Dynamics of atoms in strong laser fields I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential

In this study we present a model that we have formulated in the momentum space to describe atoms interacting with intense laser fields. As a further step, it follows our recent theoretical approach in which the kernel of the reciprocal-space time-dependent Schrödinger equation (TDSE) is replaced by a finite sum of separable potentials, each of them supporting one bound state of atomic hydrogen (Tetchou Nganso et al. 2013). The key point of the model is that the nonlocal interacting Coulomb potential is expanded in a Coulomb Sturmian basis set derived itself from a Sturmian representation of Bessel functions of the first kind in the position space. As a result, this decomposition allows a simple spectral treatment of the TDSE in the momentum space. In order to illustrate the credibility of the model, we have considered the test case of atomic hydrogen driven by a linearly polarized laser pulse, and have evaluated analytically matrix elements of the atomic Hamiltonian and dipole coupling interaction. For various regimes of the laser parameters used in computations our results are in very good agreement with data obtained from other time-dependent calculations.     

Carrier-envelope phase measurement using plasmonic-field-enhanced high-order harmonic generation of H atom in few-cycle laser pulses

We investigate the plasmonic-field-enhanced high-order harmonic generation (HHG) of H atom driven by few-cycle laser pulses, by solving the time-dependent Schrödinger equation (TDSE). Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase (CEP) of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.     

Comparative study of photoionization of atomic hydrogen by solving the one- and three-dimensional time-dependent Schrödinger equations

We develop a numerical scheme for solving the one-dimensional (1D) time-dependent Schrödinger equation (TDSE), and use it to study the strong-field photoionization of the atomic hydrogen. The photoelectron energy spectra obtained for pulses ranging from XUV to near infrared are compared in detail to the spectra calculated with our well-developed code for accurately solving the three-dimensional (3D) TDSE. For XUV pulses, our discussions cover intensities at which the ionization is in the perturbative and nonperturbative regimes. For pulses of 400 nm or longer wavelengths, we distinguish the multiphoton and tunneling regimes. Similarities and discrepancies between the 1D and 3D calculations in each regime are discussed. The observed discrepancies mainly originate from the differences in the transition matrix elements and the energy level structures created in the 1D and 3D calculations.     

Scattering-amplitude phase in spiderlike photoelectron momentum distributions

The spiderlike structures in the photoelectron momentum distributions of ionized electrons from the hydrogen atom are numerically simulated by using a semiclassical rescattering model(SRM) and solving the time-dependent Schrodinger equation(TDSE),focusing on the role of the phase of the scattering amplitude.With the SRM,we find that the spiderlike legs shift to positions with smaller transverse momentum values while increasing the phase.The spiderlike patterns obtained by SRM and TDSE are in good agreement upon considering this phase.In addition,the time differences in electron ionization and rescattering calculated by SRM and the saddle-point equations are either in agreement or show very similar laws of variation,which further corroborates the significance of the phase of the scattering amplitude.     

Above-threshold ionization of hydrogen and hydrogen-like ions by X-ray pulses

This paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A ² and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L ²-integrable B-spline functions for the radial coordinate and spherical harmonics Y _lm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c ²)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 ? 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B⁴⁺. Perturbative and TDSE calculations are compared.     

Solution of Quantum Mechanical Problems Using Finite Element Method and Parametric Basis Functions

New computational schemes, symbolic-numerical algorithms and programs implementing the high-accuracy finite element method (FEM) for the solution of quantum mechanical boundary-value problems (BVPs) are reviewed. The elliptic BVPs in 2D and 3D domains are solved using the multivariable FEM and Kantorovich method using parametric basis functions. We demonstrate and compare the efficiency of the proposed calculation schemes, algorithms, and software by solving the benchmark BVPs that describe the scattering on a barrier and a well, the bound states of a helium atom, and the quadrupole vibration in a collective nuclear model.     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

Multiphoton and tunneling ionization of atoms in an intense laser field

We study the ionization probabilities of atoms by a short laser pulse with three different theoretical methods,i.e.,the numerical solution of the time-dependent Schro¨dinger equation(TDSE),the Perelomov-Popov-Terent’ev(PPT) theory,and the Ammosov-Delone-Krainov(ADK) theory.Our results show that laser intensity dependent ionization probabilities of several atoms(i.e.,H,He,and Ne) obtained from the PPT theory accord quite well with the TDSE results both in the multiphoton and tunneling ionization regimes,while the ADK results fit well to the TDSE data only in the tunneling ionization regime.Our calculations also show that laser intensity dependent ionization probabilities of a H atom at three different laser wavelengths of 600 nm,800 nm,and 1200 nm obtained from the PPT theory are also in good agreement with those from the TDSE,while the ADK theory fails to give the wavelength dependence of ionization probability.Only when the laser wavelength is long enough,will the results of ADK be close to those of TDSE.     

Scattered wave packet formalism for open quantum systems: Comparison with the non-Markovian time-dependent Schrödinger equation

Computational comparison is presented between the scattered wave packet formalism and the non-Markovian time-dependent Schrödinger equation (TDSE). These two approaches have been developed to deal with open quantum systems. We employ these methods to study the dynamics of a Gaussian wave packet scattering from the Eckart barrier. It is shown that strongly oscillatory Green functions required in the integration of the non-Markovian TDSE significantly increase computational effort even for one-dimensional problems. Computational results indicate that the scattered wave packet formalism can achieve higher accuracy and can be several orders of magnitude faster than the integration of the non-Markovian TDSE.     

分子高次谐波产生过程中同位素效应的理论研究

本文通过求解非玻恩-奥本海默近似条件下的一维含时薛定谔方程比较研究了H2+和HD+分子离子体系高次谐波谱的特征.数值计算结果表明,对于H2+体系干涉最小值对激光强度和分子初始振动态都很敏感,与此不同,HD+体系的干涉最小值的变化只依赖于初始振动态的选取.此外,借助于时频分布和电离几率,计算结果得到了合理的解释.     

Gaussian basis sets of triple and quadruple zeta valence quality for correlated wave functions

Contracted basis sets of triple and quadruple zeta (TZ and QZ, respectively) valence quality for the atoms from H to Ar are presented. They have been determined from fully-optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree–Fock (HF) calculations. Sets of Gaussian polarization functions optimized at the Møller–Plesset second-order (MP2) level were added to the TZ and QZ basis sets. This extends earlier work on segmented contracted double zeta valence basis sets. The performance of the basis sets are assessed in molecular HF and MP2 calculations for a sample of diatomic molecules by a comparison of energies, dissociation energies, and dipole moments with results obtained numerically or using basis sets reported in the literature. By fitting the directly calculated values through two extrapolation schemes, estimates of the complete basis set limit for second order correlation energy have been obtained. In addition, results for MP2-R12/A calculations to establish the basis set convergence for the standard calculations are also presented.     

Efficient solver for time-dependent Schr?dinger equation with interaction between atoms and strong laser field

We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schr?dinger equation(TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula(RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos(SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation(HHG) in these interaction systems.     

分子高次谐波产生过程中同位素效应的理论研究简

本文通过求解非玻恩-奥本海默近似条件下的一维含时薛定谔方程比较研究了H+2和HD+分子离子体系高次谐波谱的特征.数值计算结果表明,对于H+2体系干涉最小值对激光强度和分子初始振动态都很敏感,与此不同,HD+分子离子体系的干涉最小值的变化只依赖于初始振动态的选取.此外,借助于时频分布和电离几率,计算结果得到了合理的解释.     

数值研究二维含时薛定谔方程

采用二维渐近边界条件,将任意极化激光与原子相互作用的二维含时Schr(o)dinger方程无穷空间初值问题转化为有界空间的初边值问题,近而将截断后的初边值问题离散成线性正则方程组,而后利用辛算法求解正则方程得到含时波函数.最后利用含时波函数求得高次谐波谱,证明二维渐近边界条件和辛算法是合理而有效的.     

H2+和HD+分子体系高次谐波发射效率的理论研究

本文通过求解一维含时薛定谔方程, 比较研究了H2+和HD+分子离子体系的高次谐波发射效率. 数值计算结果表明, 在相同激光条件下, 不对称分子体系能产生更高强度的谐波谱. 此外, 借助时频分布, 电离几率和电子-核波包密度概率分布图, 对计算结果做出了合理的解释.     

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H₂O)₂) systems agree well with experiments and computational results obtained with other band-structure and basis-set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.     

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.     

Ultrafast photoionization of ions and molecules by orthogonally polarized intense laser pulses: Effects of the time delay

We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schr?dinger equations(TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays Td, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.     

Photoelectron momentum distributions of Ne and Xe dimers in counter-rotating circularly polarized laser fields

The strong-field ionization of dimers is investigated theoretically in counter-rotating circularly polarized laser fields. By numerically solving the two-dimensional (2D) time-dependent Schrödinger equation (TDSE) with the single-electron approximation (SEA) frame, we present the photoelectron momentum distributions (PMDs) and photoelectron angular distribution (PADs) of aligned Ne and Xe dimers. It is found that the PMDs and PADs strongly depend on the time delays by counter-rotating circularly polarized laser pulses. The results can be explained by the ultrafast photoionization model and the evolution of electron wave packets for Ne and Xe dimers. Besides, We make a comparison of PMDs between Ne atom and Ne dimer.     

啁啾脉冲对氢分子离子解离动力学的影响

本文通过数值求解一维含时薛定谔方程,理论研究了超短啁啾脉冲（5-fs,790-nm）对处于低振动态氢分子离子解离动力学的影响. 研究过程中有效利用流算符的方法得到不同激光强度下的解离几率及核波包密度分布. 结果表明：低强度的啁啾脉冲可显著增强低振动态氢分子离子的解离过程,使解离过程提前发生并在较短的时间内获得较多的解离产物, 并给出相应的理论解释.