Competition of resonant and nonresonant paths in resonance-enhanced two-photon single ionization of He by an ultrashort extreme-ultraviolet pulse

Implementation of the Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Diatomic Molecules

We present a computational approach that implements the time-dependent complete-active-space self-consistent-field method, as introduced in [Phys. Rev. A 88, 023402 (2013)]. Our implementation addresses the challenge of diatomic molecules subjected to an intense laser pulse by considering the full dimensionality of the problem using prolate spheroidal coordinates. The method incorporates the gauge-invariant frozen-core approximation, boosts the evaluation of the electron-electron interaction term using finite-element discrete-variable representation with Neumann expansion, and utilizes an exponential time differencing scheme tailored for the stable propagation of the stiff nonlinear orbital functions. We have successfully applied this methodology to study high-harmonic generation in diatomic molecules such as H2, LiH, and N2, shedding light on the impact of electron correlations in these systems.

Differential Measurement of Electron Ejection after Two-Photon Two-Electron Excitation of Helium

We report the measurement of the photoelectron angular distribution of two-photon single-ionization near the 2p^{2} ^{1}D^{e} double-excitation resonance in helium, benchmarking the fundamental nonlinear interaction of two photons with two correlated electrons. This observation is enabled by the unique combination of intense extreme ultraviolet pulses, delivered at the high-repetition-rate free-electron laser in Hamburg (FLASH), ionizing a jet of cryogenically cooled helium atoms in a reaction microscope. The spectral structure of the intense self-amplified spontaneous emission free-electron laser pulses has been resolved on a single-shot level to allow for post selection of pulses, leading to an enhanced spectral resolution, and introducing a new experimental method. The measured angular distribution is directly compared to state-of-the-art theory based on multichannel quantum defect theory and the streamlined R-matrix method. These results and experimental methodology open a promising route for exploring fundamental interactions of few photons with few electrons in general.

Anisotropic dynamics of two-photon ionization: An attosecond movie of photoemission

Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach because of the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by two-photon transitions through intermediate bound states. Using spectrally and angularly resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude toward the photoelectron quantum state. This allows reconstructing in space, time, and energy the complete formation of the photoionized wave packet.

Revealing the Target Electronic Structure with Under-Threshold RABBITT

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps faithfully the discrete energy levels and the corresponding oscillator strengths. We demonstrate this sensitivity by considering the Ne atom driven by the combination of the XUV and IR pulses at the fundmanetal laser frequency in the 800 and 1000 nm ranges.

Time-dependent optimized coupled-cluster method for multielectron dynamics. IV. Approximate consideration of the triple excitation amplitudes

We present a cost-effective treatment of the triple excitation amplitudes in the time-dependent optimized coupled-cluster (TD-OCC) framework called TD-OCCDT(4) for studying intense laser-driven multielectron dynamics. It considers triple excitation amplitudes correct up to the fourth-order in many-body perturbation theory and achieves a computational scaling of O(N⁷), with N being the number of active orbital functions. This method is applied to the electron dynamics in Ne and Ar atoms exposed to an intense near-infrared laser pulse with various intensities. We benchmark our results against the TD complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and TD Hartree-Fock (TDHF) methods to understand how this approximate scheme performs in describing nonperturbatively nonlinear phenomena, such as field-induced ionization and high-harmonic generation. We find that the TD-OCCDT(4) method performs equally well as the TD-OCCDT method, almost perfectly reproducing the results of the fully correlated TD-CASSCF with a more favorable computational scaling.

Asymmetries in ionization of atomic superposition states by ultrashort laser pulses

Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.

Quantum control and characterization of ultrafast ionization with orthogonal two-color laser pulses

We study ultrafast ionization dynamics using orthogonally polarized two-color (OTC) laser pulses involving the resonant "first plus second" (ω + 2ω) scheme. The scheme is illustrated by numerical simulations of the time-dependent Schrödinger equation and recording the photoelectron momentum distribution. On the basis of the simulations of this resonant ionization, we identify signatures of the dynamic Autler-Townes effect and dynamic interference, in which their characterization is not possible in the spectral domain. Taking advantage of the OTC scheme we show that these dynamical effects, which occur at the same time scale, can be characterized in momentum space by controlling the spatial quantum interference. In particular, we show that with the use of this control scheme, one can tailor the properties of the control pulse to lead to enhancement of the ionization rate through the Autler-Townes effect without affecting the dynamic interference. This enhancement is shown to result from constructive interferences between partial photoelectron waves having opposite-parity, and found to manifest by symmetry-breaking of the momentum distribution. The scenario is investigated for a prototype of a hydrogen atom and is broadly applicable to other systems. Our findings may have applications for photoelectron interferometers to control the electron dynamics in time and space, and for accurate temporal characterization of attosecond pulses.

Complete Characterization of Phase and Amplitude of Bichromatic Extreme Ultraviolet Light

Intense, mutually coherent beams of multiharmonic extreme ultraviolet light can now be created using seeded free-electron lasers, and the phase difference between harmonics can be tuned with attosecond accuracy. However, the absolute value of the phase is generally not determined. We present a method for determining precisely the absolute phase relationship of a fundamental wavelength and its second harmonic, as well as the amplitude ratio. Only a few easily calculated theoretical parameters are required in addition to the experimental data.

Short-wavelength free-electron laser sources and science: a review

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.

Time delays in two-photon ionization

We present results of ab initio numerical simulations of time delays in two-photon ionization of the helium atom using the attosecond streaking technique. The temporal shifts in the streaking traces consist of two contributions, namely, a time delay acquired during the absorption of the two photons from the extreme-ultraviolet field and a time delay accumulated by the photoelectron after photoabsorption. In the case of a nonresonant transition, the absorption of the two photons is found to occur without time delay. In contrast, for a resonant transition a substantial absorption time delay is found, which scales linearly with the duration of the ionizing pulse. The latter can be related to the phase acquired during the transition of the electron from the initial ground state to the continuum and the influence of the streaking field on the resonant structure of the atom.

Modulation of attosecond beating in resonant two-photon ionization

We present a theoretical study of the photoelectron attosecond beating due to interference of two-photon transitions in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, both the phase shift and frequency of the sideband beating significantly vary with photon energy. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a nonholographic interferometric means to reconstruct coherent metastable wave packets. We characterize these phenomena by means of a general analytical model that accounts for the effect of both intermediate and final resonances on two-photon processes. The model predictions are in excellent agreement with those of accurate ab initio calculations for the helium atom in the region of the N=2 doubly excited states.