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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 figures

We report on the measurement of electron emission after the interaction of strong laser pulses with atoms and molecules. These electrons originate from high-lying Rydberg states with quantum numbers up to $n \lesssim 120$ formed by frustrated field ionization. Simulations show that both tunneling ionization by a weak dc field and photoionization by the black-body radiation contribute to delayed electron emission on the nano- to microsecond scale. We measured ionization rates from these Rydberg states by coincidence spectroscopy. Further, the dependence of the Rydberg-state production on the ellipticity of the driving laser field proves that such high-lying Rydberg states are populated through electron recapture. The present experiment provides detailed quantitative information on Rydberg production by frustrated field ionization.

We propose a protocol to probe the ultrafast evolution and dephasing of coherent electronic excitation in molecules in the time domain by the intrinsic streaking field generated by the molecule itself. Coherent electronic motion in the endohedral fullerene \Necsixty~is initiated by a moderately intense femtosecond UV-VIS pulse leading to coherent oscillations of the molecular dipole moment that persist after the end of the laser pulse. The resulting time-dependent molecular near-field is probed through the momentum modulation of photoemission from the central neon atom by a time-delayed attosecond XUV pulse. Our ab-initio time-dependent density functional theory and classical trajectory simulations predict that this self-streaking signal accurately traces the molecular dipole oscillations in real time. We discuss the underlying processes and give an analytical model that captures the essence of our ab-initio simulations.

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.

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 appendix

We theoretically study time-resolved photoemission in atoms as probed by attosecond streaking. We review recent advances in the study of the photoelectric effect in the time domain and show that the experimentally accessible time shifts can be decomposed into distinct contributions that stem from the field-free photoionization process itself and from probe-field induced corrections. We perform accurate quantum-mechanical as well as classical simulations of attosecond streaking for effective one-electron systems and determine all relevant contributions to the time delay with attosecond precision. In particular, we investigate the properties and limitations of attosecond streaking for the transition from short-ranged potentials (photodetachment) to long-ranged Coulomb potentials (photoionization). As an example for a more complex system, we study time-resolved photoionization for endohedral fullerenes $A$@$\text{C}_{60}$ and discuss how streaking time shifts are modified due to the interaction of the $\text{C}_{60}$ cage with the probing infrared streaking field., Comment: Submitted to J.Phys.Conf.Ser. (ICPEAC 2013 conference proceedings) on 27.09.2013, accepted on 28.10.2013, final version submitted on 15.11.2013

We present the first numerical simulation of the time delay in the photoionization of the simplest diatomic molecule H$_2^+$ as observed by attosecond streaking. We show that the strong variation of the Eisenbud-Wigner-Smith time delay as a function of energy and emission angle becomes observable in the streaking time shift provided laser field-induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive Cohen-Fano (or two-center) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fragments are detected in coincidence.

We revisit the time-resolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of 2p and 2s electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The B-spline R-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multi- electron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking process by solving the time-dependent Schr\"odinger equation on the single-active-electron level. The resulting accurate total relative streaking time shifts between 2s and 2p emission lie well below the experimental data. We identify the presence of unresolved shake-up satellites in the experiment as a potential source of error in the determination of streaking time shifts., Comment: 8 pages, 4 figures v2: final published version

The production of very-high-$n$, $n\sim300$-500, strontium Rydberg atoms is explored using a crossed laser-atom beam geometry. $n$$^{1}$S$_{0}$ and $n$$^{1}$D$_{2}$ states are created by two-photon excitation via the 5s5p $^{1}$P$_{1}$ intermediate state using radiation with wavelengths of $\sim$~461 and $\sim$ 413 nm. Rydberg atom densities as high as $\sim 3 \times 10^{5}$ cm$^{-3}$ have been achieved, sufficient that Rydberg-Rydberg interactions can become important. The isotope shifts in the Rydberg series limits are determined by tuning the 461 nm light to preferentially excite the different strontium isotopes. Photoexcitation in the presence of an applied electric field is examined. The initially quadratic Stark shift of the $n$$^{1}$P$_{1}$ and $n$$^{1}$D$_{2}$ states becomes near-linear at higher fields and the possible use of $n{}^{1}$D$_{2}$ states to create strongly-polarized, quasi-one-dimensional electronic states in strontium is discussed. The data are analyzed with the aid of a two-active-electron (TAE) approximation. The two-electron Hamiltonian, within which the Sr$^{2+}$ core is represented by a semi-empirical potential, is numerically diagonalized allowing calculation of the energies of high-$n$ Rydberg states and their photoexcitation probabilities., Comment: 28 pages, 8 figures

We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline close-coupling basis, and a technique based on exterior complex scaling (ECS) implemented in the same basis used for the time propagation. These methods allow to monitor the population of continuum states in wavepackets created with ultrashort pulses in different regimes. Applications include photo cross sections and anisotropy parameters in the spectral region of doubly excited resonances, time-resolved photoexcitation of autoionizing resonances in an attosecond pump-probe setting, and the energy and angular distribution of correlated wavepackets for two-photon double ionization., Comment: 19 pages, 12 figures

We present fully ab initio simulations of attosecond streaking for ionization of helium accompanied by shake-up of the second electron. This process represents a prototypical case for strongly correlated electron dynamics on the attosecond timescale. We show that streaking spectroscopy can provide detailed information on the Eisenbud-Wigner-Smith time delay as well as on the infrared field dressing of both bound and continuum states. We find a novel contribution to the streaking delay that stems from the interplay of electron-electron and infrared-field interactions in the exit channel. We quantify all the contributions with attosecond precision and provide a benchmark for future experiments., Comment: 5 pages, 4 figures

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.

We analyze the formation of the low-energy structure (LES) in above-threshold ionization spectra first observed by Quan et al.\ \cite{quan09} and Blaga et al.\ \cite{blaga09} using both quasi-classical and quantum approaches. We show this structure to be largely classical in origin resulting from a two-dimensional focusing in the energy-angular momentum plane of the strong-field dynamics in the presence of the atomic potential. The peak at low energy is strongly correlated with high angular momenta of the photoelectrons. Quantum simulations confirm this scenario. Resulting parameter dependences agree with experimental findings \cite{quan09,blaga09} and, in part, with other simulations \cite{liu10,yan10,kast11}., Comment: 12 pages, 6 figures

Attosecond streaking of atomic photoemission holds the promise to provide unprecedented information on the release time of the photoelectron. We show that attosecond streaking phase shifts indeed contain timing (or spectral phase) information associated with the Eisenbud-Wigner-Smith time delay matrix of quantum scattering. However, this is only accessible if the influence of the streaking infrared (IR) field on the emission process is properly accounted for. The IR probe field can strongly modify the observed streaking phase shift. We show that the part of the phase shift ("time shift") due to the interaction between the outgoing electron and the combined Coulomb and IR laser fields can be described classically. By contrast, the strong initial-state dependence of the streaking phase shift is only revealed through the solution of the time-dependent Schr\"odinger equation in its full dimensionality. We find a time delay between the hydrogenic 2s and 2p initial states in He+ exceeding 20as for a wide range of IR intensities and XUV energies.

We investigate the role of electron correlation in the two-photon double ionization of helium for ultrashort XUV pulses with durations ranging from a hundred attoseconds to a few femtoseconds. We perform time-dependent ab initio calculations for pulses with mean frequencies in the so-called "sequential" regime (photon energy above 54.4 eV). Electron correlation induced by the time correlation between emission events manifests itself in the angular distribution of the ejected electrons, which strongly depends on the energy sharing between them. We show that for ultrashort pulses two-photon double ionization probabilities scale non-uniformly with pulse duration depending on the energy sharing between the electrons. Most interestingly we find evidence for an interference between direct ("nonsequential") and indirect ("sequential") double photo-ionization with intermediate shake-up states, the strength of which is controlled by the pulse duration. This observation may provide a route toward measuring the pulse duration of FEL pulses., Comment: 9 pages, 6 figures