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.     

Sub‐cycle Dynamics of High Harmonic Generation of Ne Atoms Excited by Attosecond Pulses and Driven by Near‐infrared Laser Fields: A Self‐Interaction‐Free TDDFT Approach

In the framework of the self‐interaction‐free time‐dependent density‐functional theory (TDDFT), we have performed three‐dimensional ab initio calculations of Ne atoms in near‐infrared (NIR) laser fields subject to excitation by a single extreme ultraviolet (XUV) attosecond pulse (SAP). The TDDFT equations are solved accurately and efficiently by means of the time‐dependent generalized pseudo spectral (TDGPS) method. We have explored the transient dynamical behavior of the sub‐cycle high harmonic generation (HHG) for transitions from the excited states to the ground state and found oscillation structures with respect to the time delay between the SAP and NIR fields. We investigate the harmonic emission spectrum from singly excited state 2p3s, 2p4s, 2p3d, 2p5s, 2p4d and 2p6s, 2p5d and the virtual states 2p3p‐, 2p4f‐ and 2p4p+ as the function of time delay. We explore the sub‐cycle Stark shift phenomenon in NIR fields and its influence on the photon emission process. Our analysis reveals several novel features of the sub‐cycle transient HHG dynamics and spectra, the quantum interference pattern between different multiphoton excitation pathways, and we identify the mechanisms responsible for the observed peak splitting in the photon emission spectra.     

Real-time propagation of the reduced one-electron density matrix in atom-centered orbitals: application to multielectron dynamics of carbon clusters C(n) in the strong laser pulses

We present a time-dependent density functional theory (TDDFT) study on the electron dynamics of small carbon clusters C(n) (n = 9, 10) exposed to a linearly polarized (LP) or circularly polarized (CP) oscillating electric field of ultrafast laser with moderate laser intensity. The multielectron dynamics is described by propagating the reduced one-electron density matrix in real-time domain. The high harmonic generation (HHG) spectra of emission as well as the time evolution of atomic charges, dipole moments and dipole accelerations during harmonic generation are calculated. The microscopic structure-property correlation of carbon chains is characterized. It is found that the electron responses of C(n) to the laser field oscillation become nonadiabatic as the field intensity is larger than 1.4 x 10(13) W/cm(2). The nonadiabatic multielectron effect is displayed by an explicit fluctuation on the induced atomic charges and the instantaneous dipole acceleration and by observing the additional peaks other than those predicted from the spectral selection rule in HHG spectra of C(n) as well. The origin of these additional peaks is elucidated. The atomic charges of C(n) in LP and CP laser pulses experience different type of oscillations as expected. In the linear structure C9, the atomic charges at the two ends experience larger amplitude oscillations than those near the chain center whereas the induced charges on each atom of C10 experience the equal amplitude oscillations in the CP laser pulse.     

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.     

Positioning of bound electron wave packets in molecules revealed by high-harmonic spectroscopy

By solution of the time-dependent two-electron Schr?dinger equation, we demonstrate that strong-field ionization in combination with electron correlation can localize bound electron wave packets in molecules. The wave packet creation is revealed by the emission spectrum in high-order harmonic generation, which is sensitive to the ionization and recombination phase difference between different ionization channels. For hydrogen molecules at stretched internuclear distance, we find that the ionization phase difference between the gerade and ungerade channels is in the range from π and 1.5π, indicating that the bound wave packet either is initially on the same side as the outgoing electron or is delocalized.     

Dynamic imaging of molecules using high order harmonic generation

We review recent progress towards imaging the electronic wavefunctions and nuclear dynamics of small molecules using the high order harmonics emitted when a molecule experiences an intense laser field. We illustrate that the essence of high harmonic emission is contained in the recombination amplitude between the continuum portion of the electronic wavefunction, that is formed through field ionization and which is accelerated and driven back to recollide in the laser field, and the bound electronic state. We review for the non-specialist some recent experimental and theoretical work dealing with high harmonic generation (HHG) in molecules. Particular attention is paid to two types of experiment recently performed in our group. The first of these types of experiment is the measurement of signatures of molecular electronic structure using HHG from molecules with a fixed orientation in space. The second is the use of HHG to track extremely fast proton rearrangement following ionization in light molecules, using the intrinsic temporal variation of the recolliding electron energy to extract these dynamics from measurements of the high harmonics.     

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na2: experiment and quantum mechanical calculations

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wave packets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na ₂ ⁺ ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecular ion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na⁺-transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excited bound Rydberg state. This conclusion is supported by the theoretical simulation.     

Excitation and charge transfer in He++H collisions

For the conflictive case of He⁺+H collisions, we present a norm-method optimization of the parameters included in the (often used) two-electron translation factor of Errea et al. As surmised in a previous publication, a strong cut-off is needed at short internuclear distances to prevent the translation factor from marring the properities of the molecular expansion there. With a basis of 16 molecular states, we present the first calculations including translation factors, of total and partial charge exchange and excitation cross sections in He⁺+H collisions, as well as the alignment parameter A₂₀ for hydrogen excitation. Good agreement with experiment is reached up to the energy range where ionization and charge exchange cross sections are comparable.     

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     

Electron response of metallic clusters to strong laser pulses and energetic ion collisons

We investigate the electron dynamics of Na₉ ⁺ excited by strong fs laser pulses and fast proton collisions. Non-perturbative numerical simulations are performed using time-dependent density-functional methods on a semiclassical and fully quantal level. Both excitation mechanisms induce pronounced dipole oscillations accompanied by rapid ionization.     

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     

Long-range energy transfer and ionization in extended quantum systems driven by ultrashort spatially shaped laser pulses

The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schr?dinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has been explored within a linear three-dimensional model, including the two z coordinates of the electrons and the internuclear distance R. An efficient energy transfer from the laser-excited H atom (atom A) to the other H atom (atom B) and the ionization of the latter have been found. It has been shown that the physical mechanisms of the energy transfer as well as of the ionization of atom B are the Coulomb attraction of the laser driven electron of atom A by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions strongly overlap in the domain of atom B.     

High-order Harmonic Generation of Aligned Acetylene in Elliptically Polarized Strong Laser Fields?

We perform an experimental study on high-order harmonic generation (HHG) of aligned acetylene molecules induced by a 35-fs 800-nm strong laser field, by using a home-built HHG spectrometer. It is observed that the molecular HHG probability declines with increasing the laser ellipticity, which is in consistence with the deduction from the well-known tunneling-plus-rescattering scenario. By introducing a weak femtosecond laser pulse to nonadiabatically align the molecules, we investigated the molecular orbital effect on the HHG in both linearly and elliptically polarized driving laser fields. The results show that the harmonic intensity is maximum for the molecular axis aligned perpendicularly to the laser electric field. It indicates that both the highest occupied molecular orbitals (HOMO) and HOMO-1 contribute to the strong-field HHG of acetylene molecules. Our study should pave the way for understanding the interaction of molecules with ultrafast strong laser fields.     

Electronic optical response of molecules in intense fields: comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches

Time-dependent Hartree-Fock (TD-HF) and time-dependent configuration interaction (TD-CI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (760 nm, 3 cycles). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TD-CI simulations using singly excited states with and without perturbative corrections for double excitations [TD-CIS(D) and TD-CIS, respectively] are generally in good agreement with the TD-HF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than approximately 0.1. The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TD-HF and TD-CI calculations cannot model ionization directly. The TD-HF and TD-CIS simulations are in good accord because the excitation energies obtained by linear response TD-HF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CIS excitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CIS excitation energies, the TD-CIS(D) response is generally stronger than TD-CIS.     

Resonant Ionic,Covalent Bond,and Steric Characteristics Present in 1Σu+ States of Li2

The molecular bonding in the excited states of the alkali dimers involves the resonant ionic, covalent bond and steric interactions. We show here the case of the ¹Σ_u⁺ states of Li₂ by ab initio calculation. These interactions as functions of the internuclear distance lead to complex potential energy curves, providing an important application for high resolution laser spectroscopy. The spectroscopic constants for the 4 and 5 ¹Σ_u⁺ states are obtained for the first time.     

Many-photon dynamics of photobleaching

A detailed dynamical theory of photobleaching by periodical sequences of laser pulses is presented. The theory is used for interpretation of recent experiments with pyrylium salts. Our simulations are based on first-principles simulations of photoabsorption cross-sections and on empirical rate constants. Two competitive channels of photobleaching, namely, photobleaching from the lowest excited singlet and triplet states and from higher excited states, are found to explain different intensity dependences of the photobleaching rates in different samples. The process includes two-photon excitation from the ground state to the first or second excited singlet states and one-photon excitation from the first singlet or triplet states to higher excited states. The fluorescence follows double-exponential dynamics with two characteristic times. The first and the shorter one is the equilibrium settling time between the ground and the lowest triplet states. The second characteristic time, the time of photobleaching, is responsible for the long-term dynamics. The effective rate of photobleaching from the first excited singlet and lowest triplet states depends differently on the irradiance in comparison with the photobleaching in higher states. The first channel is characterized by a quadratic intensity dependence in contrast to the second channel that shows a cubic dependence. The competition between these photobleaching channels is very sensitive to the rate constants as well as to the repetition rate, the pulse duration, and the peak intensity. The double-exponential decay of the fluorescence is explained by the spatial inhomogeneity of the light beam. The findings in this work are discussed in terms of the possibility of using many-photon-induced photobleaching for new three-dimensional read-write devices.     

Radiative excitation of the harmonic oscillator with applications to stereomutation in chiral molecules

We present theoretical considerations and quantitative numerical simulations of the coherent radiative excitation of chiral molecules exhibiting a double well potential in the electronic ground state (with stable enantiomers) and a harmonic oscillator potential with achiral minimum geometry in the excited electronic state following a scheme proposed in [33]. The one-dimensional short time dynamics is presented on the femtosecond time scale. We demonstrate the phenomena of quasiexponential, radiationless decay of the survival probability in the excited electronic state by simple harmonic oscillator wave packet motion, as well as coherent periodic chiral stereomutation. The differences and similarities of the excited state harmonic oscillator dynamics with two quite different ground state potentials are discussed. A designed pulse sequence allows for chemically efficient laser controlled stereomutation with high enantiomeric specificity. The results are discussed in relation to Friedrich Hund's early work on stereomutation by tunneling and in relation to our current understanding of chiral molecules including dynamical chirality and anharmonic vibrational dynamics on the femtosecond time scale and the violation of parity and other fundamental symmetries.     

Photoelectron spectroscopy of S1 toluene: I. Photoionization propensities of selected vibrational levels in S1 toluene

Laser photoelectron spectra have been obtained following the preparation of eight vibrational states in S(1) toluene. For four of the vibrational states (up to approximately 550 cm(-1) excess energy) excitation and ionization with nanosecond laser pulses give rise to photoelectron spectra with well-resolved vibrational peaks. For the other states (>750 cm(-1) excess energy) the photoelectron spectra show a loss of structure when nanosecond pulses are used, as a result of intramolecular dynamics [see Whiteside et al., J. Chem. Phys. 123, 204317 (2005), following paper]. A number of vibrational peaks in the photoelectron spectra are assigned, and we find that the common series of ion vibrational peaks observed following the ionization of p-fluorotoluene in various S(1) vibrational states is not reproduced in toluene.