Role of higher excited electronic states on high harmonic generation in H2(+)--a time-independent Hermitian Floquet approach

We have theoretically studied the role of high-lying molecular electronic states on the high harmonic generation (HHG) in H(2)(+) within the framework of a time-independent Hermitian nonperturbative three-dimensional Floquet technique for continuous wave monochromatic lasers of intensities of 2.59 × 10(13), 4.0 × 10(13), and 5.6 × 10(13) W∕cm(2), and wavelengths of 1064, 532, and 355 nm. To evaluate the HHG spectra, the resonance Floquet quasienergy and the Fourier components of the Floquet state corresponding to the initial vibrational-rotational level v = 0, J = 0 have been computed by solving the time-independent close-coupled Schro?dinger equation following the Floquet method. The calculations include seven molecular electronic states in the basis set expansion of the Floquet state. The electronic states considered, apart from the two lowest 1sσ(g) and 2pσ(u) states, are 2pπ(u), 2sσ(g), 3pσ(u), 3dσ(g), and 4fσ(u). All the concerned higher excited molecular electronic states asymptotically degenerate into the atomic state H(2 l) with l = 0, 1. The computations reveal signature of significant oscillations in the HHG spectra due to the interference effect of the higher molecular electronic states for all the considered laser intensities and wavelengths. We have attempted to explain, without invoking any ionization, the dynamics of HHG in H(2)(+) within the framework of electronic transitions due to the electric dipole moments and the nuclear motions on the field coupled ground, the first and the higher excited electronic states of this one-electron molecular ion.     

Multiphoton ion pair spectroscopy (MPIPS) with ultrashort laser pulses for the H2 molecule

Time-dependent Schr?dinger equation, TDSE, simulations have been performed in order to prepare and study via MPIPS the evolution of vibrational wave packets on the ion pair electronic state potentials B'B1Sigma(u)(+) and Hh1Sigma(g)(+) of the H2 molecule. Using ab initio potential surfaces and transition moments, we present two- and three-photon excitation schemes with ultrashort pulses (tau 相似文献   

Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

A mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.

     

Ultrafast dynamics and coherent oscillations in ethylene and ethylene-d4 excited at 162 nm

The fifth harmonic (162 nm, 11 fs), generated in a short argon cell from 12 fs Ti-sapphire laser pulses, was used to excite C2H4 and C2D4 in the maximum of the first pi pi* transition. Around 10% of the molecules were excited to the pi3s Rydberg state instead. The subsequent motion of the wave packet, moving over the potentials from the Franck-Condon region down to the ground state, was monitored by nonresonant ionization at 810 nm with mass-selective detection of the ion yield. Five time constants (from approximately 20 fs in excited states to 0.6-11 ps in the hot ground state) and four coherent oscillations (CC stretch and torsion vibrations or hindered free rotation) were determined for each isotopomer. The initial relaxation follows a superposition of CC twist and stretch coordinates; this explains a surprisingly small deuterium isotope effect of the initial time constant (21 versus 24 fs). Also the vibrations in the Franck-Condon region have such a mixed character and a correspondingly small isotope shift. From the perpendicular minimum the wave packet reaches (within 17 or 21 fs for the two isotopomers) a conical intersection via a direction that also involves partial hydrogen migration. This is concluded from the detection of ethylidene (CH3CH), formed simultaneously with ground-state ethylene. This carbene isomerizes in the ground state within 0.6 ps (1.6 ps for CD3CD) to ethylene. Two time constants for dissociation (4.5 and 11 ps) in the hot ground state were also identified. The small yields of bimolecular reactions (photodimerization, addition reactions involving a "suddenly polarized" excited state, carbene reactions) are interpreted in terms of the short lifetimes. It is pointed out that the relaxation path starting from the Rydberg state merges into that from the pi pi* state; nevertheless, there is a wavelength dependence in the photochemistry of olefins, because due to a momentum effect the wave packet remembers from which state it came.     

New coherent state representation for the imaginary time propagator with applications to forward-backward semiclassical initial value representations of correlation functions

There have been quite a few attempts in recent years to provide an initial value coherent state representation for the imaginary time propagator exp(-betaH). The most notable is the recent time evolving Gaussian approximation of Frantsuzov and Mandelshtam [J. Chem. Phys. 121, 9247 (2004)] which may be considered as an expansion of the imaginary time propagator in terms of coherent states whose momentum is zero. In this paper, a similar but different expression is developed in which exp(-betaH) is represented in a series whose terms are weighted phase space averages of coherent states. Such a representation allows for the formulation of a new and simplified forward-backward semiclassical initial value representation expression for thermal correlation functions.     

Extended states of a shallow donor located near a semiconductor–insulator interface

Scattering of a conduction electron by a charged shallow donor located near a semiconductor–insulator interface in the semiconductor or by a charged center embedded in the insulator is considered within the model of a hydrogenlike atom in a semi-infinite space. The interface influence is allowed for by spatial confinement of the electron envelope wave function. The impurity electrostatic image at the interface is taken into account. The problem is separable in prolate spheroidal coordinates and thus is solvable exactly. A rapidly convergent expansion is proposed for the angular eigenfunctions. The radial eigenfunctions are calculated directly by numerical integration of the radial boundary value problem. Expansions of the scattering wave function and the scattering amplitude in terms of the eigenfunctions of the problem are obtained. Using the extended and localized state wave functions, the photoionization cross section of a shallow donor near a semiconductor–insulator interface is calculated. It is presented as a superposition of the oscillator strengths of transitions to the partial extended eigenstates that constitute the scattering wave function. Near the interface, the cross section is enhanced significantly and redistributed over the direction of photoionized electron escape. The photoionization threshold follows the localized state energy varying with the donor–interface distance. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 435–456, 1998     

The external-field approximation in quantum optics

A canonical transformation is presented in which the effect of a coherent, classical, externally applied field (represented by a Glauber coherent state) is transferred from the boundary conditions to the hamiltonian, resulting in the addition of an external, classical field to the hamiltonian, while still retaining in it the effect of internal radiation fields in a second-quantized form. This procedure justifies the use of the external-field approximation in cases where internal-radiation effects have to be retained to all orders in the correlation functions. Examples of such cases are (a) radiative damping of a collision-broadened molecular sample and (b) long-range correlations in near-critical conditions where retardation effects prevail in the intermolecular forces.     

Are there quantum beats from vacuum-induced coherence?

In a recent paper by Hegerfeldt and Plenio [1] it has been argued that for a certain class of V-level systems quantum beats could be observed even if the system was not in a coherent superposition of the upper levels. The beat frequency would be different to the upper level splitting. In their analysis, this was an effect of the quantum vacuum field which generated a coherent superposition of the upper levels in the course of the interaction. Their derivation is reanalyzed here using standard techniques which lead to a master-equation. Calculating the weak probe absorption spectrum, one finds that — as expected — the experimentally accessible, physical levels are the eigenstates of the combined system consisting of the atom and the vacuum which by definition do not couple. Thus, a coherent superposition will not be generated starting from a true, renormalized upper state and therefore quantum beating will only occur if an initial coherent superposition of renormalized upper levels is provided.This article was processed by the author using the LAT_EX style filepljour2 from Springer-Verlag.     

Dynamical symmetry analysis of ionization and harmonic generation of atoms in bichromatic laser pulses

Recently the effect of the relative phase ? in a high‐intensity (～10¹⁴ W/cm²) two‐color (bichromatic) CW laser with frequencies ω and 2ω on the high‐order harmonic generation (HHG) was studied within the framework of the non‐Hermitian quantum mechanics (NHQM) [Phys Rev A 2004, 69, 043404/1]. Here we emphasize the study of symmetries in bichromatic HHG spectra within the framework of the conventional Hermitian QM, and in particular by taking the duration of the laser pulse into consideration (an effect that has not been included in the non‐Hermitian studies due to the time asymmetry problem in NHQM). The phase dependence of HHG and intense‐field ionization probability in a 1D Xe atom with symmetric field‐free potential and symmetric initial wave function were studied numerically and analytically. From simulations based on a single‐particle response it can be seen that the HHG spectra is symmetric with respect to inversion in the relative phase between the two colors ? only if ionization is forbidden in the system and the laser pulse is an adiabatic one. The HHG spectra is symmetric with respect to a π‐shift in ? whenever the laser pulse is an adiabatic one, either for bound or open (ionized) systems. The ionization probability is symmetric both to inversion or π‐shift in ?; the component probabilities (right‐ and left‐ionization probabilities) have the same ?‐dependence, up to a shift of π. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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.     

A thermodynamic approach to studying the influence of viscoelasticity on the apparent coefficient of quadratic electrostriction

A problem encountered in quadratic electrostriction research in polymers is that viscoelasticity is usually not taken into account in theoretical predictions of intrinsic electrostriction whereas the apparent value obtained by experiment is a superposition of “true” electrostriction and spurious contributions from other cross-effects and viscoelasticity. A new approach is proposed to study how the “true” electrostriction constant is obscured by viscoelastic material behavior and to treat the influence of other relaxational phenomena in a systematic way. The method is purely macroscopic to ensure general applicability to different experimental situations and to avoid the use of any model or of assumptions on the molecular structure. Irreversible thermodynamics is used to derive the time-dependent equation of state of the viscoelastic dielectric. Once the dynamic equation of state has been obtained, all the tools that have been developed in the literature to study the irreversible thermodynamics of other systems, like fluids, for example, become directly applicable to the given problem. © 1996 John Wiley & Sons, Inc.     

Automerization reaction of cyclobutadiene and its barrier height: an ab initio benchmark multireference average-quadratic coupled cluster study

The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3 kcal mol(-1), which is higher than the best earlier theoretical estimate of 4.0 kcal mol(-1). This result is confirmed by including into the reference space the orbitals of the CC sigma bonds beyond the standard pi orbital space. It places the present value into the middle of the range of the measured data (1.6-10 kcal mol(-1)). An adiabatic singlet-triplet energy gap of 7.4 kcal mol(-1) between the transition state (1)B(tg) and the first triplet (3)A(2g) state is obtained. A low barrier height for the CBD automerization and a small DeltaE((3)A(2g),(1)B(1g)) gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Optimal control for maximally creating and maintaining a superposition state of a two-level system under the influence of Markovian decoherence

Reducing decoherence is an essential step toward realizing general-purpose quantum computers beyond the present noisy intermediate-scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields are applied to qubits are often adopted. We numerically study DD using a two-level model system (qubit) under the influence of Markovian decoherence by using quantum optimal control theory with slightly modified settings, in which the physical objective is to maximally create and maintain a specified superposition state in a specified control period. An optimal pulse is numerically designed while systematically varying the values of dephasing, population decay, pulse fluence, and control period as well as using two kinds of objective functionals. The decrease in purity due to the decoherence limits the ability to maintain a coherent superposition state; we refer to the state of maximal purity that can be maintained as the saturated value. The optimally shaped pulse minimizes the negative effect of decoherence by gradually populating and continuously replenishing the state of saturated purity.     

Effect of enzyme concentration on the dynamic behavior of a membrane-bound enzyme system

The dynamic behavior of the reaction-diffusion system, composed of glucose oxidase (EC 1.1.3.4) immobilized at a uniform concentration in a membrane, used as a glucose electrode is represented by a diffusion equation with a nonlinear reaction-term in one-dimensional space. The mathematical model is analyzed by computer simulation, that is, numerical integration of the equation under various initial and boundary conditions, to examine the effect of enzyme concentration on the response characteristics (responsiveness and linearity in response) of the electrode. The analysis of the responses of the system to stepwise changes in the boundary value (glucose concentration in simple solution) infers that the enzyme concentration governs the patterns of the spatial distributions of the substrates (glucose and dissolved oxygen) in steady states and transient responses. It is also revealed that the response characteristics of the electrode are optimized with concentration of immobilized enzyme and that the system establishes the steady states at the same spatial distributions of the substrates, regardless of the boundary value. The diffusion of the substrates and the oxygen concentration also have significant effects on the response characteristics of the electrode.     

A framework model based on the Smoluchowski equation in two reaction coordinates

The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a square on which diffusion takes place and an isolated empty state. Boundary conditions on opposite sides of the square correspond to transitions between the empty state and the square. The two-dimensional (2D) model can be reduced to a 1D single-particle model by adiabatic elimination. A finite element solution of the 2D boundary value problem is described. The method used to construct the 2D model can be adapted to state spaces that have been constructed by other authors to model K+ conduction through gramicidin, proton conduction through dioxolane-linked gramicidin, and chloride conduction through the bacterial H(+)-Cl- antiporter.     

Application of discrete variable representation to planar H(2) (+) 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 Schro?dinger 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.     

Influence de la Structure de Diverses Fonctions sur l'Evaluation de l'Energie de Correlation

The influence of various correlation functions, multiplying the monoelectronic space function, is studied and applied to the Helium atom and its isoelectronic series. We used Slater-type basis orbitals and the ground and first excited states have been studied, taking into account the virial and cusp conditions. In the ground state, a very good value for the correlation energy is obtained, using a function of the type For the excited states, this type of function overestimates the assumed value of the correlation energy.     

Polarized states of hybrid aligned nematic layers

Electric polarization arising in hybrid aligned nematic liquid crystal layers with rigid boundary conditions is studied numerically by solving the torques equation and Poisson equation. Three phenomena that give rise to the polarization are taken into account: flexoelectricity, surface polarization and adsorption of ions. The director orientation within the layer, as well as the distribution of electric potential and space charge density are calculated for layers deformed by an external magnetic field. The role of the ionic space charge is investigated. For a particular set of parameters of a model substance, the voltage arising between the layer surfaces varies from 10^-1 V (in an extremely pure nematic) to 10^-3 V (in material with a typical ion concentration). The surface polarization yields an additional voltage (of the order 10^-2 V) nearly independent of the ion concentration. The effect of simultaneous flexoelectric polarization and ion adsorption is evidently different from a linear superposition of their separate contributions. The flexoelectric polarization leads to partial separation of ions of opposite signs. In the case of positive flexoelectric coefficients, a thin sublayer of positive charge arises at the planar-orienting boundary plate. The negative charge is displaced towards the homeotropically aligning plate. The magnitude of this effect increases with the magnetic field. The surface phenomena introduce additional subsurface charges.