Probing time-ordering in two-photon double ionization of helium on the attosecond time scale

We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization (TPDI) of helium by an attosecond XUV pulse. The Eisenbud-Wigner-Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular distribution of the emitted electron pair. Our fully-dimensional ab-initio quantum mechanical simulations provide benchmark data for experimentally accessible observables.Comment: 8 pages, 5 figures; revised version, added appendi

Certification of Confluence Proofs using CeTA

CeTA was originally developed as a tool for certifying termination proofs which have to be provided as certificates in the CPF-format. Its soundness is proven as part of IsaFoR, the Isabelle Formalization of Rewriting. By now, CeTA can also be used for certifying confluence and non-confluence proofs. In this system description, we give a short overview on what kind of proofs are supported, and what information has to be given in the certificates. As we will see, only a small amount of information is required and so we hope that CSI will not stay the only confluence tool which can produce certificates.Comment: 5 pages, International Workshop on Confluence 201

Certified Rule Labeling

The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence certificates based on decreasing diagrams for the first time. The power of the method is illustrated by an experimental evaluation on a (standard) collection of confluence problems

Time-dependent complete-active-space self-consistent-field method for atoms: Application to high-harmonic generation

We present the numerical implementation of the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method [Phys. Rev. A, 88, 023402 (2013)] for atoms driven by a strong linearly polarized laser pulse. The present implementation treats the problem in its full dimensionality and introduces a gauge-invariant frozen-core approximation, an efficient evaluation of the Coulomb mean field scaling linearly with the number of basis functions, and a split-operator method specifically designed for stable propagation of stiff spatial derivative operators. We apply this method to high-harmonic generation in helium, beryllium, and neon and explore the role of electron correlations.Comment: 13 pages, 8 figure

Anomalous Fano Profiles in External Fields

We show that external control of Fano resonances in general leads to complex Fano $q$-parameters. Fano line shapes of photo-electron and transient absorption spectra in presence of an infrared control field are investigated. Computed transient absorption spectra are compatible with a recent experiment [C. Ott {\it et al.}, Science 340, 716 (2013)] but suggest a modification of the interpretation proposed there. Control mechanisms for photo-electron spectra are exposed: control pulses applied {\em during} excitation modify the line shapes by momentum boosts of the continuum electrons. Pulses arriving {\em after} excitation generate interference fringes due to infrared two-photon transitions

Probing scattering phase shifts by attosecond streaking

Attosecond streaking is one of the most fundamental processes in attosecond science allowing for a mapping of temporal (i.e. phase) information on the energy domain. We show that on the single-particle level attosecond streaking time shifts contain spectral phase information associated with the Eisenbud-Wigner-Smith (EWS) time delay, provided the influence of the streaking infrared field is properly accounted for. While the streaking phase shifts for short-ranged potentials agree with the associated EWS delays, Coulomb potentials require special care. We show that the interaction between the outgoing electron and the combined Coulomb and IR laser fields lead to a streaking phase shift that can be described classically

Attosecond two-photon interferometry for doubly excited states of helium

We show that the correlation dynamics in coherently excited doubly excited resonances of helium can be followed in real time by two-photon interferometry. This approach promises to map the evolution of the two-electron wave packet onto experimentally easily accessible non-coincident single electron spectra. We analyze the interferometric signal in terms of a semi-analytical model which is validated by a numerical solution of the time-dependent two-electron Schr\"odinger equation in its full dimensionality.Comment: 5 pages, 4 figure