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

University Of California - Merced, Merced CA

Investigators

Abstract

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