Two-electron Momentum Distributions Research Articles

Ellipticity dependence of anticorrelation in the nonsequential double ionization of Ar.

Within the framework of the improved quantitative rescattering (QRS) model, we simulate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization (NSDI) of Ar by elliptically polarized laser pulses with a wavelength of 788 nm at an intensity of 0.7 × 1014 W/cm2 for the ellipticities ranging from 0 to 0.3. Only the CMDs for recollision excitation with subsequent ionization (RESI) are calculated and the contribution from recollision direct ionization is neglected. According to the QRS model, the CMD for RESI can be factorized as a product of the parallel momentum distribution (PMD) for the first released electron after recollision and the PMD for the second electron ionized from an excited state of the parent ion. The PMD for the first electron is obtained from the laser-free differential cross sections for electron impact excitation of Ar+ calculated using state-of-the-art many-electron R-matrix theory while that for the second electron is evaluated by solving the time-dependent Schrödinger equation. The results show that the CMDs for all the ellipticities considered here exhibit distinct anticorrelated back-to-back emission of the electrons along the major polarization direction, and the anticorrelation is more pronounced with increasing ellipticity. It is found that anticorrelation is attributed to the pattern of the PMD for the second electron ionized from the excited state that, in turn, is caused by the delayed recollision time with respect to the instant of the external field crossing. Our work shows that both the ionization potential of the excited parent ion and the laser intensity play important roles in the process.

Nonsequential double ionization of Ne with elliptically polarized laser pulses

We show through simulation that the improved quantitative rescattering model (QRS) can successfully predict the nonsequential double ionization (NSDI) process by intense elliptically polarized laser pulses. Using the QRS model, we calculate the correlated two-electron and ion momentum distributions of NSDI in Ne exposed to intense elliptically polarized laser pulses with a wavelength of 788 nm at a peak intensity of $5.0\ifmmode\times\else\texttimes\fi{}{10}^{14}$ W/${\mathrm{cm}}^{2}$. We analyze the asymmetry in the doubly charged ion momentum spectra observed by Kang et al. [Phys. Rev. Lett. 120, 223204 (2018)] in going from linearly to elliptically polarized laser pulses. Our model reproduces the experimental data well. Furthermore, we find that the ellipticity-dependent asymmetry arises from the drift velocity along the minor axis of the elliptic polarization. We explain how the correlated electron momentum distributions along the minor axis provide access to the subcycle dynamics of recollision. From these findings, we expect that we can extend the QRS model for NSDI toward more complicated laser fields in the future.

Soft parameters in Coulomb potential of noble atoms for nonsequential double ionization: Classical ensemble model and simulations

We propose a procedure based on the classical ensemble model to determine the soft parameter in the Coulomb potential of noble atoms, the important parameters used in the simulations of nonsequential double ionizations (NSDI). These parameters are determined based on two conditions: ensuring the positive kinetic energy of two electrons and preventing the atom from autoionization. The optimal values of the soft parameters for He, Ne, Ar, Kr, and Xe atoms are around 0.85, 1.1, 1.5, 1.8, and 2.0 a.u., respectively. The classically allowed initial position of electrons is analytically derived from soft parameters. A simulation of NSDI using 2,000,000 particles has been done using the obtained parameters to achieve the probability distribution of the single and double ionizations. The procedure is comprehensively illustrated for Ar and He atoms and the result in this study is validated by comparing the ratio of double to single ionization yield and correlated two-electron momentum distributions with that in recent experiments.

Recollision of excited electron in below-threshold nonsequential double ionization

Recollision is the most important post-tunneling process in strong-field physics, but so far has been restricted to interaction between the first ionized electron and the residual ion in nonsequential double ionization. Here we identify the role of recollision of the second ionized electron in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method. We will reproduce the experimentally observed cross-shaped and anti-correlated patterns in correlated two-electron momentum distributions, and the transition between them. Both the cross-shaped and anti-correlated patterns are attributed to recolliding trajectories of the second electron. The effect of recollision of the second electron is significantly enhanced by the stronger Coulomb potential of the higher valence residual ion, and is further strengthened by the recapture process of the second electron. Our work paves a potential way to image ultrafast dynamics of atoms and molecules in intense laser field.

Single-cycle versus multicycle nonsequential double ionization of argon

Using an improved quantitative rescattering model, we calculate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization of Ar exposed to intense laser pulses with a wavelength of 790 nm at a peak intensity of $1.0\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. We analyze the drastic variations in the CMDs that were observed by K\"ubel et al. [New J. Phys. 16, 033008 (2014)] in the transition from near-single-cycle to multicycle driving laser pulses. Our model reproduces their experimental data well. We also find that the transition from near-single-cycle to multicycle driving laser pulses depends strongly on the details of the pulse envelope. Special attention is paid to the mechanisms responsible for the cross-shaped structure observed experimentally with 4 fs pulses. Our analysis reveals that the cross-shaped structure in the carrier-envelope phase-averaged CMD for near-single-cycle pulses can be attributed to strong backward scattering of the recolliding electron as well as the narrow momentum distributions of the tunnel-ionized electrons compared to those for long pulses. This also explains why the cross-shaped distributions collapse to a rather structureless distribution when the pulse duration is increased to 8 fs.

Anticorrelation in nonsequential double ionization of helium

We calculate the correlated two-electron momentum distributions for nonsequential double ionization of helium in a 400-nm laser pulse with a peak intensity of $6.5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^{2}$, which is below the recollision threshold, by using the quantitative rescattering model in which the lowering of the threshold due to the presence of the electric field at the instant of recollision is taken into account. While distinct correlated back-to-back emission of the electrons along the polarization direction is predicted in accord with other existing theoretical simulations, we suggest an alternative mechanism that is responsible for the anticorrelation. At intensities below the recollision threshold, recollision excitation can only take place when the barrier of the Coulomb potential is sufficiently suppressed by the electric field. The excited electron begins to ionize at a ``delayed'' recollision time after a crossing of the field and hence the probability of being tunnel-ionized after the subsequent peak of the field is increased. It is demonstrated that the ``delayed'' recollision time predominantly determines the parallel momentum distribution of the tunneling electron and plays a decisive role in forming anticorrelation.

Investigation of the dependence of multiple recollision on laser wavelength in the nonsequential double ionization process

This paper investigates the recollision dynamics of the nonsequential double ionization process induced by linearly polarized laser pulses with the three-dimensional classical ensemble model. The results show that the correlated two-electron momentum distribution is contaminated by the double recollision events for sufficiently short laser wavelength. When the laser wavelength increases from near-infrared to mid-infrared, the single-recollision events are more prominent than the double-recollision one. Moreover, the mechanisms governing the nonsequential double ionization process are also thoroughly studied in the case of double-recollision.

Evidence of potential change in nonsequential double ionization* *Project supported by the National Natural Science Foundation of China (Grant No. 11274219), the Science and Technology Planning Project of Guangdong Province of China (Grant No. 180917124960522), and the Program for Promotion of Science at Universities in Guangdong Province of China (Grant No. 2018KTSCX062).

Recently, the quantitative rescattering model (QRS) for nonsequential double ionization (NSDI) is modified by taking into account the potential change (PC) due to the presence of electric field at the time of recollision. Using the improved QRS model, we simulate the longitudinal momentum distributions of doubly charged ions He2+ by projecting the correlated two-electron momentum distributions for NSDI of He onto the main diagonal. The obtained results are compared directly with the experimental data at different intensities. It is found that when the PC is considered, the width of momentum distributions reduces and the agreement between theory and experiment is improved.

Nonsequential double ionization of Ar in near-single-cycle laser pulses.

Using the improved quantitative rescattering (QRS) model, we simulate the correlated two-electron momentum distributions (CMD) for nonsequential double ionization (NSDI) of Ar by near-single-cycle laser pulses with a wavelength of 750 nm at an intensity of 2.8 × 1014 W/cm2. With the accurate cross sections obtained from fully quantum mechanical calculations for both electron impact excitation and electron impact ionization of Ar+, we unambiguously identify the contributions from recollision direct ionization (RDI) and recollision excitation with subsequent ionization (RESI). Our analysis reveals that RESI constitutes the main contribution to NSDI of Ar under the conditions considered here. The simulated results are directly compared with experimental measurements [Bergues et al., Nature Commun. 3, 813 (2012)] in which each NSDI event is tagged with the carrier-envelope phase (CEP). It is found that the overall pattern of both the CEP-resolved and the CEP-averaged CMDs measured in experiment are well reproduced by the QRS model, and the cross-shaped structure in the CEP-averaged CMD is attributed to the strong forward scattering of the recolliding electron as well as the depletion effect in tunneling ionization of the electron from an excited state of the parent ion.

Laser-induced nonsequential double ionization of helium: classical model calculations

We have investigated the double ionization of helium induced by 45 fs, 394 nm linearly polarized laser pulses for intensities (2.5–150) × 1014 W cm−2. The time evolution of the process was determined by applying the classical ensemble approximation (CEA) model. The results of the calculations obtained for the double-to-single ionization ratio, the momentum distribution of the He2+ recoil ion and the correlated two-electron momentum distribution are compared with the recent experimental data of Henrichs et al (2018 Phys. Rev. A 98 043405). The standard CEA model failed to reproduce the basic features of the experiment. A considerable improvement in the description of the experimental data was achieved by including a two-step process in the model: the formation of a transient double excited state in the first step, and the simultaneous release of the two electrons via ‘over the barrier ionization’ in the second step.

Mechanisms of nonsequential double ionization process of argon by near-single cycle laser pulse

In this paper, the near-single cycle laser pulse is used to trigger the nonsequential double ionization process of argon atom due to its ability to eliminate the contamination from secondary recollisions. The mechanisms and distributions of recollision-ionization channels are thoroughly investigated for two representative laser intensities which provide returning energies well below and above the recollision-ionization threshold of argon. The results indicate that recollision-induced excitation with subsequent ionization and direct ionization mechanisms are dominant for low and high intensity of laser, respectively. In addition, the extraction of cross-shaped structure in the correlated two-electron momentum distribution is presented along with the investigation to understand the origin of this interesting structure.

Intensity dependence in nonsequential double ionization of helium

Using the quantitative rescattering model, we simulate the correlated two-electron momentum distributions for nonsequential double ionization of helium by 800 nm laser pulses at intensities in the range of (2 - 15) × 1014 W/cm2. The experimentally observed V-shaped structure at high intensities [A. Rudenko et al., Phys. Rev. Lett. 99, 263003 (2007)] is attributed to the strong forward scattering in laser-induced recollision excitation and the asymmetric momentum distribution of electrons that are tunneling-ionized from the excited states. The final-state electron repulsion also plays an important role in forming the V-shaped structure.

Quantitative rescattering theory for nonsequential double ionization**Project supported by the National Natural Science Foundation of China (Grant No. 11274219), the Science and Technology Planning Project of Guangdong Province of China (Grant No. 180917124960522), and the Program for Promotion of Science at Universities in Guangdong Province of China (Grant No. 2018KTSCX062).

We review the recently improved quantitative rescattering theory for nonsequential double ionization, in which the lowering of threshold due to the presence of electric field at the time of recollision has been taken into account. First, we present the basic theoretical tools which are used in the numerical simulations, especially the quantum theories for elastic scattering of electron as well as the processes of electron impact excitation and electron impact ionization. Then, after a brief discussion about the properties of the returning electron wave packet, we provide the numerical procedures for the simulations of the total double ionization yield, the double-to-single ionization ratio, and the correlated two-electron momentum distribution.

Streaking strong-field double ionization

Double ionization in intense laser fields can comprise electron correlations, which manifest in the non-independent emission of two electrons from an atom or molecule. However, experimental methods that directly access the electron emission times have been scarce. Here, we explore the application of an all-optical streaking technique to strong-field double ionization both theoretically and experimentally. We show that both sequential and non-sequential double ionization processes lead to streaking delays that are distinct from each other and single ionization. Moreover, coincidence detection of ions and electrons provides access to the emission time difference, which is encoded in the two-electron momentum distributions. The experimental data agree very well with simulations of sequential double ionization. We further test and discuss the application of this method to non-sequential double ionization, which is strongly affected by the presence of the streaking field.

Revisiting the recollisional excitation-tunneling process in strong-field nonsequential double ionization of helium

We revisit the excitation-tunneling process in nonsequential double ionization (NSDI) of helium in an 800-nm laser field. The correlated two-electron momentum distributions are calculated by using the improved quantitative rescattering (QRS) model, in which the lowering of the threshold energy due to the presence of an electric field at the instant of recollision is taken into account. In the framework of the QRS model, the correlated two-electron momentum distributions for excitation-tunneling in NSDI can be factorized as a product of the returning-electron wave packet (RWP) and the field-free differential cross section (DCS) for electron impact excitation of the parent ion multiplied by the tunneling ionization rate of electrons in the excited states. The RWPs, which describe the momentum distribution of the returning electrons, are obtained within the strong-field approximation for high-order above-threshold ionization. The DCSs for electron impact excitation of ${\mathrm{He}}^{+}$ are calculated using the state-of-the-art many-electron $R$-matrix theory, and the tunneling ionization rates for electrons in the excited states are evaluated by solving the time-dependent Schr\"odinger equation. The calculated correlated two-electron momentum distribution shows that the fourfold symmetry with regard to the parallel momentum components is broken. This is in contradiction to the prevalent view that the correlation pattern for excitation-tunneling in NSDI is symmetric with respect to the coordinate axes. By including the recollisional ($e,2e$) process, the predicted correlated two-electron momentum distributions are found to be in good qualitative agreement with experiment.

The role of electron-electron repulsion to the nonsequential double ionization mechanisms

In this study the classical three-dimensional ensemble model is utilized for investigating the role of final state electron-electron repulsion in forming the ultimate correlated two-electron momentum distribution. For the first time, a comprehensive analysis has been made to thoroughly understand such repulsive force associating with each microscopic mechanism of nonsequential double ionization. The helium exposed to 800-nm laser with two representative intensities of 3.5×1014 W/cm2 and 4.5×1014 W/cm2 is used for illustration. The results indicate the dominance of electron-electron repulsion in direct and recollision-induced excitation with subsequential ionizations. While its contribution in case of exchanging-state mechanism gradually emerges as the laser intensity increases.

Revisiting the recollisional ( e, 2e ) process in strong-field nonsequential double ionization of helium

We present numerical simulations on the correlated two-electron momentum distributions for the recollisional ($e, 2e$) process in nonsequential double ionization (NSDI) of helium by an 800-nm laser field at an intensity around $4.5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$, based on the improved quantitative rescattering model, in which the lowering of the kinetic energy required for the electrons to escape from the parent ion due to the presence of electric field at the time of recollision has been taken into account. According to the QRS model, the correlated two-electron momentum distributions for laser-induced ($e, 2e$) collision in NSDI can be factorized as a product of the returning-electron wave packet (RWP) and the field-free differential cross section (DCS) for ionization of the parent ion by the impact of the laser-induced returning electron. The RWPs which describe the momentum distribution of the returning electrons are obtained within the strong-field approximation for high-order above threshold ionization. In the calculations of the DCSs for electron impact ionization of ${\mathrm{He}}^{+}$, the precollision Coulomb interaction between the incident electron and the parent ion and the postcollision Coulomb interaction between the two outgoing electrons are considered. In addition, the dynamic screening (DS) of the three-body Coulomb interactions in the final state, due to the fact that the strength of the interaction of any two particles is affected by the presence of the third one, has also been taken into account. It has been found that while the postcollision Coulomb interaction is responsible for the observed fingerlike structure, the precollision Coulomb interaction changes the orientation of the two fingers from $\mathsf{V}$-type to parallel, the final state DS reduces the separation of the two fingers, and the lowering of threshold energy shifts the two fingers towards smaller momenta. All these effects improve the agreement of the simulated results with the experimental results.

Doubly-excited state effects on two-photon double ionization of helium by time-delayed, oppositely circularly-polarized attosecond pulses

We study two-photon double ionization (TPDI) of helium by a pair of time-delayed (non-overlapping), oppositely circularly-polarized attosecond pulses whose carrier frequencies are resonant with 1Po doubly-excited states. All of our TPDI results are obtained by numerical solution of the two-electron time-dependent Schrödinger equation for the six-dimensional case of circularly-polarized attosecond pulses, and they are analyzed using perturbation theory (PT). As compared with the corresponding nonresonant TPDI process, we find that the doubly-excited states change the character of vortex patterns in the two-electron momentum distributions for the case of back-to-back detection of the two ionized electrons in the polarization plane. The doubly-excited states also completely change the structure of fixed-energy, two-electron angular distributions. Moreover, both the fixed-energy and energy-integrated angular distributions, as well as the two-electron energy distributions, exhibit a periodicity with time delay τ between the two attosecond pulses of about 69 as, i.e. the beat period between the doubly-excited state and the He ground state. Using PT we derive an expression for an angle-integrated energy distribution that is sensitive to the slower beat period ∼1.2 fs between different doubly-excited states as well as to the long timescale ∼17 fs of autoionization lifetimes. However, with our current computer codes we are only able to study numerically the time-dependent phenomena occurring on an attosecond time scale.

Kinematical vortices in double photoionization of helium by attosecond pulses

Two-armed helical vortex structures are predicted in the two-electron momentum distributions produced in double photoionization (DPI) of the He atom by a pair of time-delayed elliptically polarized attosecond pulses with opposite helicities. These predictions are based upon both a first-order perturbation theory analysis and numerical solutions of the two-electron, time-dependent Schr\odinger equation in six spatial dimensions. The helical vortex structures originate from Ramsey interference of a pair of ionized two-electron wave packets, each having a total angular momentum of unity, and appear in the sixfold differential DPI probability distribution for any energy partitioning between the two electrons. The vortex structures are exquisitely sensitive to the time delay between the two pulses, their relative phase, their ellipticity, and their handedness; moreover, they occur in a variety of electron detection geometries. However, the vortex structures only occur when the angular separation $\ensuremath{\beta}={cos}^{\ensuremath{-}1}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}}_{2})$ between the electron momenta ${\mathbf{p}}_{1}$ and ${\mathbf{p}}_{2}$ is held fixed. The vortex structures can also be observed in the fourfold differential DPI probability distribution obtained by averaging the sixfold differential probability over the emission angles of one electron. Such kinematical vortices are a general phenomenon that may occur in any ionization process, initiated by two time-delayed short pulses with opposite ellipticities, for particular detection geometries.

Recoil-ion-momentum spectrum for few-photon double ionization of helium

We provide an efficient and accurate numerical method to deduce the recoil-ion-momentum spectrum of He from the two-electron momentum distribution, which is obtained by solving the full-dimensional time-dependent Schr\"odinger equation. We apply this method to study the ion spectra of one-photon double ionization and two-photon sequential and nonsequential double ionization of He. The present calculations agree rather well with the absolute magnitude of the recoil-ion triply differential cross sections published recently [S. A. Abdel-Naby, M. S. Pindzola, and J. Colgan, Phys. Rev. A 86, 013424 (2012); S. A. Abdel-Naby et al., Phys. Rev. A 87, 063425 (2013)]. Nevertheless, significant differences are also found in several detailed features of the spectra and straightforward physical analysis indicates that the present results appear more reasonable, which should be confirmed by future experiments or additional independent calculations.