Topological excitations in Bose-Einstein condensates: Existence, stability, dynamics, and interactions

玻色-爱因斯坦凝聚中的拓扑激发：存在性、稳定性、动力学和相互作用

• 批准号: 0505663
• 负责人: Ricardo Carretero
• 金额: $ 9.19万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505663&HistoricalAwards=false
• 关键词: Topological; excitations; Bose; Einstein; condensates

Nonlinear media host a wide variety of localized coherent structures(solitons, wavetrains, vortices, spirals, etc.) with complex intrinsicproperties and interactions that, in turn, give rise to emergent patternswith nontrivial dynamics. The theme of the proposed research is a detailedexamination of vortices generated in dispersive nonlinear media.The main focus is to extend and deepen the understanding of vortexstructures, their existence and dynamical stability as well as theirinteractions and mesoscopic lattices in nonlinear media such asBose-Einstein condensates and related fields (such as nonlinear optics).We propose to follow a step-by-step methodology in studying thegeneration, stability and dynamics of vortices in a progression ofscenaria of increasing complexity, extending from single vortices, to few vortices, to vortex lattices. Specifically, we plan to study:(1) Vortex generation through dynamical instabilities and externalmanipulations such as phase imprinting and via instabilities driven byrapidly moving impurities (focused laser beams).(2) Dynamics and stability of single vortices (a.k.a. atoms) in thepresence of external traps and manipulation of vortices by translating theexternal traps or by using localized optical "tweezers".(3) Interactions between vortices and formation, stability and dynamicsof vortex dipoles (a.k.a. molecules/dipoles).(4) Finally, we intend to investigate, by cross-fertilizing ideas frommaterial science, large arrays of vortices, their crystallization andstructural phase transitions into regular vortex lattices (a.k.a. crystals).In the 1920's Bose and Einstein predicted that a gas at low density andultra-cold temperatures undergoes a transition towards what is nowadayscalled a Bose-Einstein condensate (BEC). The most important characteristicof a BEC is that all atoms occupy the same quantum state creating a macroscopiclump of coherent matter. BECs are to matter what laser is to light. BECs allowfor direct manipulation and observation of quantum effects at the macroscopiclevel, providing ultimate control over matter. Since their recentexperimental realization (for which the 2001 Physics Nobel prize wasgranted), BECs have been at the focus of an intensive and ever growingexperimental and theoretical effort. Vortices are fundamental coherent,topologically charged, nonlinear excitations that emerge in BECs; butwhich also play a profound role in exciting and important fields such assuperconductivity and superfluidity (which were the theme of the 2003Physics Nobel prize). Interestingly enough, they also arise in our dailylife in the form of hydrodynamic vortices in water or in air. There arestrong parallels (as well as differences) between such fluid vortices andthese ultra-cold, superfluid vortices that we plan to examine anddelineate. The outcome of this research will shed light into the patternformation and interaction of such vortex structures in Bose-Einsteincondensates. Since the underlying equation that describes the BECs alsodescribes the behavior of coherent light embedded in a nonlinearmaterial, the research hereby proposed will also be applicable toproblems of optical waveguides and fiber bundles, photonic crystals, andlight storage in optical traps, all of which are active research areas atthe forefront of optical technologies. The proposed research haspotential applications to quantum-optical storageand quantum computing for the next generation of computers.The research effort is part of an ongoing collaboration betweenthe PI and Co-PI and involves more than a dozen coworkers that blend inexpertise in fields as diverse as dynamical systems, nonlinear optics,condensed matter, materials science and scientific computing. Speciallyattractive is the prospect that our results will be partially driven andcould be relevant to current experimental research conducted in BECexperiments. This highly inter-disciplinary research program will alsoinvolve a major educational component through the direct involvement ofgraduate research assistants and postdoctoral fellows.

非线性介质中存在着各种各样的局域相干结构（孤子、波列、涡旋、螺旋等）。with complex复杂intrinsicproperties内在properties属性and interactions相互作用that，turn转，give rise上升to emergent紧急patterns模式with nontrivial平凡dynamics动态.本论文的研究主题是对色散非线性介质中产生的涡旋进行详细的研究，其主要目的是扩展和深化对非线性介质中涡旋结构、涡旋的存在性、动力学稳定性、涡旋间的相互作用以及介观晶格的理解，如玻色-爱因斯坦凝聚等（如非线性光学）。我们建议遵循一个逐步的方法来研究漩涡的产生，稳定性和动力学，从单一的漩涡，到很少的漩涡，到漩涡格子。具体而言，我们计划研究：（1）通过动力学不稳定性和外部操纵，如相位印记和通过快速移动的杂质（聚焦激光束）驱动的不稳定性产生涡旋。(2)单涡的动力学和稳定性（也称为原子）和通过平移外部陷阱或通过使用局部光学“镊子”来操纵涡旋。(3)涡旋与涡旋偶极的形成、稳定性和动力学之间的相互作用（又名分子/偶极子）。(4)最后，我们打算研究，从材料科学的交叉思想，大阵列的漩涡，他们的结晶和结构相变到规则的漩涡晶格（a.k.a.）。在20世纪20年代，玻色和爱因斯坦预言，在低密度和超冷温度下的气体会经历向现在称为玻色-爱因斯坦凝聚（BEC）的转变。BEC最重要的特征是所有的原子占据相同的量子态，产生一个宏观的相干物质块。BEC之于物质就像激光之于光。BEC允许在宏观水平上直接操纵和观察量子效应，提供对物质的最终控制。自从它们最近的实验实现（2001年诺贝尔物理学奖授予）以来，BEC一直是一个密集的和不断增长的实验和理论努力的焦点。涡旋是BEC中出现的基本相干、拓扑荷电、非线性激发;但它在超导和超流等令人兴奋的重要领域也发挥着深远的作用（这是2003年诺贝尔物理学奖的主题）。有趣的是，它们也出现在我们的日常生活中，以水或空气中的流体动力学漩涡的形式出现。在这种流体涡旋和我们计划研究和描述的超冷、超流体涡旋之间有很强的相似之处（也有区别）。这一研究结果将有助于揭示玻色-爱因斯坦凝聚体中涡旋结构的形成和相互作用。由于描述BEC的基本方程也描述了嵌入非线性材料中的相干光的行为，因此本文提出的研究也适用于光波导和光纤束、光子晶体以及光阱中的光存储问题，所有这些都是光学技术前沿的活跃研究领域。这项研究计划在量子光存储和量子计算方面有潜在的应用，可以用于下一代计算机。这项研究工作是PI和Co-PI之间正在进行的合作的一部分，涉及十几名同事，他们在动力系统、非线性光学、凝聚态、材料科学和科学计算等领域都有专业知识。特别有吸引力的是前景，我们的结果将部分驱动，并可能是相关的，目前的实验研究进行的BEC实验。这个高度跨学科的研究计划也将涉及一个主要的教育组成部分，通过研究生研究助理和博士后研究员的直接参与。