CAREER: Chaotic transport -- from fundamental theory to applications in atomic physics

非线性动力学历来在解释多样和复杂的原子过程中起着基本作用，这一作用反过来又刺激了经典和量子混沌的许多理论进展。原子和光学技术的进步为原子系统混沌的实验研究提供了前所未有的控制和精度水平，这一趋势仍在继续。例如，高度局域化的初始状态（如超短光脉冲、里德堡波包和超冷原子的局域化系综）的时间演化可以在混沌势内演化和分散时进行测量，从而探测混沌相空间中的详细分形结构。然而，这种精密工具突出了理论非线性动力学的基本缺陷；没有一般的框架（在符号动力学意义上）能够对真实物理系统中由输运表现出的混沌行为的多样性进行分类。该提案的重点是双重的：(i)它将利用混沌动力学的新进展来激励，指导和解释能够以前所未有的分辨率探测混沌相空间的实验。这些包括混沌输运、电离和里德伯波包的控制，以及对超冷原子在光学陷阱中混合和损失的新混沌途径的阐明。（ii）它将开发一个非线性动力学工具箱，可以提取一个精确的（符号动力学）模型的混沌输运结构的哈密顿系统具有两个自由度。这个模型可以精确到任意程度，甚至对于表现出混乱和规则混合的系统也是如此。的前期成功？同伦叶动力学？在描述相空间传输将作为这个程序的关键组成部分。最后，认识到同伦叶动力学在高维空间的自然拓扑扩展，该建议将解决超过两个自由度的混沌传输的挑战，目前存在的技术要少得多。

Nonlinear dynamics has historically played a fundamental role in explaining diverse andcomplex atomic processes, a role which in turn has stimulated numerous theoreticaladvances in classical and quantum chaos. This trend continues as advances in atomicand optical techniques provide an unprecedented level of control and precision forexperimental studies of chaos in atomic systems. For example, the time evolution ofhighly localized initial states (e.g. ultrashort optical pulses, Rydberg wavepackets, andlocalized ensembles of ultracold atoms), can be measured as they evolve and dispersewithin a chaotic potential, thereby probing the detailed fractal structure in the chaoticphase space. Such precision tools, however, highlight a fundamental deficiency intheoretical nonlinear dynamics; there exists no general framework (in the sense ofsymbolic dynamics) capable of classifying the diversity of chaotic behavior exhibited bytransport in real physical systems.The focus of this proposal is twofold: (i) It will exploit new advances in chaotic dynamicsto motivate, guide, and interpret experiments capable of probing chaotic phase spacewith unprecedented resolution. These include the chaotic transport, ionization, andcontrol of Rydberg wavepackets as well as the elucidation of novel chaotic pathways forthe mixing and loss of ultracold atoms in optical traps. (ii) It will develop a nonlineardynamics toolbox that can extract an accurate (symbolic dynamics) model for thestructure of chaotic transport in Hamiltonian systems with two degrees of freedom. Thismodel can be made arbitrarily precise, even for systems exhibiting a mixture of chaosand regularity. The prior success of ?homotopic lobe dynamics? in describing phasespace transport will serve as a key ingredient of this program. Finally, recognizing thenatural topological extension of homotopic lobe dynamics to higher dimensional spaces,this proposal will address the challenge of chaotic transport in more than two degrees offreedom, for which far fewer techniques currently exist.