CAREER: Solitons in Bose-Einstein Condensates: Generation, Manipulation and Pattern Formation

职业：玻色-爱因斯坦凝聚中的孤子：生成、操纵和模式形成

• 批准号: 0349023
• 负责人: Panayotis Kevrekidis
• 金额: $ 40.08万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0349023&HistoricalAwards=false
• 关键词: CAREER; Solitons; Bose; Einstein; Condensates

Abstract: CAREER Award DMS-0349023Panayotis Kevrekidis, University of Massachusetts at AmherstTitle: CAREER: Solitons in Bose-Einstein Condensates: Generation, Manipulation and Pattern FormationThe aim of this project is to examine the behavior of solitary wavestructures in the setting of atomic physics (Bose-Einstein Condensates). Solitons as per their structural robustness and quasi-elastic interactions are natural building blocks that have been used for information transmission in optical settings in the past and could naturally be extended as information carriers in this new matter wave setup. Furthermore, these structures can be appropriately manipulated, waveguided or used to construct various patterns at this microscopic (atomic) level. The study will be undertaken at three different levels: (1) The level of creating these solitary waves by taking advantage of instabilities and/or experimentally available mechanisms (such as the Feshbach resonance); (2) The one of manipulating the waves (either dragging them by means of an optical tweezers or waveguiding them through junctions); (3) And, finally, at the level of combining them to create patterns and to identify their steady states and structural transitions. These steps will be carried through for the two principal types of interactions: a) For attractive interactions between the atoms (e.g., for focusing nonlinearities and negative scattering lengths as in the case of lithium); b) For repulsive interactions (e.g., for defocusing nonlinearities and positive scattering lengths as in the case of rubidium and sodium). The models that will be examined will be both continuum models of partial differential equations with external potentials (linear or quadratic, or combination thereof), as well as quasi-discrete ones (relevant for periodic external potentialsas in the case of the so-called optical lattice). The techniques that will be used will involve regular and singular perturbationmethods, linear and modulational stability analysis, regular and possibly exponential asymptotics, numerical bifurcation theory as well as direct numerical simulations and also molecular dynamics techniques (to study patterns and their structural transitions). The main focus of this research project is a detailed study of solitary waves generated in the very controllable, ultra-low temperature, atomic physics context of Bose-Einstein condensates (BECs). Since their recent experimental realization (for which the 2001 Physics Nobel prize was awarded), BECs have been the center of an intensive and ever growing experimental and theoretical effort in the Mathematics and Physics communities. The examination of BECs has also strong ties with a deeper understanding of the exciting and important fields of superconductivity and superfluidity (which were the theme of the Physics Nobel prize in 2003). From a Mathematical Physics perspective, one of the most interesting and appealing aspects of studying BECs is their rich nonlinear wave phenomenology, the wide variety of possible settings (one to three dimensions) and the detailed experimental control that permits a precise engineering/manipulation of the external conditions under which these waves dynamically evolve.The main purpose of this research effort is to extend and deepen our understanding of the fundamental structures and waves and their roleand importance in BECs, but also more generally (due to the similarmathematical description) in nonlinear optics (optical fibers andwaveguides) as well as wave physics. As an aside, it should be noted that this effort will heavily rely on computational resources and the concomitant use of numerical codes that model these phenomena; it should also be remarked that one of the longer term perspectives of this activity on matter waves is to conceive and construct novel devices that would guide and more generally control the motion of the matter waves and could potentially be used for quantum information processing at the nanoscale. These aspects lead us to expect that significant benefits may result from the implementation of this project in areas of strategic federal interest such as high performance computing and materials and manufacturing.

摘要：Amhersttitle的马萨诸塞州大学的职业奖DMS-0349023Panayotis Kevrekidis：职业：Bose-Einstein的孤子凝结：solitons condense：生成，操纵和模式形成该项目的目的是检查该项目的行为，以检查在原子质物理学（besemic condensecte）的行为。根据孤子的结构鲁棒性和准弹性相互作用是自然的构建块，过去曾在光学设置中用于信息传输，并且自然可以在此新物质波浪设置中作为信息载体扩展。此外，这些结构可以在此显微镜（原子）水平上进行适当操纵，波导或用于构造各种模式。该研究将以三个不同的水平进行：（1）通过利用不稳定性和/或实验可用的机制（例如Feshbach共振）来创建这些孤立波的水平； （2）操纵波动的之一（通过光学镊子拖动它们，或者通过交界处将它们拖动）； （3）最后，在结合它们以创建模式并确定其稳态和结构过渡的水平上。这些步骤将用于两种主要类型的相互作用类型：a）对于原子之间的有吸引力的相互作用（例如，将非线性和负散射长度集中到锂中）； b）用于排斥相互作用（例如，用于脱落非线性和正散射长度，如Rubidium和Sodium）。将要检查的模型既是具有外部电势（线性或二次或其组合）的部分微分方程的连续模型，也将是准分子 - 二氧化转化的模型（在所谓的光学lattice的情况下，与周期性外部电势相关）。将使用的技术将涉及规则和奇异的扰动方法，线性和调节稳定性分析，规则和可能的指数渐近学，数值分叉理论以及直接的数值模拟以及分子动力学技术（用于研究模式及其结构过渡）。该研究项目的主要重点是一项详细的研究，对玻色 - 因斯坦冷凝物（BEC）的非常可控制的超低温度，原子理环境产生的孤立波。自从他们最近的实验性实现（2001年诺贝尔奖获得了奖项）以来，BEC一直是数学和物理社区中越来越多的实验和理论努力的中心。对BEC的研究还具有牢固的联系，对超导性和超流量的令人兴奋和重要的领域有了更深入的了解（这是2003年诺贝尔奖的主题）。从数学物理学的角度来看，研究BEC的最有趣和最吸引人的方面之一是它们丰富的非线性波浪现象学，各种各样的环境（一到三个维度）（一到三个维度）以及详细的实验控制，允许精确的工程/操纵对外部条件的动态性和深度的理解。在BEC中的重要性，但在非线性光学器件（光纤和波导）以及波理物理学中更普遍（由于相似的描述）。顺便说一句，应该指出的是，这项工作将在很大程度上依赖计算资源以及对这些现象建模的数值代码的伴随使用；还应该指出的是，这种活动对物质波的长期观点之一是设想和构建新型设备，这些设备将指导并更普遍地控制物质波的运动，并有可能用于纳米级的量子信息处理。这些方面使我们期望在战略联邦利益领域（例如高性能计算，材料和制造业）中实施该项目可能会带来重大收益。