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：职业生涯奖DMS-0349023帕纳约蒂斯·凯夫瑞基迪斯，马萨诸塞大学阿默斯特分校题目：职业：玻色-爱因斯坦凝聚体中的孤子：产生、操纵和图案形成本项目的目的是研究原子物理(玻色-爱因斯坦凝聚体)中孤立波结构的行为。由于孤子的结构健壮性和准弹性相互作用，孤子是过去在光学环境中用于信息传输的天然构件，在这种新的物质波体系中自然可以扩展为信息载体。此外，这些结构可以被适当地操纵、导波或用于在这种微观(原子)水平上构建各种图案。这项研究将在三个不同的层面上进行：(1)利用不稳定性和/或实验上可用的机制(如Feshbach共振)来创造这些孤立波的层面；(2)操纵波的层面(要么用光镊子拖拽它们，要么通过结点将它们导波)；(3)最后，在组合它们以创建图案并识别它们的稳定状态和结构转变的层面上。这些步骤将针对两种主要类型的相互作用进行：a)对于原子之间的吸引相互作用(例如，对于聚焦非线性和负散射长度，例如在锂的情况下)；b)对于排斥相互作用(例如，对于离焦非线性和正散射长度，例如对于Rb和Na的情况)。将研究的模型将是具有外部势(线性或二次，或其组合)的偏微分方程组的连续模型，以及准离散模型(与周期性外部势有关，例如在所谓的光学晶格的情况下)。将使用的技术将涉及规则和奇异微扰方法、线性和调制稳定性分析、规则和可能的指数渐近、数值分叉理论以及直接的数值模拟，以及分子动力学技术(用于研究图案及其结构转变)。这个研究项目的主要焦点是详细研究在非常可控的、超低温的原子物理背景下产生的玻色-爱因斯坦凝聚体(BEC)中的孤立波。自从它们最近的实验实现(2001年诺贝尔物理学奖获得者)以来，BEC一直是数学和物理界密集且不断增长的实验和理论工作的中心。对BEC的研究也与对超导和超流(这是2003年诺贝尔物理学奖的主题)这两个令人兴奋和重要的领域有更深的理解有很大的联系。从数学物理的角度来看，研究BEC最有趣和最吸引人的方面是它们丰富的非线性波现象学、广泛的可能设置(一维到三维)和详细的实验控制，允许对这些波动态演化的外部条件进行精确的工程/操作。这项研究的主要目的是扩展和加深我们对BEC的基本结构和波及其在BEC中的作用和重要性的理解，以及在非线性光学(光纤和光波导)和波物理中更一般的(由于相似的数学描述)。另外，应该指出的是，这一努力将严重依赖于计算资源和对这些现象进行建模的数值代码的伴随使用；还应该指出，物质波这一活动的长期前景之一是构思和构建新的设备，这些设备将指导和更广泛地控制物质波的运动，并可能被用于纳米级的量子信息处理。这些方面使我们预计，在高性能计算、材料和制造等具有战略意义的联邦领域实施该项目可能会产生显著的好处。