"Attosecond technology realizes the century-old dream of direct measurement of electron dynamics at the atomic scale. The ensuing experimental cornucopia, with many publications in Nature and Science, underscores the need for better analytic tools to explain the data, as a step towards a better physical foundation for a truly multi-disciplinary science. Current theoretical technique must be substantially improved to properly address some recent experimental controversies, such as measurements of quantum tunneling time. In particular, high harmonic generation (HHG), crucial to many experiments in attosecond science, requires a clearer ""physical picture"" than semi-classical models allow. A major goal of this proposal is to provide a theoretical framework for the experiments performed by Prof. Keller's group (ETH, Zurich) and others, and thereby to bring light to current debates. The research will develop analytic techniques to calculate quantum tunneling time in HHG, and better explain other steps of the HHG process, in particular the generation of attosecond pulses via quantum path interference and the interaction of the continuum electron with the laser pulse. The analysis will address both quantum and classical regimes of HHG: e.g., the quantum tunneling calculation will use a path integral approach, the interaction of the continuum electron with the laser field will employ plasma physics techniques, etc. Both of these approaches match well with the Fellow's background: the path integral approach was previously used to study escape from a potential well, and the Fellow's dissertation focuses on the interaction of charged particles with E&M fields. The project offers a possibility of close collaboration with the Fellow's graduate institution of Princeton University and other major research centers."