛顿)物理学达到了极限，我们需要对自然的一种非常不同的描述，即量子力学。 在过去的二十年里，对超冷原子的实验为物理学家提供了一个前所未有的机会，以一种非常可控的方式观察奇异的量子物理世界。通常，大约有10,000-10,000个原子的气体(每个原子都非常小)被冷却到超低温，并被困在一个 空间的局部区域。然后，原子可能会受到额外的空间限制(从而降低系统的维度)，以及调整原子相互作用的方式的可能性。这相当于在实验室里创造了一个量身定做的量子系统，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来描述，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、相互激励的动力；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。 对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，即所谓的“自旋”。自旋是一种内部自由度(即与原子的空间性质无关)，没有牛顿类似物。自旋导致原子被归类为费米子或玻色子。费米子是非常反社会的，这意味着它们不喜欢合作行为。另一方面，玻色子更喜欢协调一致的行为。熟悉的激光是一个很好的例子，其中玻色子(在这种情况下是光子)的集体性质导致了相干光束，这对于费米子来说是无法实现的，因为他们不合作的行为。 我的项目是通过对低维超冷原子气体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与其三维(3D)气体具有非常不同的性质。被称为玻色-爱因斯坦凝聚(BEC)的现象是一个典型的例子，表明维度对量子气体的集体性质有深刻的影响。具体地说，均匀的3D玻色子气体可以具有BEC(其中所有原子可以有效地描述为单个物体的一种新的物质状态)，而均匀的1D玻色气体不允许具有BEC。此外，许多用于处理3D系统的理论工具不适用于较低的维度，因此需要对系统的维度不敏感的多体问题的新公式。 量子计算、超导和二维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，对电子设备变得越来越小的需求(即，携带电流的电子必须以非常小的、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，并有助于刺激未来的实验和理论研究。

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.