Single Active Electron Model Research Articles

Comparative study of photoelectron momentum distributions from Kr and CO2 near a backward rescattering caustic by carrier-envelope-phase mapping

We study carrier-envelope-phase- (CEP-) dependent photoelectron momentum distributions (PEMDs) of Kr atoms and randomly oriented ${\mathrm{CO}}_{2}$ molecules exposed to sub-two-cycle intense infrared fields with linear polarization. The adiabatic theory predicts that, at fixed laser parameters (intensity, pulse duration, and CEP), the PEMDs for targets with equal ionization potentials considered across a backward rescattering caustic have identical shapes and only their absolute values depend on the target. We choose Kr and ${\mathrm{CO}}_{2}$ as targets with almost identical ionization potentials (approximately $14$ eV) to explore this behavior of PEMDs. We find that the measured PEMDs for Kr and ${\mathrm{CO}}_{2}$ have cutoff structures, which are associated with the caustics, with identical decaying profiles. We also reveal that CEP-dependent PEMDs around the cutoff exhibit target dependence, reflecting the differences in the differential cross sections (DCSs) of elastic rescattering and tunneling ionization rates. Furthermore, we extract the DCSs from the measured PEMDs around the cutoffs at different CEPs based on the adiabatic theory. The extracted DCSs agree with ones calculated by using the single-active-electron (SAE) scattering model, which includes all multiple-scattering processes, with orientation averaging for ${\mathrm{CO}}_{2}$. In contrast, the independent-atom model, which only considers single-scattering processes, cannot reproduce the extracted DCSs of ${\mathrm{CO}}_{2}$ at low scattering momenta. This finding indicates that multiple scattering is not negligible in the momentum range of 1.5--2.5 a.u. The extracted DCSs also show interference features assigned to multicenter scattering of O-O and C-O. These results confirm that the signature of electron interference is retained after orientation averaging, indicating that the internuclear distances of the constituent atoms can be retrieved from the CEP-dependent PEMDs for randomly oriented molecules using the SAE model.

High-order harmonic generation in the water window from mid-IR laser sources

We investigate the harmonic response of neon atoms to mid-IR laser fields ($2000--3000$ nm) using a single active electron (SAE) model and the fully ab initio all-electron $R$ matrix with time dependence (RMT) method. The laser peak intensity and wavelength are varied to find suitable parameters for high-harmonic imaging in the water window. Comparison of the SAE and RMT results shows qualitative agreement between them as well as parameters such as the cutoff frequency predicted by the classical three-step model. However, there are significant differences in the details, particularly in the predicted conversion efficiency. These details indicate the possible importance of multielectron effects, as well as a strong sensitivity of quantitative predictions on specific aspects of the numerical model.

Dynamic Core Polarization in High Harmonic Generation from Solids: The Example of MgO Crystals.

Previously, the strong field processes in solids have always been explained by the single-active-electron (SAE) model with a frozen core excluding the fluctuation of background electrons. In this work, we demonstrate the strong field induced dynamic core polarization effect and propose a model for revealing its role in high harmonic generation (HHG) from solids. We show that the polarized core induces an additional polarization current beyond the SAE model based on the frozen cores. It gives a new mechanism for HHG and leads to new anisotropic structures, which are experimentally observed with MgO. Our experiments indicate that the influences of dynamic core polarization on HHG are obvious for both linearly and elliptically polarized laser fields. Our work establishes the bridge between the HHG and the dynamic changes of the effective many-electron interaction in solids, which paves the way to probe the ultrafast electron dynamics.

Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation.

We report successful implementation of the time-dependent second-order many-body perturbation theory using optimized orthonormal orbital functions called time-dependent optimized second-order many-body perturbation theory to reach out to relatively larger chemical systems for the study of intense-laser-driven multielectron dynamics. We apply this method to strong-field ionization and high-order harmonic generation of Ar. The calculation results are benchmarked against ab initio time-dependent complete-active-space self-consistent field, time-dependent optimized coupled-cluster double, and time-dependent Hartree-Fock methods, as well as a single active electron model to explore the role of electron correlation.

Wavepacket golden rule treatment of interparticle Coulombic decay in paired quantum dots.

The interparticle Coulombic decay process in paired quantum dots is studied by electron dynamics calculations. We consider a pair of Coulomb-coupled one-electron charged gallium arsenide quantum dots embedded in a nanowire. The two-electron decay process is approximately described by a single active electron model. Within this model, we employ the time-dependent wavepacket approach to the Fermi golden rule (introduced in the context of vibrational predissociation) to calculate autoionization rates, which are compared to exact rates obtained from fully correlated two-electron dynamics calculations. We found that the approximate decay rates agree well with the exact results in the limit of sufficiently separated quantum dots. Finally, we explore whether the short-range behavior of the new model can be further enhanced by the inclusion of local exchange effects by means of regularization of the Coulomb-potential based on a Jastrow-Slater wavefunction. The proposed method may open a route to study the interparticle Coulombic decay in more intricate systems, e.g., paired metal-nanoparticle-quantum dot systems.

Rescattering photoelectron spectroscopy of the CO2 molecule: Progress towards experimental discrimination between theoretical target-structure models

Author(s): Okunishi, M; Ito, Y; Sharma, V; Aktar, S; Ueda, K; Lucchese, RR; Dnestryan, AI; Tolstikhin, OI; Inoue, S; Matsui, H; Morishita, T | Abstract: Photoelectron momentum distributions (PEMDs) generated in strong-field ionization of randomly oriented CO2 molecules by intense infrared laser pulses at 1300-, 1450-, and 1650-nm wavelengths are measured experimentally and analyzed theoretically. The experimental PEMDs extracted along the outermost backward rescattering caustic are well reproduced by theoretical calculations based on the recently derived factorization formula with an analytical returning photoelectron wave packet (RWP). The sensitivity of the theoretical results to the target structure models used in the calculations is investigated. It is shown that RWPs obtained in the single-active-electron (SAE) approximation and by the Hartree-Fock method have only minor differences. On the other hand, differential cross sections (DCSs) for elastic scattering of a photoelectron on the parent molecular ion calculated by ab initio, SAE, and independent-atom model methods are considerably different. This difference almost disappears after averaging over molecular orientations, so the present experiment does not enable us to discriminate between the different target structure models. However, we show that such a discrimination should become possible by measuring PEMD with aligned molecules. This will provide an access to the rich target structure information contained in the DCS.

Energy band splitting and high-order harmonic generation from a doped semiconductor

We theoretically investigate the high-order harmonic generation (HHG) from laser–solid interaction in a doped semiconductor by solving the one-dimensional time-dependent Schrödinger equation within the single active electron model. The results show that the energy band of the valence and the low conduction band can be split into a small band in the doped semiconductor. The splitting band gap can be controlled by changing the depth of the potential well of the doped semiconductor, and the second HHG plateau can be enhanced. We also demonstrate the energy band structures in coordinate space with different numbers of dopant. Time-dependent population imaging is used to illustrate the change of the splitting band gap with different depths of the potential well of the doped semiconductor.

Quantum coherent control of the photoelectron angular distribution in bichromatic-field ionization of atomic neon

We investigate the coherent control of the photo\-electron angular distribution in bichromatic atomic ionization. Neon is selected as target since it is one of the most popular systems in current gas-phase experiments with free-electron lasers (FELSs). In particular, we tackle practical questions, such as the role of the fine-structure splitting, the pulse length, and the intensity. Time-dependent and stationary perturbation theory are employed, and we also solve the time-dependent Schr\"odinger equation in a single-active electron model. We consider neon ionized by a FEL pulse whose fundamental frequency is in resonance with either $2p-3s$ or $2p-4s$ excitation. The contribution of the non\-resonant two-photon process and its potential constructive or destructive role for quantum coherent control is investigated.

Differential cross sections for ionizations of H and H2 by 75 keV proton impact

We have calculated total, partial and fully differential cross sections (FDCSs) for ionizations of H and H2 by 75 keV proton impact within the framework of the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximation. Applying the single active electron model, the interaction between the projectile and the target ion is taken into account in the impact parameter picture. Extension of the CDW-EIS model to the molecular target is performed using the two-effective center approximation. The obtained results are compared with those of experimental and other theoretical data when available. The agreements between the theories and the experimental data are generally reasonable except for some cases of the FDCSs.

Numerical studies of light-matter interaction driven by plasmonic fields: The velocity gauge

Theoretical approaches to strong field phenomena driven by plasmonic fields are based on the length gauge formulation of the laser-matter coupling. From the theoretical viewpoint it is known there exists no preferable gauge and consequently the predictions and outcomes should be independent of this choice. The use of the length gauge is mainly due to the fact that the quantity obtained from finite elements simulations of plasmonic fields is the plasmonic enhanced laser electric field rather than the laser vector potential. In this paper we develop, from first principles, the velocity gauge formulation of the problem and we apply it to the high-order harmonic generation (HHG) in atoms. A comparison to the results obtained with the length gauge is made. It is analytically and numerically demonstrated that both gauges give equivalent descriptions of the emitted HHG spectra resulting from the interaction of a spatially inhomogeneous field and the single active electron (SAE) model of the helium atom. We discuss, however, advantages and disadvantages of using different gauges in terms of numerical efficiency.

Spatial interference during the ionization of noble gas atoms by few-cycle XUV laser pulses

We have investigated the spatial interference effects, which appear during the ionization of noble gas atoms by few-cycle XUV laser pulses. By using ab initio calculations, and single active electron model potentials, we have studied how the spatial interference pattern is influenced by the atomic species of the target.

Recombination-amplitude calculations of noble gases, in both length and acceleration forms, beyond the strong-field approximation

Transition of an electron from a free to a bound state is critical in determining the qualitative shape of the spectrum in high-order harmonic generation (HHG), and in tomographic imaging of orbitals. We calculate and compare the recombination amplitude, from a continuum state described by a plane wave and an outgoing scattering eigenstate, to the bound state for the noble gases that are commonly used in HHG. These calculations are based on the single active electron model and the Hartree-Fock-Slater method, using both the length form and the acceleration form of the dipole matrix element. We confirm that the recombination amplitude versus emitted photon energy strongly depends upon the wavefunction used to describe the free electron. Depending on the choice of the wavefunction and the dipole form, the square of the absolute value of the recombination amplitude can differ by almost two orders of magnitude near the experimentally measured Cooper minima. Moreover, only the outgoing scattering eigenstates with the length form roughly predict the experimentally observed Cooper minimum for Ar (~50 eV) and Kr (~85 eV). We provide a detailed derivation of the photorecombination cross sections (PRCSs) from photo ionization cross sections (PICSs) calculated by the relativistic random phase approximation (RRPA)., For Ar, Kr and Xe, compare the total PICSs calculated using our recombination amplitudes with that obtained from RRPA. We find that PICS calculated using the outgoing scattering eigenstates with the length form is in better agreement with the RRPA calculations than the acceleration form.

Polarization of high harmonic generated spectra in H+2ion

We study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as a function of the angle between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs in the first or second half of the emitted spectrum. In particular, the differences are accentuated for , while for higher angles, until the perpendicular orientation, almost all the harmonics present similar characteristics.

Control of the high harmonic generation spectra by changing the molecule-laser field relative orientation

The time dependent Schrödinger equation of a homonuclear diatomic molecule in the presence of a linearly polarized laser field is numerically solved by means of a split-operator parallel code. The calculations are carried out by assuming a single active electron model with fixed nuclei; a simplified two-dimensional model of the system is used. The highly nonlinear response of the electron wave function to the laser electric field stimulates the molecule to emit electromagnetic radiation consisting of a wide plateau of odd harmonics of the laser field. It is shown that the emitted spectrum can be finely controlled by changing the angle between the laser electric field and the molecular axis; this can be used to achieve a tunable source of high frequency radiation.

Generation of an isolated sub-100 attosecond pulse in the water-window spectral region

We propose a scheme to generate isolated attosecond pulses in the water-window spectral region. Based on the numerical solutions of the single active electron model, we investigate high-order harmonic generation in helium atoms driven by a multi-cycle two-colour optical field synthesized by an intense 2000 nm, 20 fs pulse and its frequency-doubled pulse. When the latter is slightly detuned and properly phase shifted with respect to the fundamental laser pulse, an ultra-broad extreme ultraviolet supercontinuum with a spectral width of 130 eV can be generated in the 270–400 eV spectral regions. A supercontinuum from 280–340 eV in the water window can be selected to yield an isolated 67 attosecond pulse without employing any phase compensation. This water window coherent x-ray pulse with less than 100 attosecond duration is a potential tool for studying the ultrafast electronic dynamics of biological samples in water.

Perturbation theory analysis of attosecond photoionization

Ionization of an atom by a few-cycle attosecond xuv pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. Within the PT approach, we present an ab initio parametrization of the ionized electron angular distribution (AD) using rotational invariance and symmetry arguments. This parametrization gives analytically the dependence of the AD on the carrier envelope phase (CEP), the polarization of the pulse, and on the ionized electron momentum direction, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$. For the general case of an elliptically polarized pulse, we show that interference of the first- and second-order transition amplitudes causes a CEP-dependent asymmetry (with respect to $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}\ensuremath{\rightarrow}\ensuremath{-}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$) and both elliptic and circular dichroism effects. All of these effects are maximal in the polarization plane and depend not only on the CEP but also on the phase of dynamical atomic parameters that enter our parametrization of the AD. Within the single active electron model of an atom, for an initial $s$ or $p$ state we define all dynamical parameters in terms of radial matrix elements (analytic expressions for which are given for the Coulomb and zero-range potentials). For ionization of the H atom by linearly polarized pulses, our PT results are in excellent agreement with results of numerical solutions of the time-dependent Schr\"odinger equation of Peng et al. [New J. Phys. 10, 025030 (2008)]. Also, our numerical results show that the asymmetries and dichroism effects at low electron energies have a different physical origin from those at high electron energies. Moreover, our results for Gaussian and cosine-squared pulse shapes are in good qualitative agreement. Finally, we show that our analytic formulas may prove useful for determining few-cycle extreme ultraviolet (xuv) pulse characteristics, such as the CEP and the polarization.

High-resolution spatial and temporal microscopy with intense-laser-induced rescattering electrons

Following the recent developments in intense laser techniques, ultrafast phenomena of the order of a few femtoseconds to attoseconds have been discussed. We are developing new methods for ultrafast imaging for transient atomic and molecular systems. We apply the recently developed quantitative rescattering theory together with a fitting procedure to extract effective potentials as well as elastic differential cross sections of the target ions with free electrons within the single active electron model. Using experimental photoelectron spectra for rare gas atoms of Ne, Ar, Kr, and Xe, we show that the extracted atomic potentials are in good agreement with those obtained theoretically. The current method of retrieval does not require precise knowledge of the peak laser intensities. The results show that accurate charge distribution of target ions indeed can be retrieved from experimental photoelectron spectra generated by lasers, thus paving the way for using infrared laser pulses for dynamic chemical imaging of transient states of molecules with temporal resolution of few femtoseconds.

Dynamic resonances and tunnelling in the multiphoton ionization of argon

We present results of wavepacket simulations for multiphoton ionization in argon. A single active electron model is applied to estimate the single-electron ionization rates and photoelectron energy distributions for λ = 390 nm light with intensities up to I = 2 × 1014 W cm−2. The multiphoton ionization rates are compared with R-matrix Floquet calculations and found to be in very good agreement. The photoelectron energy distribution is used to study the nature of ionization at the higher intensities. Our results are consistent with recent calculations and experiments which show the imprint of the tunnelling process in the multiphoton regime. For few-cycle intense pulses, we find that the strong modulation of intensity and increased bandwidth leads to dynamic mixing of the 3d and 5s resonances.

Momentum distribution of highly charged ions formed by strong laser fields

Momentum distributions of highly charged ions produced by a strong laser pulse with duration of ∼ 200 fs and maximum intensity of ∼50-70 PW/cm2 are studied. Due to the spatial variation of the laser intensity within the beam focus, different charge states are produced during a single laser shot. The measured widths of the momentum distribution of the product ions exhibit a linear dependence on the ionization potential of the ions for various rare gas atoms. Such a linear dependence is analyzed theoretically using the single active electron model.

Momentum distribution of multiply charged ions produced by intense(50–70‐PW∕cm2)lasers

We investigate both theoretically and experimentally the momentum distribution of multiply charged ions ionized by an intense multicycle laser field with a maximum intensity of $\ensuremath{\sim}(50--70)\phantom{\rule{0.3em}{0ex}}\mathrm{PW}∕{\mathrm{cm}}^{2}$. Ions with different charge states are produced during a single laser shot due to a spatial variation of the laser intensity within the beam focus. The measurements show approximately a simple linear relation between the width of the momentum distributions and the ionization potential of the ions. Such a power law scaling appears to be universal for various rare gas atoms used (He, Ne, Ar). We analyze this ionization dynamics using a quasiclassical tunneling theory for a single active electron model assuming that the interaction between electrons is negligible in such a strong field limit. We show that for the relatively long pulses used in the present work ($\ensuremath{\sim}200\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ or $\ensuremath{\sim}80\phantom{\rule{0.3em}{0ex}}\text{cycles}$) the effect of the laser envelope plays an important role in the ionization process.