Single Active Electron Approximation Research Articles

Regulation of Continuum Harmonic Generation by Using Near-infrared Chirped Pulses

It has been known that the broadband of continuum harmonics, a regular periodicity or a wide smooth range, is essential for generating attosecond pulses. However, the high-order rescatterings of electrons (HOR) can significantly affect this important part of high-order harmonic spectra. In the present work, we apply the method suggested in our previous studies to limit the HOR effect on the continuum harmonics by using up-chirped pulses with frequency increasing in time to regulate the high-order harmonic generation of an asymmetric molecule such as CO subjected to a near-infrared laser. To do so, we numerically calculate the high-order harmonic spectra using the time-dependent wave functions obtained within the framework of the single-active electron approximation. To analyze and regulate the HOR effect, we use the time-frequency analysis together with the kinetic energy maps obtained from the equation of electron motion in the laser electric field. These techniques reveal the high-order harmonic dynamics, especially the effect of chirped pulse on the manifestation of continuum harmonics. Based on this, we release the notice on choosing appropriate parameters to obtain the optimal continuum range of harmonics. Although the detailed analysis is given for the CO molecule, the method suggested is applicable for other polar molecules.

Strong-field molecular ionization beyond the single active electron approximation.

This work explores quantitative limits to the single-active electron approximation, often used to deal with strong-field ionization and subsequent attosecond dynamics. Using a time-dependent, multiconfiguration approach, specifically the time-dependent configuration interaction method, we solve the time-dependent Schrödinger equation for the two-electron dihydrogen molecule with the possibility of tuning at will the electron-electron interaction by an adiabatic switch-on/switch-off function. We focus on signals of the single ionization of H2 under a strong near-infrared, four-cycle, linearly polarized laser pulse of varying intensity and within a vibrationally frozen molecular model. The observables we address are post-pulse total ionization probability profiles as a function of the laser peak intensity. Three values of the internuclear distance R taken as a parameter are considered, R = Req = 1.4 a.u. for the equilibrium geometry of the molecule, R = 5.0 a.u. for an elongated molecule, and R = 10.2 a.u. for a dissociating molecule. The most striking observation is the non-monotonous behavior of the ionization probability profiles at intermediate elongation distances with an instance of enhanced ionization and one of partial ionization quenching. We give an interpretation of this in terms of a resonance-enhanced-multiphoton ionization mechanism with interfering overlapping resonances resulting from excited electronic states.

Multielectron effect in XUV light-driven strong-field ionization beyond the dipole approximation

By applying the time-dependent density-functional theory, we theoretically investigate the multielectron effect in the extreme UV (XUV) light-driven ionization of atoms and diatomic molecules beyond the dipole approximation. Compared to the theoretical results obtained in the single active electron approximation, the multielectron effect leads to more tilted photoelectron angular momentum distributions (PADs) toward the light propagation direction. According to our analysis, this might be due to photon momentum sharing between multiple electrons. Furthermore, we study the multielectron effect on the birth time delay phenomenon in the ionization of a hydrogen molecule. By extracting the interference minima of the PADs, we demonstrate that the birth time delay is hardly affected by the multielectron effect. The present work provides a better understanding of the association between the nondipole effect and the multielectron effect.

Attosecond Transient Absorption Below the Excited States

In this study, the attosecond transient absorption (ATA) spectrum below the excited states of the helium atom was investigated by numerically solving the fully three-dimensional time-dependent Schrödinger equation. Under single-active electron approximation, the helium atom was illuminated by a combined field comprising of extreme ultraviolet (XUV) and delayed infrared (IR) fields. The response function demonstrates that the absorption near the central frequency (ωX) of the XUV field is periodically modulated during the overlapping between the XUV and IR pulses. Using the time-dependent perturbation, the absorption near ωX is attributed to the wavepacket excited by the XUV pulse. The wave function oscillating at the frequency of the XUV pulse was obtained. Furthermore, the chirp-dependent absorption spectrum near ωX potentially provides an all-optical method for characterizing the attosecond pulse duration. Finally, these results can extend to other systems, such as solids or liquids, indicating a potential for application in photonic devices, and they may be meaningful for quantum manipulation.

Simulation of High Harmonic Generation in Xenon Based on Time-Dependent Density-Functional Theory

Abstract The high harmonic generation (HHG) in xenon is studied by using the time-dependent density-functional theory for active 4th and 5th atomic shells. The HHG spectra are calculated for different intensities and carrier-envelope phases of a laser pulse. The HHG spectrum shows enhancement at the frequency region near 100 eV, where the HHG yield is by more than an order of magnitude higher than in the single-active electron approximation. The high accuracy of the obtained results is confirmed by comparing the calculated HHG spectra with experimental results.

Ultrafast plasmonic photoemission in the single-cycle and few-cycle regimes

Due to the highly increased interest in the development of state-of-the-art applications of photoemission in ultrafast electron microscopy, development of photocathodes and many more applications, a correct theoretical understanding of the underlying phenomena is needed. Within the framework of the single active electron approximation the most accurate results can be obtained by the direct solution of the time-dependent Schrödinger equation (TDSE). In this work, after a brief presentation of a numerically improved version of a mixed 1D-TDSE method, we investigated the characteristics of electron spectra obtained from the surface of metal nanoparticles irradiated with ultrashort laser pulses. During our investigation different decay lengths of the plasmonic-enhanced incident field in the vicinity of the metal were considered. Using the simulated spectra we managed to identify the behavior of the cutoff energy as a function of decay length in the strong-field, multiphoton and transition regimes.

Phase dependence of resonant and antiresonant two-photon excitations

Measurements of the phase of two-photon matrix elements are presented for resonant and antiresonant two-color ionization of helium. A tunable, narrow-bandwidth, near-infrared (NIR) laser source is used for extreme ultra-violet (XUV) high-harmonic generation (HHG). The 15th harmonic of the laser is used within (1+1') XUV+NIR two-photon ionization, and tuned in and out of resonance with members of the 1s$n$p $^1$P$_1$ ($n=3,4,5$) Rydberg series, covering a broad spectral range with high spectral resolution. The technique allows to observe characteristic rapid changes in the phase of the two-photon matrix elements around the resonances and, previously unobserved, at the antiresonances between the resonances. Similar effects are observed for (1+2') XUV+NIR three-photon ionization. The experimental results are compared to a perturbative model and to numerical solutions of the time-dependent Schr\"odinger equation (TDSE) in the single active electron (SAE) approximation, elucidating the origin and dependences of the observed phenomena.

Energy and angular distributions of electrons from sodium atoms photo-ionized with femtosecond laser pulses

We studied photoelectron angular distributions (PADs) and energy spectra of sodium atoms photo-ionized with intense short laser pulses in the near-infrared region. Energy spectra of photoelectrons due to multistep ionization of sodium atoms through intermediate levels 5p, 6p, 7p, and 4f were observed in above threshold ionization (ATI) at laser intensities of 2 × 1013 W cm−2 and 1 × 1013 W cm−2. The PADs from the 5p(4f) state for zero, first, second and third order ATI peaks were measured. We observed that for the two selected laser intensities the angular distribution of photoelectrons showed only slight variations. The PADs exhibit main lobes within ∼60° degrees from the laser polarization and additional lobes that become more pronounced with the increasing ATI peak number. Besides a general analytical representation of the observed angular dependences, the experimental PADs for each ATI peak were fitted with Legendre polynomials accounting for different ionization channels. The good agreement between the experimental data and fitting functions allowed to evaluate the contributions of the ionization channels to the observed ATI orders. The calculations of the photoelectron spectra by numerically solving the time-dependent Schrödinger equation in a single active electron approximation produced agreement with the experiment in the main features of the spectra, while differences in more subtle details were observed.

Numerical and laboratory attoclock simulations on noble-gas atoms

We conduct a systematic theoretical study of strong field tunneling ionization of noble-gas atoms, from He to Kr, by elliptically polarized laser pulses in the so-called attoclock setup. Our theoretical model is based on a numerical solution of the time-dependent Schr\"odinger equation in the single active electron approximation. We simulate laboratory measurements utilizing few optical cycle pulses to benchmark our calculations against experiment. We further conduct ``numerical attoclock'' simulations with short, nearly single-cycle pulses to test various tunneling ionization models. We examine the attoclock offset angles as affected by the target orbital structure and the laser pulse intensity. Finally, we exclude a finite tunneling time scenario and attribute the attoclock offset angle entirely to the Coulomb field of the ion remainder as was recently demonstrated for the hydrogen atom [U. S. Sainadh et al., Nature (London) 568, 75 (2019)].

Systematic study of Coulomb confinement resonances of atoms trapped inside charged fullerenes

An earlier work of Dolmatov et al. [Phys. Rev. A 73, 013201 (2006)] on Ne inside a charged fullerene ($\mathrm{Ne}@{\mathrm{C}}_{60}^{\mathrm{q}=\ensuremath{-}3,\ensuremath{-}5}$) has revealed the presence of two unusually large confinement resonances termed Coulomb confinement resonances (CCRs); the first CCR is narrow and the second one is broad and their origins are attributed to the presence of charge on the fullerene surface. The present work extends this study to other subshells and also to other systems such as $\mathrm{Ar}@{\mathrm{C}}_{60}^{\mathrm{q}}$ and $\mathrm{Xe}@{\mathrm{C}}_{60}^{\mathrm{q}}$ using relativistic random phase approximation, but with an aim to investigate the genesis of the CCRs. Further, a detailed analysis of these resonances within a single active electron approximation unearths an interesting difference associated with the origin of these two CCRs. The photoionized electron is temporally trapped in the ${\mathrm{C}}_{60}$ confinement well for the case of narrow resonance and in the atomic well region for the case of broad resonance. Also, the present work shows that the broad resonance can occur even for the case of $q=0$ and is demonstrated for $\mathrm{Xe}@{\mathrm{C}}_{60}^{\mathrm{q}}$ as a test case.

Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods

In contrast to the conventional finite difference methods, two transient phase methods have been effectively used in the present work to directly compute the photoionization phase shift and Wigner time delay of confined atoms (A@C60) in the single-active electron (SAE) approximation. The different phase methods: (A) employing logarithmic derivatives at shell boundaries, and (B) Born approximation are verified with the help of well-established finite difference methods in SAE approximation and sophisticated many-electron techniques. In this work, confinement oscillations on the dipole phase and photoelectron group delay following ionization from 1s subshell of H@C60, 3p subshell of Ar@C60 and 5p subshell of Xe@C60 are analyzed. The comparison with many-body calculation shows that the features in the time delay of a confined system are governed mainly by the effects of screening apart from that due to the external potential. A systematic study and comparison of the results from phase methods and many-electron techniques indicate that these techniques can be effectively used in the analysis of photoionization phase shift and time delay in confined atoms.

Extracting photoelectron spectra from the time-dependent wave function: Comparison of the projection onto continuum states and window-operator methods

Over the last three decades numerous numerical methods for solving the time-dependent Schr\"{o}dinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.

Ellipticity dependence of excitation and ionization of argon atoms by short-pulse infrared radiation

When atoms or molecules are exposed to strong short-pulse infrared radiation, ionization as well as "frustrated tunneling ionization" (FTI) can occur, in which a portion of the almost ionized electrons recombine into the initial ground or an excited bound state. We analyze the ellipticity dependence of the relative signals that are predicted in a single-active electron approximation (SAE), the validity of which is checked against a parameter-free multi-electron \hbox{$R$-matrix} (close-coupling) with time dependence approach. We find good agreement between the results from both models, thereby providing confidence in the SAE model potential to treat the process of interest. Comparison of the relative excitation probabilities found in our numerical calculations with the predictions of Landsman {\it et al.}\ (New Journal of Physics {\bf 15} (2013) 013001) and Zhao {\it et al.}\ (Optics Express {\bf 27} (2019) 21689) reveals good agreement with the former for short pulses. For longer pulses, the ellipticity dependence becomes wider than that obtained from the Landsman {\it et al.} formula, but we do not obtain the increase compared to linearly polarized radiation predicted by Zhao {\it et al.}

Static-field ionization model of He-like ions for diagnostics of light-field intensity

We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z \le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10\%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30\% for He and 2\% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as $1/Z$.

The influence of polarization of noble-gas atoms in strong laser field on high-order harmonic generation

We study the ionization and high-order harmonic generation by argon atoms subjected into the intense laser pulse based on the numerical solution of the time-dependent Kohn-Sham equations. We demonstrate that atom polarization leads to significant screening of the external electric field and decrease in the atom ionization probability. At high leaser-pulse intensity, the suppression of depletion lead to enhancement of the HHG yield in comparison with the single-active electron approximation, which neglects the polarization effect.

Above-threshold ionization driven by few-cycle spatially bounded inhomogeneous laser fields

In this work, we study the main features of the photoelectrons generated when noble gas atoms are driven by spatially bounded inhomogeneous strong laser fields. These spatial inhomogeneous oscillating fields, employed to ionize and accelerate the electrons, result from the interaction between a pulsed low intensity laser and bow-tie shaped gold nanostructures. Under this excitation scheme, energy-resolved above-threshold ionization (ATI) photoelectron spectra have been simulated by solving the one-dimensional (1D) time-dependent Schrödinger equation (TDSE) within the single active electron (SAE) approximation. These quantum mechanical results are supported by their classical counterparts, obtained by the numerical integration of the Newton–Lorentz equation. By using near-infrared wavelengths (0.8–3 μm) sources, our results show that very high energetic electrons (with kinetic energies in the keV domain) can be generated, far exceeding the limits obtained by using conventional, spatially homogeneous fields. This new characteristic can be supported considering the non-recombining electrons trajectories, already reported by Neyra and coworkers (Neyra E, et al 2018 J. Opt. 20, 034002). In order to build a real representation of the spatial dependence of the plasmonic-enhanced field in an analytic function, we fit the generated ’actual’ field using two Gaussian functions. We have further analyzed and explored this plasmonic-modified ATI phenomenon in a model argon atom by using several driven wavelengths at intensities in the order of 1014 W cm−2. Throughout our contribution we carefully scrutinize the differences between the ATI obtained using spatially homogeneous and inhomogeneous laser fields. We present the various physical origins, or correspondingly distinct physical mechanisms, for the ATI generation driven by spatially bounded inhomogeneous fields.

Angular dependence of strong field sequential double ionization for neon and acetylene simulated with time-dependent configuration interaction using CIS and CISD-IP.

Strong field ionization is fundamentally important for attosecond spectroscopy and coherence control. However, the modeling beyond the single active electron approximation is still difficult. Time-dependent configuration interaction with singly excited configurations and a complex absorbing potential (TDCIS-CAP), can be used to simulate single and double ionization by intense laser fields. When the monocation does not have degenerate states, TDCIS-CAP starting from a Hartree-Fock calculation of the cation is suitable for simulating the second ionization step. When the monocation has two or more degenerate states, the simulations should treat these degenerate states equivalently. CISD-IP (single and double excitation configuration interaction with ionization) can be used to treat degenerate states of the cation on an equal footing by representing the cation wavefunctions with ionizing single (1 hole) and double (2 holes/1 particle) excitations from the neutral molecule. Since CISD-IP includes single excitations for each of the monocation states, time dependent CISD-IP with a complex absorbing potential (TDCISDIP-CAP) can also be used to simulate ionization to the dications states. In this work, TDCIS-CAP and TDCISDIP-CAP have been used to simulate the angular dependence of ionization of the neon cation and acetylene cation. In both cases, the second electron is ionized predominantly from an orbital perpendicular to the orbital involved in the first ionization. The TDCISDIP-CAP simulations show some features involving interactions between the monocation states that are not seen in the TDCIS-CAP simulations.

Effect of multielectron polarization in the strong-field ionization of the oriented CO molecule

We discuss the mechanism by which the inclusion of multielectron polarization improves the solution of the time-dependent Schr\"{o}dinger equation (TDSE) for the oriented CO molecule in a strong external laser pulse within the single-active-electron (SAE) approximation. A challenging problem of using the SAE approximation is that the active electron, instead of undergoing ionization, may be driven by the external field to lower-lying orbitals. For the oriented CO molecule, dipole coupling to the lower-lying bound states of the potential depends on the orientation angle, thereby affecting the orientation-dependent ionization dynamics. By including multielectron polarization, the external field is turned off within the molecular radius, thereby minimizing dipole coupling of the highest occupied molecular orbital to the lower-lying states of the potential. We discuss how turning off the external field within an appropriate molecular radius without accounting for the induced dipole term in the effective potential beyond this radial cut-off distance, constitutes an effective and accurate approach to describe strong-field ionization of CO and to minimize dipole coupling to lower-lying bound states.

Control of Rydberg-state population with realistic femtosecond laser pulses

We investigate computationally a method for ultrafast preparation of alkali metal atoms in their Rydberg states using a three-dimensional model potential in the single active electron approximation. By optimizing laser pulse shapes that can be generated with modern waveform synthesizers, we propose pulses for controlling the population transfer from the ground state to a preselected set of Rydberg states. Dynamical processes under the optimized pulses are shown to be much more complicated than in the traditional optical two-photon preparation of Rydberg states.

Multiple strong field ionization of metallocenes: Applicability of ADK rates to the production of multiply charged transition metal (Cr, Fe, Ni, Ru, Os) cations

The reactions of a neutral molecule with a singly charged ion in the gas phase have been studied extensively in connection with catalytic reactions, interstellar and planetary atmospheric chemistry, and the MALDI process. In contrast, the reactions of a neutral molecule with a multiply charged ion have rarely been reported, in part because it is difficult to produce such ions in abundance. In this study, we report the production of multiply charged transition metal cations from metallocenes in intense femtosecond laser fields. The most highly charged metals observed at 3 × 1015 W cm−2 are Cr6+, Fe6+, Ni6+, Ru7+, and Os8+. The production of carbon-containing cations originating in cyclopentadienyl ligands is small relative to that of metal cations because the ligands are dominantly liberated as neutral fragments. Metal cations having higher charges are formed by the sequential (stepwise) tunnel ionization of the singly (doubly) charged metal cations that are liberated from the excited metallocene cation (dication). The experimentally measured and theoretically calculated saturation intensities of cation generation are compared. The quasiclassical tunneling theory under a single active electron approximation has been known to underestimate the saturation intensity of singly charged metal cations. However, we investigate that this theory overestimates the saturation intensity of multiply charged metal cations referred to as an enhanced ionization. Moreover, the degree of overestimation becomes significant as the charge number of the metal cation increases. The characteristic deviation of the theoretical predictions from the experimental results is a key issue for the future clarification of the multiple-tunneling ionization processes. We suggest that the polarizabilities depending on the charge number, and presumably the excitation of cations, might be important in the multiple ionization of transition metals. In addition, the production of multiply charged metal cations in abundance, and the reduced production of carbon and hydrocarbon fragment cations achieved by femtosecond laser ionization, will be valuable as sources of multiply charged metal cations for future ion–molecule reaction studies.