Classical Dynamics of H<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> in an Intense Laser Field by Using the Symplectic Method

The classical dynamics of 1D H₂⁺ in an intense field are discussed. The initial conditions are chosen at random in the field-free case, and then the Hamiltonian canonical equations of H₂⁺ system in the intense laser field are solved numerically by mean of the symplectic method under these initial conditions. The probabilities of survival, dissociation, ionization, and Coulomb explosion of H₂⁺ system in the intense laser field are obtained for different laser intensity based on the classical theory.     

The Enhancement of Efficiency of High-order Harmonic in Intense Laser Field Based on Asymptotic Boundary Conditions and Symplectic Algorithm

Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schrödinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities     

Dynamics of electronic motion in hydrogen atom under parallel strong oscillating magnetic field and intense laser fields

The mechanism of ionization of an H atom interacting with intense laser electric fields is altered when a strong, oscillating magnetic field is applied along a direction parallel to the laser field. In this first study, these two strongly nonperturbative situations have been combined together and the corresponding time‐dependent (TD) Schrödinger equation has been numerically solved without using any basis set. The electric field arising out of the magnetic field and the magnetic field arising out of the laser electric field are found to be negligibly small, thereby not affecting the results. There are two main, apparently counter‐intuitive results from this study of parallel fields of the same frequency but different field strengths: (1) In presence of an oscillating magnetic field, the ionization rate due to the laser field diminishes, and (2) increasing the laser intensity, keeping the magnetic field strength the same, makes the electron density ionize with a lesser rate, in contrast to the situation with intense lasers in the absence of a strong TD magnetic field. © 2015 Wiley Periodicals, Inc.     

The quantitative analysis of enhancement of high-order harmonics in two-color intense laser fields

The time-dependent Schr?dinger equation of the interaction of laser pulse with He⁺ is solved by using the asymptotic boundary condition and symplectic algorithm in fundamental laser-field and two-color laser fields. We find that the conversion efficiency of high-order harmonic generation (HHG) is higher in the two-color laser fields than in the fundamental laser field, especially for the combination of ω ₀ − 19ω ₀. To explain these phenomena, the ionization, the average distance, the probability of first excited sate, and the transition probability are calculated. We give the qualitative and quantitative analysis for the enhancement of conversion efficiency of HHG.     

Classical dynamics of 3D Hydrogen molecular ion in intense laser fields

The classical trajectory method is used to study the dynamics of 3D Hydrogen molecular ion interacting with intense laser fields. In the 3D classical model, a three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser field is considered. The motion of electron and nucleus is described by the classical Hamiltonian canonical equations. The probabilities of ionization, dissociation and Coulomb explosion as functions of time are calculated and the average distances from electron to the mass-center for various laser parameters are implemented by symplectic method. The dynamics of in two-color laser fields are also investigated. We compare our results with the corresponding quantum-mechanical calculations and find they produce similar qualitative features in many cases.     

双光子共振四波差频产生的真空紫外激光特性研究

The character of tunable Vacuum-Ultraviolet（VUV）laser generated by two-photon resonant four wave difference frequency mixing in Xenon was studied. The intense VUV laser was generated in the wavelength range of 151-171 nm using 6P［1/2,0］level of Xe atom as the two-photon resonant state. The pulse intensity of VUV laser was estimated to be 0.2 μJ,and the conversion efficiency relative to the wavelength-fixed laser was determined to be 0.1%. The line width of VUV laser was found to be 0.3 cm-1 from the laser-induced fluorescence spectrum of A-X（0,0）rotational line profiles of jet-cooled CO,which was much broader than those of the two employed dye lasers（0. 1 cm-1）,mainly due to the saturation broadening of Xe level by intense laser field. The dependencies of VUV intensity on Xe pressure and two dye laser intensities were also investigated in this experiment.     

Open-loop and closed-loop control of dissociative ionization of ethanol in intense laser fields

The relative yield of the C-O bond breaking with respect to the C-C bond breaking in ethanol cation C2H5OH+ is maximized in intense laser fields (10(13)-10(15) Wcm2) by open-loop and closed-loop optimization procedures. In the open-loop optimization, a train of intense laser pulses are synthesized so that the temporal separation between the first and last pulses becomes 800 fs, and the number and width of the pulses within a train are systematically varied. When the duration of 800 fs is filled with laser fields by increasing the number of pulses or by stretching all pulses in a triple pulse train, the relative yield of the C-O bond breaking becomes significantly large. In the closed-loop optimization using a self-learning algorithm, the four dispersion coefficients or the phases of 128 frequency components of an intense laser pulse are adopted as optimized parameters. From these optimization experiments it is revealed that the yield ratio of the C-O bond breaking is maximized as far as the total duration of the intense laser field reaches as long as approximately 1 ps and that the intermittent disappearance of the laser field within a pulse does not affect the relative yields of the bond breaking pathways.     

Time-dependent multiconfiguration theory for electronic dynamics of molecules in intense laser fields: a description in terms of numerical orbital functions

The equations of motion (EOMs) for spin orbitals in the coordinate representation are derived within the framework of the time-dependent multiconfiguration theory developed for electronic dynamics of molecules in intense laser fields. We then tailor the EOMs for diatomic (or linear) molecules to apply the theory to the electronic dynamics of a hydrogen molecule in an intense, near-infrared laser field. Numerical results are presented to demonstrate that the time-dependent numerical multiconfiguration wave function is able to describe the correlated electron motions as well as the ionization processes of a molecule in intense laser fields.     

TD-CI simulation of the strong-field ionization of polyenes

Ionization of ethylene, butadiene, hexatriene, and octatetraene by short, intense laser pulses was simulated using the time-dependent single-excitation configuration-interaction (TD-CIS) method and Klamroth's heuristic model for ionization (J. Chem. Phys.2009, 131, 114304). The calculations used the 6-31G(d,p) basis set augmented with up to three sets of diffuse sp functions on each heavy atom as well as the 6-311++G(2df,2pd) basis set. The simulations employed a seven-cycle cosine pulse (ω = 0.06 au, 760 nm) with intensities up to 3.5 × 10(14) W cm(-2) (E(max) = 0.10 au) directed along the vector connecting the end carbons of the linear polyenes. TD-CIS simulations for ionization were carried out as a function of the escape distance parameter, the field strength, the number of states, and the basis set size. With a distance parameter of 1 bohr, calculations with Klamroth's heuristic model reproduce the expected trend that the ionization rate increases as the molecular length increases. While the ionization rates are too high at low intensities, the ratios of ionization rates for ethylene, butadiene, hexatriene, and octatetraene are in good agreement with the ratios obtained from the ADK model. As compared to earlier work on the optical response of polyenes to intense laser pulses, ionization using Klamroth's model is less sensitive to the number of diffuse functions in the basis set, and only a fraction of the total possible CIS states are needed to model the strong field ionizations.     

Description of molecular dynamics in intense laser fields by the time-dependent adiabatic state approach: application to simultaneous two-bond dissociation of CO2 and its control

We theoretically investigated the dynamics of structural deformations of CO(2) and its cations in near-infrared intense laser fields (approximately 10(15) W cm(-2)) by using the time-dependent adiabatic state approach. To obtain "field-following" adiabatic potentials for nuclear dynamics, the electronic Hamiltonian including the interaction with the instantaneous laser electric field is diagonalized by the multiconfiguration self-consistent-field molecular orbital method. In the CO(2) and CO(2+) stages, ionization occurs before the field intensity becomes high enough to deform the molecule. In the CO(2)(2+) stage, simultaneous symmetric two-bond stretching occurs as well as one-bond stretching. Two-bond stretching is induced by an intense field in the lowest time-dependent adiabatic state |1> of CO(2)(2+), and this two-bond stretching is followed by the occurrence of a large-amplitude bending motion mainly in the second-lowest adiabatic state |2> nonadiabatically created at large internuclear distances by the field from |1>. It is concluded that the experimentally observed stretched and bent structure of CO(2)(3+) just before Coulomb explosions originates from the structural deformation of CO(2)(2+). We also show in this report that the concept of "optical-cycle-averaged potential" is useful for designing schemes to control molecular (reaction) dynamics, such as dissociation dynamics of CO(2), in intense fields. The present approach is simple but has wide applicability for analysis and prediction of electronic and nuclear dynamics of polyatomic molecules in intense laser fields.     

Communication: phase space approach to laser-driven electronic wavepacket propagation

We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the periodic von Neumann basis with biorthogonal exchange recently introduced for the calculation of the energy eigenstates of time-independent quantum systems [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. (in press) [e-print arXiv:1201.2299v1]]. While the individual elements in this basis set are time-independent, a small subset is chosen in a time-dependent manner to adapt to the evolution of the wavepacket in phase space. We demonstrate the accuracy and efficiency of the present propagation method by calculating the electronic wavepacket in a one-dimensional soft-core atom interacting with a superposition of an intense, few-cycle, near-infrared laser pulse and an attosecond extreme-ultraviolet laser pulse.     

Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions

Dynamics of molecules in an intense laser field is studied in terms of the quantum electronic wave packet coupled with classical nuclear motions. The equations of motion are derived taking a proper account of molecular interactions with the vector potential of a classical electromagnetic field, along with the nonadiabatic interaction due to the breakdown of the Born-Oppenheimer approximation. With the aid of electronic structure calculations, the present method enables us to track, in an ab initio manner, the dynamics of polyatomic molecules in an intense field. Preliminary calculations are carried out for the vibrational state of LiF and a collision of Li+F under an intense laser pulse, which are limited to the domain of no ionization.     

Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: an ab initio electronic state study

A theory of quantum electron wavepacket dynamics that nonadiabatically couples with classical nuclear motions in intense optical fields is studied. The formalism is intended to track the laser-driven electron wavepackets in terms of the linear combination of configuration-state functions generated with ab initio molecular orbitals. Beginning with the total quantum Hamiltonian for electrons and nuclei in the vector potential of classical electromagnetic field, we reduce the Hamiltonian into a mixed quantum-classical representation by replacing the quantum nuclear momentum operators with the classical counterparts. This framework gives equations of motion for electron wavepackets in an intense laser field through the time dependent variational principle. On the other hand, a generalization of the Newtonian equations provides a matrix form of forces acting on the nuclei for nonadiabatic dynamics. A mean-field approximation to the force matrix reduces this higher order formalism to the semiclassical Ehrenfest theory in intense optical fields. To bring these theories into a practical quantum chemical package for general molecules, we have implemented the relevant ab initio algorithms in it. Some numerical results in the level of the semiclassical Ehrenfest-type theory with explicit use of the nuclear kinematic (derivative) coupling and the velocity form for the optical interaction are presented.     

Resonant multiphoton ionization of xenon in intense sub-ps-laser pulses

We observe that resonant ionization plays a dominant role in the multiphoton ionization (MPI) of xenon at wavelengths around 600 nm, irrespective of the detuning of multiples of the photon energy from excited states of the undisturbed atom. Angular distributions of energy resolved photoelectrons allow to identify excited states which are strongly ac-Stark shifted in the intense laser field and which serve as intermediate resonances in MPI processes. Angular distributions measured at different wavelengths show that the ac-Stark shift of excited states can be larger than the photon energyhω. Our results support the model proposed by Freeman et al.     

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schr?dinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.     

Theoretical description of dissipative vibrational dynamics using the density matrix in the state representation

Ultrafast dissipative dynamics of vibrational degrees of freedom in molecular systems in the condensed phase are studied here. Assuming that the total system is separable into a relevant part and a reservoir, the dynamics of the relevant part can be described by means of a reduced statistical density operator. For a weak or intermediate coupling between the relevant part and the reservoir, it is possible to derive a second-order master equation for this operator. Using a representation of the reduced statistical operator in an appropriate molecular basis set, vibrational dynamics in a variety of potential energy surfaces can be studied. In the numerical calculations, we focus on the dissipative dynamics under the influence of external laser fields. In the first example, vibrational wave-packet dynamics and time-resolved pump-probe spectroscopy of molecular systems with nonadiabatically coupled excited-state potential energy surfaces is presented. In the second part, we show how an intense laser field modifies the wave-packet motion onto two radiatively coupled potential energy surfaces. Finally, the controlled preparation of definite vibrational states in a triatomic molecule with infrared laser pulses is considered taking relaxation and dephasing processes into account. © 1996 John Wiley & Sons, Inc.     

超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。     

Explicit symplectic integrators of molecular dynamics algorithms for rigid-body molecules in the canonical, isobaric-isothermal, and related ensembles

The authors propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isobaric-isothermal ensembles. They also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, they can perform a MD simulation more stably than by conventional nonsymplectic algorithms. They applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. They found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.