Topological Chaos for Atomic Characterization and Control

University Of California - Merced, Merced CA

Investigators

Abstract

Recent decades have seen dramatic improvement in the ability to prepare, manipulate, and control quantum systems with ever increasing fidelity on smaller and smaller time scale and with finer and finer spatial resolution. This has opened new scientific and technological frontiers, for example, in quantum information processing, manipulation of quantum gases, and the control of Rydberg (highly excited) atoms. Though such systems are inherently quantum mechanical, much intuition about the behavior of such systems is based on the underlying classical models for such systems. Classically chaotic models present particular difficulties, due to the extreme complexity and number of classical trajectories. This research seeks to utilize newly developed theoretical (e.g. topological) tools to classify chaotic trajectories in atomic systems and to use these trajectories to compute transport properties (e.g. decay rates) and energy levels of such systems. Such topological tools will also be applied to problems in the control of Rydberg atoms. Through graduate and undergraduate research experiences, this work will also help train the next generation of scientists and help to nurture the newly established campus of the University of California at Merced. UC Merced was opened in 2005 and has already made a significant impact on the economy and education in California's Great Central Valley, the agricultural heart of the state. The broad theme of this proposal is the analysis and control of atomic systems through a deep structural understanding of chaotic trajectories. This is manifest in the following specific objectives. (i) Building on the prior development and computer implementation of homotopic lobe dynamics---a topological technique for classifying large-amplitude chaotic motion---decay rates and other atomic transport properties will be computed from a detailed analysis of a relatively small number of a system's periodic orbits. (ii) These classical periodic orbit computations will be augmented with quantum phase information to generate semiclassical estimates of individual chaotic energy levels. (iii) Building on the successful use of phase space turnstiles to control the ionization of quasi-1D Rydberg states, the turnstile technique will be applied to the more challenging control problem of circular Bohr-like Rydberg wavepackets. The well-established power of periodic orbit techniques has not been widely applied to "real world" problems due in large part to the difficulty of characterizing and computing the relevant orbits, especially in complex systems with a mixture of chaos and regularity. Successfully computing classical transport rates for mixed systems would thus dramatically expand the applicability of periodic orbit techniques. Furthermore, using these techniques to estimate individual quantum eigenvalues would address a long-standing question in quantum chaos: is it possible to semiclassically compute quantum spectra for general chaotic systems? Finally, applying phase-space turnstiles to 3D Bohr-like wavepackets would provide a new laboratory mechanism to rapidly control and engineer such states, e.g. increase or decrease the principle quantum number. It would also improve the general understanding of chaotic transport in higher dimensional systems.