Binary and recoil collisions in strong field double ionization of helium

The Coulomb effect in nonsequential double ionization by counter-rotating two-color elliptical polarization fields

Using a three-dimensional classical ensemble model, nonsequential double ionization (NSDI) of Ar atoms by counter-rotating two-color elliptical polarization (TCEP) fields is investigated. The major axes of the two elliptical fields are aligned in different directions. The relative alignment of the two elliptical fields strongly affects the waveform of the combined electric field and the ultrafast dynamics of NSDI in TCEP fields. Numerical results show that the correlated electron momentum distributions in the x direction evolve from a V-shaped structure near the axis to a distribution concentrated on the diagonal with the angle between the two elliptical major axes increasing. The asymmetry of the energy sharing between the two electrons during recollision results in the V-shaped structure in the correlated momentum spectrum. Back analysis indicates that the recollision times of a part of the trajectories move from the peak to the valley of the combined electric field with the angle between the two elliptical major axes increasing. Therefore, for the case of a larger angle between the two elliptical major axes, the electrons experience a longer time to escape away from the vicinity of the parent ion and thus the stronger Coulomb effect from the parent ion makes the momentum difference between two electrons small, which results in a distribution concentrated on the diagonal. This provides an effective avenue to control the electron ultrafast dynamics in NSDI.

High-Intensity Harmonic Generation with Energy Tunability Produced by Robust Two-Color Linearly Polarized Laser Fields

By using the numerical solution of the time-dependent Schrödinger equation, we theoretically explored the high-order harmonic generation process under the interaction of high-intensity two-color ultrashort driving laser pulses with atoms. The symmetry of the electric field of the laser pulse will be broken. The producing electric field was controlled at the subcycle level by an IR laser and its second harmonic, which has the unique characteristic that two sequential half-cycles become distinct, rather than merely opposite in sign. Compared with the case of the atom in the fundamental laser pulse, the harmonic efficiency showed an increase of 1∼2 orders of magnitude at specific harmonic order with this combined pulse action. Through the theoretical analysis with the “three-step model”, it was demonstrated that the enhancement of the harmonic intensity is due to the fast ionization of electrons at the ionization moment and the short time from ionization to recombination of ionized electrons. In addition, effects of the peak field amplitude ratio, the full width at half maximum, the phase delay of the two-color pulses, the laser intensity and ionization probability on the harmonic efficiency enhancement were also investigated.

Investigation of the Spatio-Temporal Characteristics of High-Order Harmonic Generation Using a Bohmian Trajectory Scheme

High-order harmonic generation of atoms irradiated by an ultrashort laser pulse was calculated by numerically solving the time-dependent Schrödinger equation and the Bohmian trajectory scheme. The harmonic spectra with the two schemes are quantitatively consistent. Using the wavelet behavior of the Bohmian trajectory, the spatio-temporal features of harmonic emission from different energy regions are analyzed. It is found that the spatio-temporal distribution of the harmonic well revealed the physical mechanism of harmonic generation. This method will contribute to the understanding of harmonic emission mechanisms in complex systems, which include many atoms.

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.

Electron correlation and recollision dynamics in nonsequential double ionization by counter-rotating two-color elliptically polarized laser fields

Nonsequential double ionization (NSDI) of Argon atoms by counter-rotating two-color elliptically polarized (TCEP) fields is investigated with a three-dimensional classical ensemble model. Different from two-color circularly polarized fields, the combined electric field in TCEP pulses has no symmetry and the ionized electron mainly returns to the parent ion from one direction. Thus the electron momentum distributions show strong asymmetry. Numerical results show with the increase of the relative phase between the two elliptical fields, the return angle of the travelling electron, i.e., the angle between the return direction of the electron and the +x direction, gradually decreases. Moreover, the dominant behavior of electron pairs evolves from anti-correlation to correlation with the relative phase increasing. This provides an avenue to control the return angle and electron correlation behavior by the relative phase between the two elliptical fields.

Magnetic-Field Effect as a Tool to Investigate Electron Correlation in Strong-Field Ionization

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory Monte Carlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

Control of concerted back-to-back double ionization dynamics in helium

Double ionization (DI) is a fundamental process that despite its apparent simplicity provides rich opportunities for probing and controlling the electronic motion. Even for the simplest multielectron atom, helium, new DI mechanisms are still being found. To first order in the field strength, a strong external field doubly ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion). The ejection into opposite directions (back-to-back motion) cannot be described to first order, making it a challenging target for control. Here, we address this challenge and optimize the field with the objective of back-to-back double ionization using a (1 + 1)-dimensional model. The optimization is performed using four different control procedures: (1) short-time control, (2) derivative-free optimization of basis expansions of the field, (3) the Krotov method, and (4) control of the classical equations of motion. All four procedures lead to fields with dominant back-to-back motion. All the fields obtained exploit essentially the same two-step mechanism leading to back-to-back motion: first, the electrons are displaced by the field into the same direction. Second, after the field turns off, the nuclear attraction and the electron-electron repulsion combine to generate the final motion into opposite directions for each electron. By performing quasi-classical calculations, we confirm that this mechanism is essentially classical.

Electron angular correlation in nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields

Electron correlation in nonsequential double ionization (NSDI) of molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that the two electrons from NSDI of molecules in counter-rotating TCCP fields show strong angular correlation and the angular correlation behavior sensitively depends on the internuclear distance. With the internuclear distance increasing, the dominant behavior of electron pairs evolves from correlation to anti-correlation. It leaves a clear imprint on the ion momentum distributions, which exhibit an inverted Y-shape distribution at a small internuclear distance and a triangle-shape distribution at a large internuclear distance. Back analysis indicates that the asymmetric electron energy sharing by soft recollision and longer time delay of double ionization are responsible for more anti-correlated emissions at large internuclear distances.

Three-electron correlations in strong laser field ionization

Strong field processes involving several active electrons reveal unambiguous dynamical signatures of the Pauli principle importance even in the nonrelativistic regime. We exemplify this statement studying three active electrons model atoms interacting with strong pulsed radiation, using an ab-initio time-dependent Schrödinger equation on a grid. In our restricted dimensionality model we are able to analyze momenta correlations of the three outgoing electrons using Dalitz plots. The different symmetries of the electronic wavefunctions, directly related to the initial state spin components, appear clearly visible.

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 10¹³ W/cm² to 5 × 10¹⁴ W/cm². We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

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.

Mapping initial transverse momenta of tunnel-ionized electrons to rescattering double ionization in nondipole regimes

We investigate the double ionization of a model Neon atom in strong middle infrared laser pulses by simulating the classical trajectories of the electron ensemble. After one electron tunnels out from the laser-dressed Coulomb barrier, it might undergo different returning trajectories depending on its initial transverse momentum, which in this wavelength may propagate along or deviate from the polarization direction. This initial transverse momentum determines the rescattering time, and thus some trajectories can have returning time longer than one optical cycle. These late-returning trajectories determine the correlated electron-electron momentum distribution for double ionization and allow us to disentangle each double ionization event from the final momentum distribution. The description of these trajectories allow us also to understand how the nondipole effects modify the correlated electron-electron momentum distribution in double ionization.

Relative phase effect of nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields

Relative phase effect of nonsequential double ionization (NSDI) of aligned molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results show that NSDI yield in counter-rotating TCCP fields sensitively depends on the relative phase of the two components, which exhibits a sin-like behavior with the period of π/2. NSDI yield achieves its maximum at the relative phase π/8 and minimum at 3π/8. Back analysis indicates the recollision time and the return angle of the electron strongly depend on the relative phase of the two components, which results in the dominant emission direction of the electrons, is different for different relative phases. This indicates that the recollision process can be steered by changing the relative phase of the two components in counter-rotating TCCP laser fields. Meantime, it provides an avenue to obtain information about the recollision time and the return angle in the recollision process from the electron momentum distribution.

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.

Frustrated double ionization of atoms in strong laser fields

With a three-dimensional classical ensemble method, we theoretically investigated frustrated double ionization (FDI) of atoms with different laser wavelengths. Our results show that FDI can be more efficiently generated with shorter wavelengths and lower laser intensities. With proper laser parameters more FDI events can be generated than normal double ionization events. The physical condition under which FDI events happen is identified and explained. The energy distribution of the FDI products - atomic ions in highly excited states - shows a sensitive wavelength dependency.

Fingerprints of slingshot non-sequential double ionization on two-electron probability distributions

We study double ionization of He driven by near-single-cycle laser pulses at low intensities at 400 nm. Using a three-dimensional semiclassical model, we identify the pathways that prevail non-sequential double ionization (NSDI). We focus mostly on the delayed pathway, where one electron ionizes with a time-delay after recollision. We have recently shown that the mechanism that prevails the delayed pathway depends on intensity. For low intensities slingshot-NSDI is the dominant mechanism. Here, we identify the differences in two-electron probability distributions of the prevailing NSDI pathways. This allows us to identify properties of the two-electron escape and thus gain significant insight into slingshot-NSDI. Interestingly, we find that an observable fingerpint of slingshot-NSDI is the two electrons escaping with large and roughly equal energies.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Enhanced double ionization rate from O2 molecules driven by counter-rotating circularly polarized two-color laser fields

We report that the nonsequential double ionization (NSDI) probability of an O ₂ target can be enhanced greatly in a counter-rotating circularly polarized two-color driving field. The field is composed of a fundamental frequency and its third harmonic, and the combined electric field traces out a four-leaf-clover pattern. The electron ionized by such a field has more chances to collide with the valence electrons in the O ₂ molecule, which significantly enhances the NSDI probability. This effect is more evident in low-intensity fields. We also find that the enhancement appears in a broad range of the field ratio of two colors and that both the NSDI yield and the underlying electronic behavior varies notably with the field ratio.

Internal collision induced strong-field nonsequential double ionization in molecules

Using the classical ensemble method, we have investigated the alignment dependence of the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of diatomic molecules driven by linearly polarized laser pulses. Our numerical results show that the correlated electron pairs are more likely to emit into the same hemisphere (side-by-side emission) for the parallel aligned molecules at the small internuclear distance, in agreement with previous experimental results. Surprisingly, as the internuclear distance increases, this side-by-side emission is more prevalent for the perpendicularly aligned molecules. Back analyzing of the classical trajectories shows that a considerable part of the NSDI events for the parallel aligned molecules at the large internuclear distances occur through an internal collision, not the well-known recollision. In the internal collision induced NSDI, the first electron tunnels through the inner barrier from the up-field core, moves directly towards the other core, and kicks out the second electron. For this type of NSDI events, the electron pairs are more likely to emit into the opposite hemispheres and thus the correlated electron momentum spectrum exhibits a more dominant back-to-back behavior in the parallel aligned molecules.

Nonsequential double ionization by co-rotating two-color circularly polarized laser fields

Nonsequential double ionization (NSDI) of Ar in co-rotating two-color circularly polarized (TCCP) laser fields is investigated with a three-dimensional classical ensemble model. Our numerical results indicate that co-rotating TCCP fields can induce NSDI by recollision process, while the yield is an order of magnitude lower than counter-rotating case. NSDI yield in co-rotating TCCP fields strongly depends on field ratio of the two colors and achieves its maximum at a ratio of 2.4. In co-rotating TCCP fields, the short recollision trajectory with traveling time smaller than one cycle is dominant. Moreover, the recollision time in co-rotating TCCP laser fields depends on the field ratio, which is mapped to the electron momentum distribution. This provides anavenue to obtain information about recollision time and access the subcycle dynamics of the recollision process.

Timing the release of the correlated electrons in strong-field nonsequential double ionization by circularly polarized two-color laser fields

With the semiclassical ensemble model, we systematically investigate the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) by the counter-rotating circularly polarized two-color (CPTC) laser pulses. Our results show that the angular distributions of the electrons in NSDI sensitively depend on the intensity ratio of the CPTC laser fields. At the small ratio, the electron pairs emit with a relative angle of about 120°, and this angle shifts to 40° as the ratio increases and finally it exhibits a wide range distribution as the intensity ratio further increases. Back analysis of the NSDI trajectories shows that this behavior results from the relative-intensity-dependence of the release time of the electron pairs in the CPTC laser fields. The release times of the electron pairs are directly mapped to the angular distribution. Our results indicate that the emission times of the correlated electrons in NSDI can be controlled with the CPTC laser fields.

Slingshot Nonsequential Double Ionization as a Gate to Anticorrelated Two-Electron Escape

At intensities below the recollision threshold, we show that recollision-induced excitation with one electron escaping fast after recollision and the other electron escaping with a time delay via a Coulomb slingshot motion is one of the most important mechanisms of nonsequential double ionization (NSDI), for strongly driven He at 400 nm. Slingshot NSDI is a general mechanism present for a wide range of low intensities and pulse durations. Anticorrelated two-electron escape is its striking hallmark. This mechanism offers an alternative explanation of anticorrelated two-electron escape obtained in previous studies.

Intensity-dependent two-electron emission dynamics in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields

Nonsequential double ionization of helium in counter-rotating two-color circularly polarized laser fields is investigated with a three-dimensional classical ensemble model. At moderate intensity, the momentum distribution of the two electrons shows a maximum in the middle of each side of the triangle of the negative vector potential. At high intensity, the momentum distribution exhibits a double-triangle structure, which is attributed to the different values of the laser intensity where the two electrons are released after recollision. At low intensity, the momentum distribution shows a shift deviating from the middle of the side of the triangle of the negative vector potential. This is because the first electrons are emitted within a narrow time window after the field maximum. In addition, at low intensity, double-recollision events and NSDI originating from doubly excited states induced by recollision are prevalent.

Anomalous ellipticity dependence in nonsequential double ionization of ArXe

Using a three-dimensional classical ensemble method, we present a theoretical study of nonsequential double ionization of ArXe dimer aligned along the minor axis of the elliptically polarized laser pulse. Numerical results show that NSDI probability firstly increases and then decreases with the laser ellipticity increasing, which is different from atoms. Moreover, the correlated electron momentum spectra from elliptical polarization are always asymmetric, and the asymmetry is enhanced as the ellipticity increases. Analysis backward in time indicates that in NSDI of ArXe aligned along the minor axis the recollision occurs via a semi-elliptical trajectory.

Controlling nonsequential double ionization of Ne with parallel-polarized two-color laser pulses

We measure the recoil-ion momentum distributions from nonsequential double ionization of Ne by two-color laser pulses consisting of a strong 800-nm field and a weak 400-nm field with parallel polarizations. The ion momentum spectra show pronounced asymmetries in the emission direction, which depend sensitively on the relative phase of the two-color components. Moreover, the peak of the doubly charged ion momentum distribution shifts gradually with the relative phase. The shifted range is much larger than the maximal vector potential of the 400-nm laser field. Those features are well recaptured by a semiclassical model. Through analyzing the correlated electron dynamics, we found that the energy sharing between the two electrons is extremely unequal at the instant of recollison. We further show that the shift of the ion momentum corresponds to the change of the recollision time in the two-color laser field. By tuning the relative phase of the two-color components, the recollision time is controlled with attosecond precision.

Correlated electron dynamics in strong-field nonsequential double ionization of Mg

Using the classical ensemble model, we systematically investigate strong-field nonsequential double ionization (NSDI) of Mg by intense elliptically polarized laser pulses with different wavelengths. Different from the noble atoms, NSDI occurs for Mg driven by elliptically and circularly polarized laser fields. Our results show that in elliptically and circularly polarized laser fields, the NSDI yield is sharply suppressed as the wavelength increases. Interestingly, the correlated behavior in the electron momentum spectra depends sensitively on the wavelengths. The corresponding electron dynamics is revealed by back tracing the classical trajectory.

Non-sequential double ionization with near-single cycle laser pulses

A three-dimensional semiclassical model is used to study double ionization of Ar when driven by a near-infrared and near-single-cycle laser pulse for intensities ranging from 0.85 × 10¹⁴ W/cm² to 5 × 10¹⁴ W/cm². Asymmetry parameters, distributions of the sum of the two electron momentum components along the direction of the polarization of the laser field and correlated electron momenta are computed as a function of the intensity and of the carrier envelope phase. A very good agreement is found with recently obtained results in kinematically complete experiments employing near-single-cycle laser pulses. Moreover, the contribution of the direct and delayed pathways of double ionization is investigated for the above observables. Finally, an experimentally obtained anti-correlation momentum pattern at higher intensities is reproduced with the three-dimensional semiclassical model and shown to be due to a transition from strong to soft recollisions with increasing intensity.

Dissection of electron correlation in strong-field sequential double ionization using a classical model

Recent experiments on strong-field sequential double ionization (SDI) have reported several observations which are regarded as evidence of electron correlation, querying the validity of the standard independent electron approximation for SDI. Here we theoretically study SDI with a classical ensemble model. The experimental results are well reproduced with this model. Back tracing of the ionization process shows that these results are ascribed to the subcycle ionization dynamics of the two electrons, not the evidences of the electron correlation in SDI. Thus, the previously reported observations are not enough to claim the breakdown of the independent electron approximation in SDI.

Recollision dynamics in nonsequential double ionization of atoms by long-wavelength pulses

Recollision dynamics and electron correlation behavior are investigated for several long laser wavelengths (1200-3000 nm) in nonsequential double ionization (NSDI) of helium using three-dimensional classical ensembles. Numerical results show that for these long wavelengths NSDI events are mainly from the multiple-return trajectory which is different from the case of 800 nm. Moreover, with increasing laser wavelength NSDI events move from the diagonal to the two axes in the correlated electron momentum distributions, and finally form an experimentally observed prominent V-shaped structure [Phys. Rev. X 5, 021034 (2015)] in the first and third quadrants. Back analysis indicates that the asymmetric energy sharing between the two electrons at recollision is responsible for the formation of the prominent V-shaped structure of 3000 nm.

Nonsequential double ionization with mid-infrared laser fields

Using a full-dimensional Monte Carlo classical ensemble method, we present a theoretical study of atomic nonsequential double ionization (NSDI) with mid-infrared laser fields, and compare with results from near-infrared laser fields. Unlike single-electron strong-field processes, double ionization shows complex and unexpected interplays between the returning electron and its parent ion core. As a result of these interplays, NSDI for mid-IR fields is dominated by second-returning electron trajectories, instead of first-returning trajectories for near-IR fields. Some complex NSDI channels commonly happen with near-IR fields, such as the recollision-excitation-with-subsequent-ionization (RESI) channel, are virtually shut down by mid-IR fields. Besides, the final energies of the two electrons can be extremely unequal, leading to novel e-e momentum correlation spectra that can be measured experimentally.

Origin of double-line structure in nonsequential double ionization by few-cycle laser pulses

We investigate nonsequential double ionization (NSDI) of molecules by few-cycle laser pulses at the laser intensity of 1.2-1.5 × 10(14) W/cm(2) using the classical ensemble model. The same double-line structure as the lower intensity (1.0 × 10(14) W/cm(2)) is also observed in the correlated electron momentum spectra for 1.2-1.4 × 10(14) W/cm(2). However, in contrast to the lower intensity where NSDI proceeds only through the recollision-induced double excitation with subsequent ionization (RDESI) mechanism, here, the recollision-induced excitation with subsequent ionization (RESI) mechanism has a more significant contribution to NSDI. This indicates that RDESI is not necessary for the formation of the double-line structure and RESI can give rise to the same type of structure independently. Furthermore, we explore the ultrafast dynamics underlying the formation of the double-line structure in RESI.

Transition of recollision trajectories from linear to elliptical polarization

Using a classical ensemble method, we revisit the topic of recollision and nonsequential double ionization with elliptically polarized laser fields. We focus on how the recollision mechanism transitions from short trajectories with linear polarization to long trajectories with elliptical polarization. We propose how this transition can be observed by meansuring the carrier-envelop-phase dependence of the correlated electron momentum spectra using currently available few-cycle laser pulses.

Resolving subcycle electron emission in strong-field sequential double ionization

Using a fully classical model, we have studied sequential double ionization (SDI) of argon driven by elliptically polarized laser pulses at intensities well in the over-barrier ionization region. The results show that ion momentum distributions evolve from the two-band structure to the four-band, six-band structure and finally to the previously obtained four-band structure as the pulse duration increases. Our analysis shows that the evolution of these band structures originates from the pulse-duration-dependent multiple ionization bursts of the second electron. These band structures unambiguously indicate the subcycle electron emission in SDI.

Transition of correlated-electron emission in nonsequential double ionization of Ar atoms

Emission of the two electrons released from nonsequential double ionization of argon atoms is anticorrelated at lower laser intensities but is correlated at higher laser intensities. Such a transition is caused by the momentum change of recollision-induced-ionization (RII) electrons. At lower laser intensities, the Coulomb repulsion between the two RII electrons dominates the motion of electrons and pushes them leaving the laser field back-to-back. At higher laser intensities, the drift momentum obtained from the laser field dominates the motion of electrons and drives them leaving the laser field side-by-side.

Mechanisms of strong-field double ionization of Xe

We perform a fully differential measurement on strong-field double ionization of Xe by 25 fs, 790 nm laser pulses in intensity region (0.4-3)×10(14) W/cm2. We observe that the two-dimensional correlation momentum spectra along the laser polarization direction show a nonstructured distribution for double ionization of Xe when decreasing the laser intensity from 3×10(14) to 4×10(13)  W/cm2. The electron correlation behavior is remarkably different with the low-Z rare gases, i.e., He, Ne, and Ar. We find that the electron energy cutoffs increase from 2.9Up to 7.8Up when decreasing the laser intensities from the sequential double ionization to the nonsequential double ionization regime. The experimental observation indicates that multiple rescatterings play an important role for the generation of high energy photoelectrons. We have further studied the shielding effect on the strong-field double ionization of high-Z atoms.

Subcycle control of electron-electron correlation in double ionization

Double ionization of neon with orthogonally polarized two-color (OTC) laser fields is investigated using coincidence momentum imaging. We show that the two-electron emission dynamics in nonsequential double ionization can be controlled by tuning the subcycle shape of the electric field of the OTC pulses. We demonstrate experimentally switching from correlated to anticorrelated two-electron emission, and control over the directionality of the two-electron emission. Simulations based on a semiclassical trajectory model qualitatively explain the experimental results by a subcycle dependence of the electron recollision time on the OTC field shape.

Strong-field double ionization through sequential release from double excitation with subsequent Coulomb scattering

We perform a triple coincidence study on differential momentum distributions of strong-field double ionization of Ar atoms in linearly polarized fields (795 nm, 45 fs, 7×10(13)  W/cm2). Using a three-dimensional two-electron atomic-ensemble semiclassical model including the tunneling effect for both electrons, we retrieve differential momentum distributions and achieve a good agreement with the measurement. Ionization dynamics of the correlated electrons for the side-by-side and back-to-back emission is analyzed separately. According to the semiclassical model, we find that the doubly excited states are largely populated after the laser-assisted recollision and large amounts of double ionization dominantly takes place through sequential ionization of doubly excited states at such a low laser intensity. Compared with the Coulomb-free and Coulomb-corrected sequential tunneling models, we verify that electrons can obtain an energy as large as ∼6.5U p through Coulomb scattering in the combined laser and doubly charged ionic fields.

Boosting photoabsorption by attosecond control of electron correlation

Electron correlation plays an essential role in a wide range of fundamentally important many-body phenomena in modern physics and chemistry. An example is the importance of electron-electron correlation in multiple ionization of multielectron atoms and molecules exposed to intense laser pulses. Manipulating the dynamic electron correlation in such photoinduced processes is a crucial step toward the coherent control of chemical reactions and photobiological processes. The generation of an attosecond extreme ultraviolet (EUV) pulse may enable such controls. Here, we show for the first time, from full-dimensional ab initio calculations of double ionization of helium in intense laser pulses (λ = 780 nm), that the electron-electron interactions can be instantaneously tuned using a time-delayed attosecond EUV pulse. Consequently, the probability of producing energetic electrons from excessive photoabsorption can be enhanced by an order of magnitude, by the attosecond control of electron-electron correlation.

Contribution of recollision ionization to the cross-shaped structure in nonsequential double ionization

With the three-dimensional classical ensemble model, we investigate the correlated electron emission in nonsequential double ionization (NSDI) of argon atoms by few-cycle laser pulses. Our calculations well reproduce the experimentally observed cross-shaped structure in the correlated two-electron momentum spectrum [ Nature Commun. 3, 813 (2012)]. By tracing these NSDI trajectories, we find that besides the process of recollision-induced excitation with subsequent ionization just before the next field maximum, the recollision ionization also significantly contributes to the cross-shaped structure.

Revealing the multi-electron effects in sequential double ionization using classical simulations

We theoretically investigated sequential double ionization (SDI) of Ar by the nearly circularly polarized laser pulses with a fully correlated classical ensemble model. The ion momentum distributions of our numerical results at various laser intensities and pulse durations agree well with the experimental results. The experimentally observed multi-electron effects embodied in the joint momentum spectrum of the two electrons is also reproduced by our correlated classical calculations. Interestingly, our calculations show that the angular distribution of the first photoelectron from the trajectories which eventually suffer SDI differs from the distribution of the photoelectrons from above-threshold ionization trajectories. This observation provides additional evidence of multi-electron effects in strong field SDI.

Correlated electron dynamics in nonsequential double ionization of molecules by mid-infrared fields

The electron dynamics in strong field nonsequential double ionization (NSDI) of nitrogen molecules by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. The numerical results show that in the MIR regime, the correlated behavior of the two electrons from NSDI is independent on the molecular alignment, contrary to the case in the near-infrared (NIR) regime where the electron correlations exhibit a strong alignment dependence. In consistent with the experimental results, our numerical results show that the longitudinal momentum spectrum of the doubly charged ion evolves from a wide single-hump structure at NIR regime into a double-hump structure when wavelength enters the MIR regime. This double-hump structure becomes more pronounced as the wavelength further increases. The responsible microscopic electron dynamics of NSDI at the MIR regime is explored by back analysis of the classical trajectories.