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We present the recent new developments of time-dependent Schrödinger equation and time-dependent density-functional theory for accurate and efficient treatment of the electronic structure and time-dependent quantum dynamics of many-electron atomic and molecular systems in intense laser fields. We extend time-dependent generalized pseudospectral (TDGPS) numerical method developed for time-dependent wave equations in multielectron systems. The TDGPS method allows us to obtain highly accurate time-dependent wave functions with the use of only a modest number of spatial grid point for complex quantum dynamical calculations. The usefulness of these procedures is illustrated by a few case studies of atomic and molecular processes of current interests in intense laser fields, including multiphoton ionization, above-threshold ionization, high-order harmonic generation, attosecond pulse generation, and quantum dynamical processes related to multielectron effects. We conclude this paper with some open questions and perspectives of multiphoton quantum dynamics of many-electron atomic and molecular systems in intense laser fields.

Synopsis We present an ab initio quantum study of below-threshold harmonic generation (BTHG) from H2 + molecules in the presence of an intense laser field by solving the time-dependent Schrödinger equation accurately in space and time. We find that multiple channels contribute to BTHG of H2 + molecules, which are related to the electron driven initially at specific time of the laser pulse from one nuclear core to another nuclear core or back to the parent core itself. The distinct contributions of these channels are distinguished by using a novel synchro squeezing time-frequency analysis.

Using an extended Lewenstein model under single-active electron (SAE) and linear combination of atomic orbital approximations, we perform a theoretical investigation of the high harmonic generation (HHG) spectrum of diatomic molecular systems in intense short-pulse laser fields. The wavelet transform and Wigner distribution, two complementary time-frequency methods, are extended for the exploration of the underlying mechanisms responsible for the fine structure of HHG peaks in the plateau regime. We found that, under some conditions, the HHG fine structure is mainly due to the interference between the long and short trajectories. The extension of the cut-off in the molecular HHG spectrum is also observed when the internuclear separation is large. Detailed analysis shows that the one-centre and two-centre terms contribute, respectively, to the low- and high-energy parts of the molecular HHG spectrum.

We present a nonperturbative quantum study of high-order above-threshold detachment of H− in intense laser fields using an accurate one-electron model potential and a new time-dependent non-Hermitian Floquet approach. Detailed exploration of the electron energy and angular distributions is pursued for the laser field intensities 1010–1011 W cm−2 and wavelength 10.6 µm. In accordance with semiclassical predictions, the electron energy spectrum exhibits a plateau region in the higher energy part. Transformation of the electron angular distributions in the plateau region is discussed. The computational method involves the complex-scaling generalized pseudospectral (CSGPS) spatial discretization of the Hamiltonian and non-Hermitian time propagation of the time-evolution operator by means of the split-operator technique in the energy representation. The approach is designed for effective treatment of multiphoton processes in very intense and/or low-frequency laser fields, which are generally more difficult to treat using the conventional time-independent Floquet matrix techniques.

A scheme is proposed for realizing quantum entanglement, information transfer, CNOT gates, and SWAP gates with superconducting-quantum-interference-device (SQUID) qubits in cavity QED. In the scheme, the two logical states of a qubit are the two lowest levels of the SQUID. An intermediate level of the SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. The method presented here does not involve a real excitation of the intermediate levels during the operations. Thus, decoherence due to energy relaxation of intermediate levels is minimized. In addition, the present method does not require the adjustment of the SQUID level spacings, which simplifies the operation significantly.

We propose a scheme for protecting one-qubit information against one erasure. The scheme operates essentially by distributing quantum information over four qubits. Two versions of the method are considered: one of them is based on two spatially separated pairs of qubits, and the other is based on one pair of qubits and two spatially separated qubits.

We explore the usefulness of a quantum fluid dynamics (QFD) approach for quantitative electronic structure calculations of many-electron systems. By combining QFD and density functional theory, a single time-dependent nonlinear QFD equation can be derived. The equation is further transformed into a diffusion-type form by an imaginary-time evolution method, whose asymptotic solution reaches a global minimum and the many-body ground-state wavefunction. The time-dependent generalized pseudospectral method is extended to solve the diffusion equation in spherical coordinates, allowing optimal and nonuniform spatial discretization and accurate and efficient solution of the diffusion function in space and time. The procedure is applied to the study of electronic energies, densities and other ground-state properties of noble gas atoms (He, Ne, Ar, Kr, Xe). The results are in good agreement with other best available values. The method offers a conceptually appealing and computationally practical procedure for the treatment of many-electron systems beyond the Hartree-Fock level.

We present an ab initio precision investigation of the time-frequency characteristics of high-order harmonic generation (HHG) calculated by solving accurately and efficiently the time-dependent Schrodinger equation by means of the time-dependent generalized pseudospectral method. We extend a new synchrosqueezing transform (SST) to obtain the time-frequency spectra of the HHG and the dynamical phase associated with the dipole-emission time profile. The SST time-frequency analysis allows us to explore the in depth dynamics and contributions of the multi-rescattering trajectories and resonant trajectories in HHG. It also exhibits the subtle details of the spectral and temporal fine structures of the HHG, providing novel insights regarding the dynamical origin of the HHG in below- and above-threshold regimes.

We perform a nonperturbative study of the effect of static magnetic fields on the multiple high-order harmonic generation (HHG) processes of atomic H in intense pulsed laser fields. The time-dependent Schr?dinger equation in three spatial dimensions can be solved accurately and efficiently by means of the recently developed time-dependent generalized pseudospectral method (Tong X M and Chu S I 1997 Chem. Phys. 217 119). We found that the presence of a static magnetic field perpendicular to the laser field polarization direction can introduce a second HHG plateau, allowing significant extension of the cut-off. The high harmonics in the second plateau reach a maximum enhancement when the cyclotron frequency of the electron is about equal to one half of the laser frequency. Through a detailed time-frequency wavelet analysis of the HHG spectra, we have identified a `synchrotron radiation'-like new mechanism responsible for the production of the second plateau.

Classical mechanics has been applied in the theoretical study of the ionization of hydrogen atoms by static electric and circularly polarized electromagnetic fields. In both cases it was assumed that the ionizing field was adiabatically switched on. In the case of circular fields the calculations were performed for the initial energies and frequencies of the field for which . For such initial conditions almost all trajectories that lead to ionization are regular. The results of adiabatic theory and numerical simulations are compared with recent experiments.

We explore the detailed topological structure of the phase-space of the recently discovered three-dimensional integrable but nonseparable Hamiltonian system with velocity dependent potential. Two three-parameter families of three-dimensional tori which foliate the phase-space are identified. The complete classification, according to their topology, of the level sets corresponding to the critical points of the energy-momentum map, is accomplished. The relationship of the three-dimensional integrable system with important physical systems of current interest, namely, the hydrogen atoms in circularly polarized (CP) fields, in crossed magnetic and electric fields and in crossed magnetic and CP fields, is discussed.

We present a non-perturbative Floquet calculation of the electron angular distributions and partial widths for multiphoton above-threshold detachment of by 1064 nm radiation. When a beam of ions is used as a target, the angular distributions in the frame where the ions are at rest can be extracted from the energy (angle-integrated) distributions in the laboratory frame. The experiments measuring the electron angular distributions are now in progress. Our calculation procedure consists of the following elements. (i) Determination of the resonance wavefunction and complex quasienergy by means of the non-Hermitian Floquet Hamiltonian formalism. The Floquet Hamiltonian is discretized by the complex-scaling generalized pseudospectral technique recently developed (by Wang and co-workers). (ii) Calculation of the angular distribution and partial widths based on an exact integral formula. The calculations were performed for the linearly polarized laser field with the wavelength 1064 nm and several intensities in the range - . With the increase of the number of photons absorbed above the threshold, the angular distributions become more stretched along the field direction manifesting, however, a few additional maxima. Besides the numerical data for the angular distributions we also present the coefficients of expansion on the basis of Legendre polynomials.

We show that the intra-band power spectrum of high-harmonic generation (HHG) in crystal can be directly used for the determination of crystalline band structure. This study is complementary to a recent all-optical inter-band gap reconstruction exclusively from the inter-band HHG spectrum. Our numerical calculations, based on a one-dimensional single-band model, demonstrates how the band structure can be determined accurately from the intra-band HHG spectrum, even with a poor initial guess of band structure and under the uncertainty of laser amplitude. The same scheme can be extended for the determination of multi-band structure directly from the practically mixed inter-/intra-band crystalline HHG spectrum.

We present a new adiabatic approach for non-perturbative treatment of multiphoton above-threshold detachment (ATD) in intense laser pulses. The electron energy distributions for the pulse detachment are expressed via the detachment transition amplitudes in the monochromatic fields, and the latter are calculated with the help of the adiabatic theory based on the smallness of the laser frequency compared with the electron affinity or ionization potential. The theory is applied to the first study of the pulse shape effects on the multiphoton ATD of the negative ion H- by 10.6 mu m radiation. Two pulse shapes are considered: a Gaussian pulse and a square pulse with smooth edges. We present the angle-resolved as well as angle-integrated ATD electron energy distributions. They contain oscillatory satellite structures to the main peaks due to interference of the electrons detached on the rising and falling edges of the pulse. Simple analytical formulae describing these subpeak structures are also presented.

The anomalous dependence of near-threshold harmonics in the molecular ion on the ellipticity of the driving near-infrared laser field is studied theoretically based on accurate solution of the time-dependent Schrodinger equation in prolate spheroidal coordinates with the help of the generalized pseudospectral method. For these harmonics, the maximum radiation energy corresponds to a non-zero ellipticity of the driving field. Our analysis reveals that the origin of the phenomenon lies in the near-resonant excitation of π-symmetry molecular orbitals. The excited states responsible for the anomalous ellipticity dependence of different near-threshold harmonics are identified. The effect is confirmed at the equilibrium internuclear separation R = 2 a.u. as well as for stretched molecules at R = 3 a.u.

A one-dimensional delta-function potential model is employed and its corres- ponding time-dependent SchrBdinger equation is solved exactly in momentum representa- tion. Several strong field effects of above-threshold detachment of a model H- ion arc explored, including an interesting temporal leakage in the below-shifted-threshold regime, non-linear dynamics of the system, and high-order harmonic generation, as well as the intensity effect of a second law-frequency laser field.

We study the electron quantum dynamics of high harmonic generation (HHG) processes of atomic hydrogen under intense near infrared (NIR) laser fields by means of the De Broglie–Bohm's framework of Bohmian mechanics. The proposed accurate 3D numerical scheme is utilized to discuss the mechanism of the multiple plateau generation and the cut-off extension, as the main characteristic features of HHG spectrum. One-color (1600 nm) and two-color (1600 nm + 800 nm) laser fields with different time delays are used to investigate the effect of pulse shape on electron dynamics and HHG process. The presented results on Bohmian trajectories and their energy content, along with the analysis of the emission time period of different groups of trajectories, provide a comprehensive and fresh electron dynamical picture and uncover novel mechanisms of the HHG processes and power spectra.

The exterior complex scaling (ECS) method is applied in the framework of time-dependent density-functional theory (TDDFT) to study high-order harmonic generation (HHG) of multielectron atoms in intense laser fields. With the help of ECS, correct outgoing-wave boundary conditions can be imposed on the wave functions at large distances. In our implementation, ECS is combined with the time-dependent generalized pseudospectral method for accurate and efficient solution of the time-dependent Kohn-Sham equations. We make use of LB94 exchange-correlation potential which appears quite accurate in calculations of unperturbed electronic structure of Ar. Calculations of HHG are performed for the laser fields with the wavelength of 800 nm and several peak intensities. The HHG spectrum exhibits an intensity-independent minimum corresponding to the photon energy of about 51 eV which is closely related to the Cooper minimum in the photoionization cross section of Ar. We found that HHG spectra calculated with the frozen-core potential (not including dynamic response of the electron density) differ significantly from those obtained by TDDFT.

We present a theoretical investigation of the multiphoton resonance dynamics driven by intense frequency-comb and cavity-mode fields inside a femtosecond enhancement cavity (fsEC). The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and laser fields. The quasienergy structure driven by the frequency-comb laser field is modified by coupling the cavity-mode field and the multiphoton resonance processes between modified quasienergy states, resulting in the generation of even-order harmonics. The high-order harmonic generation (HHG) from a two-level system driven by the laser fields can be coherently controlled by tuning the laser parameters. In particular, the tuning intensity of the cavity-mode field allows one to coherently control the HHG power spectra without changing the absolute positions of comb frequencies.

We propose a time-dependent density functional theoretical (TDDFT) approach in momentum (P) space for the study of electron transport in molecular devices under arbitrary biases. The basic equation of motion, which is a time-dependent integrodifferential equation obtained by Fourier transform of the time-dependent Kohn-Sham equation in spatial coordinate (R) space, is formally exact and includes all the effects and information of the electron transport in the molecular devices. The electron wave function is calculated by solving this equation in a finite P-space volume. This approach is free of self-energy function and memory term related to the electrodes in the R space and beyond the wide-band limit (WBL). The feasibility and power of the approach are demonstrated by the calculation of current through one-dimensional systems. Copyright c EPLA, 2009

Basis sets incorporating the interelectronic distance r12 are employed in variational calculations of the non-relativistic ground-state energies and pressures of a helium atom confined at the centre of an impenetrable spherical cavity and results are presented for a series of cavity radii Rc. The calculated values asymptotically approach the correct values in the limits Rc → 0 and Rc →∞ , and a simple analytical expression is obtained which makes accurate predictions for small cavities. The same method is also used to study two penetrable cavities modelled by Gaussian and harmonic potential wells. It is concluded that the present results are the most accurate currently available for a confined helium atom. The calculation method employs Gaussian quadrature to evaluate integrals and can very easily be adapted to any spherical confining potential.