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

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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.