Application of Coulomb wave function discrete variable representation to atomic systems in strong laser fields

Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra

Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.

Time-dependentab initioapproaches for high-harmonic generation spectroscopy

High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 10¹³ W/cm² to 5 × 10¹⁴ W/cm². We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

Dynamic Stark induced vortex momentum of hydrogen in circular fields

In this paper, we report our numerical simulation on the symmetry distortion and mechanism of the vortex-shaped momentum distribution of hydrogen atom by taking into account of the dynamic Stark effect. By deploying the strong field approximation (SFA) theory, we performed extensive simulation on the momentum pattern of hydrogen ionized by two time-delayed oppositely circularly polarized attosecond pulses. We deciphered that this distortion is originated from the temporal characteristics of the dynamic Stark phase which is nonlinear in time.

Efficient Split-Lanczos propagator for strong-field ionization of atoms

High angular momentum partial waves are indispensable in the numerical calculations of the time-dependent Schrödinger equation (TDSE) for the interaction between atoms and strong long-wavelength laser pulses. In these cases, the widely-applied Lanczos propagator, used to solve the TDSE, requires an extremely small time step to be convergent. By splitting out the centrifugal potential from the whole Hamiltonian, we demonstrate that the stiffness of the TDSE can be reduced and a rather large time step is allowed for the present Split-Lanczos propagator. Compared with the ordinary Lanczos propagator, the efficiency of the propagation can be improved by more than 100 times for large angular momentum in present tests.

Time-dependent quantum simulation of coronene photoemission spectra

Photoelectron spectroscopy is usually described by a simple equation that relates the binding energy of the photoemitted electron, Ebinding, its kinetic energy, Ekinetic, the energy of the ionizing photon, Ephoton, and the work function of the spectrometer, ϕ, Ebinding = Ephoton - Ekinetic - ϕ. Behind this equation there is an extremely rich physics, which we describe here using as an example a relatively simple conjugated molecule, namely coronene. The theoretical analysis of valence band and C1s core level photoemission spectra showed that multiple excitations play an important role in determining the intensities of the final spectrum. An explicit, time-evolving model is applied, which is able to count all possible photo-excitations occurring during the photoemission process, showing that they evolve on a short time-scale, of about 10 fs. The method reveals itself to be a valid approach to reproduce photoemission spectra of polycyclic aromatic hydrocarbons (PAHs).

Mechanisms of below-threshold harmonic generation in atoms

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

Application of discrete variable representation to planar H2+ in strong xuv laser fields

We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.

Validity of factorization of the high-energy photoelectron yield in above-threshold ionization of an atom by a short laser pulse

An analytic description for the yield, P(p), of high-energy electrons ionized from an atom by a short (few-cycle) laser pulse is obtained quantum mechanically. Factorization of P(p) in terms of an electron wave packet and the cross section for elastic electron scattering (EES) is shown to occur only for an ultrashort pulse, while in general P(p) involves interference of EES amplitudes with laser-field-dependent momenta. The analytic predictions agree well with accurate numerical results.

Momentum space analysis of multiphoton double ionization of helium by intense attosecond xuv pulses

We investigate the momentum and energy distributions of the two electrons in multiphoton double ionization of He by intense attosecond xuv pulses, based on a two-dimensional model. Two different patterns of the momentum distributions are identified, corresponding to the uncorrelated and correlated channels, respectively. Our analysis of the electron correlations focuses on two-photon and three-photon double ionization processes for different pulse durations and for different time delays after the pulses. For both two-photon and three-photon cases, a clear correlation valley in energy distributions is found when both electrons are ejected in opposite directions. This is mostly attributed to the electron correlations during the ionization of the first electron. We also find that when two electrons are ejected in the same direction, their Coulomb repulsion has an significant influence on the electron energy distributions during the postionization stage. Finally, in the case of three photon double ionization, we observe that the effects of the Coulomb repulsion become much more complicated, and a new catch-up collision phenomena is observed in the energy distributions.

Grid method for computation of generalized spheroidal wave functions based on discrete variable representation

We present an efficient and accurate grid method for computations of eigenvalues and eigenfunctions of the generalized spheroidal wave equation. Different from previous studies, our method is based on the expansion of the spheroidal wave function by discrete-variable-representation basis functions constructed from the associated Legendre polynomials. The differential operator can be expressed analytically on the grid points, which are the zeros of the associated Legendre polynomials. The resultant potential matrix is simply diagonal and evaluated directly on the same grid. The corresponding differential equation is thus converted to an eigenvalue problem of a small matrix, whose eigenvalues and eigenvectors are converged very fast. The wave functions can then be evaluated accurately at any desired point from the expansion formula with the computed eigenvectors. Compared to previous methods, our method is direct and efficient for any parameter c , either small or large.