Internal collision double ionization of molecules driven by co-rotating two-color circularly polarized laser pulses

The double ionization process of molecules driven by co-rotating two-color circularly polarized fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that a considerable part of the sequential double ionization(DI) events of molecules occur through internal collision double ionization(ICD), and the ICD recollision mechanism is significantly different from that in non-sequential double ionization(NSDI). By analyzing the results of internuclear distances R = 5 a.u. and 2 a.u., these two recollision mechanisms are studied in depth. It is found that the dynamic behaviors of the recollision mechanisms of NSDI and ICD are similar. For NSDI, the motion range of electrons after the ionization is relatively large, and the electrons will return to the core after a period of time. In the ICD process,electrons will rotate around the parent ion before ionization, and the distance of the electron motion is relatively small. After a period of time, the electrons will come back to the core and collide with another electron. Furthermore, the molecular internuclear distance has a significant effect on the electron dynamic behavior of the two ionization mechanisms. This study will help to understand the multi-electron ionization process of complex systems.

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.

Fragmentation dynamics of electron-impact double ionization of helium

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V to 1 ke V for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr's model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot,we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron–ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

Nonsequential double ionization of nonaligned diatomic molecules N_2 and O_2

Nonsequential double ionization （NSDI） processes of nonaligned diatomic molecules N2 and O2 are studied using the S-matrix theory. Our results show that the NSDI process significantly depends on the molecular symmetry and structure. The ratio of NSDI rate to single ionization rate as a function of the field intensity is obtained. It is found that N2 behaves closely with its companion atom Ar in the ratios over the entire intensity range, while O2 exhibits an obvious suppression effect, which is qualitatively consistent with the experiment.

Two-photon double ionization of helium by chirped few-cycle attosecond pulses:From nonsequential to sequential regime

The two-photon double ionization（TPDI） dynamics of helium by chirped attosecond pulses are theoretically studied by solving the two-electron time-dependent Schr o¨dinger equation in its full dimensions. We show that both the differential and the total double ionization probability can be significantly controlled by adjusting the chirp. The dependence of the TPDI on the chirp can be quite different for different photon energies, relying on the central photon energy being in the sequential region, nonsequential region, or translation region. The physics which lead to the chirp dependence for different photon energies are addressed. Present findings are well reproduced by a model based on the second-order time-dependent perturbation theory.

Electron correlations in nonsequential double ionization of argon atoms by elliptically polarized laser pulses

Using a classical ensemble model, we investigate the correlation behaviour of electrons originating from nonsequential double ionization （NSDI） of argon atoms by the elliptically polarized laser pulses. Because of the ellipticity, not only the first electron to return but also the later return of tunneled electrons contribute significantly to NSDI. We mainly discuss two kinds of events of NSDI originating from the first and the second return separately. For the NSDI resulting from the recollision of the first return, the correlated electron momentum spectrum along the long axis of the laser polarization plane reveals an obvious V-like shape, located at the first and third quadrant. However, for the NSDI resulting from the recollision of the second return, the momenta of two electrons are distributed in the four quadrants uniformly. By analysing the trajectories of these two kinds, we find that the recollision energy and the laser phase at recollision are different for the first and second returning trajectories, which are responsible for the difference in the correlated behavior of the final electron momentum.

Effect of elliptical polarizations on nonsequential double ionization in two-color elliptically polarized laser fields

Using the classical ensemble model, we investigate the nonsequential double ionization（NSDI） of Ar and Mg in the two-color elliptically polarized laser pulse for different elliptical polarizations. Numerical results show that for Ar atoms the NSDI yield increases as the ellipticity increases, which is different from the case of Mg atoms. Moreover, the correlated behavior in the correlated electron momentum along the x direction and ion momentum distributions of Ar atoms are influenced by the ellipticity. By statistical analysis of different times, we can conclude that the ellipticity may be responsible for the NSDI processes. The correlated momenta distributions along the x direction at the recollision time are demonstrated and the results show that the travelling time and ellipticity can affect the emitted directions of both electrons.

Dynamic Interference Photoelectron Spectra in Double Ionization:Numerical Simulation of 1D Helium

We report our numerical simulation on the dynamic interference photoelectron spectra for a one-dimensional （1D） He model exposed to intense ultrashort extreme ultraviolet （XUV） laser pulses. The results demonstrate an unambiguous interference feature in the photoelectron spectra, and the interference is unveiled to originate from the dynamic Stark effect. The interference photoelectron spectra are prompted for intense sub-femtosecond XUV laser pulses in double ionization. The stationary phase picture is corroborated qualitatively in the two-electron system. The ability of probing the dynamic Stark effect by the photoelectron spectra in a pragmatic experiment of single-photon double ionization of He may shed light on further investigation on multi-electron atoms and molecules.

Double Ionization Dynamics of Molecular Hydrogen in Ultrashort Intense Laser Fields

We experimentally investigate the double ionization pulses. The total kinetic energy release of the two of molecular hydrogen subjected to ultrashort intense laser coincident H＋ ions, which provides a diagnosis of different processes to double ionization of H2, is measured for two different pulse durations, i.e., 25 and 5 fs, and various laser intensities. It is found that, for the long pulse duration （i.e., 25 fs）, the double ionization occurs mainly via two processes, i.e., the charge resonance enhanced ionization and recollision-induced double ionization. Moreover, the contributions from these two processes can be significantly modulated by changing the laser intensity. In contrast, for a few-cycle pulse of 5 fs, only the recollsion-induced double ionization survives, and in particular, this process could be solely induced by the first-return reeollision at appropriate laser intensities, providing an efficient way to probe the sub-laser-cycle molecular dynamics.

Influence of Coulomb force between two electrons on double ionization of He-like atoms

In strong-field double ionization,two electrons are ionized by intense laser field.These two electrons move in the laser field and the state is described by a Coulomb-Volkov state,where the repulsive Coulomb state describes the relative motion of the two electrons and the Volkov state describes the center-of-mass motion of the two electrons in the laser field.In the frame of scattering theory,we derive a simple analytical formula of the double ionization of He-like atoms.The effect of the Coulomb force between two electrons on the double ionization process is discussed.Numerical studies disclose that the Coulomb force enhances the ionization rate of high-energy electrons but suppresses the ionization rate of the lowest-energy electrons.

Evidence of potential change in nonsequential double ionization

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.

The effect of electron initial longitudinal velocity on the non-sequential double ionization process in an elliptically polarized laser field

The effect of initial longitudinal velocity of the tunnelled electron on the non-sequential double ionization （NSDI） process in an elliptically polarized laser field is studied by a semiclassical model. We find that the non-zero initial longitudinal velocity has a suppressing effect on single-return collision （SRC） events in the double ionization process, more specifically, it results in an obvious reduction in the center part of the correlation momentum distributions in the direction of the major polarization axis （z axis） and makes the distribution of single-return collision in the minor polarization axis （x axis） become narrower.

Relative phase effect of nonsequential double ionization in Ar by two-color elliptically polarized laser field

We investigated the nonsequential double ionization(NSDI)in Ar by two-color elliptically polarized laser field with a three-dimensional(3D)classical ensemble method.We study the relative phase effect of NSDI and distinguish two particular recollision channels in NSDI,which are recollision–impact ionization(RII)and recollision-induced excitation with subsequent ionization(RESI),according to the delay-time between the recollision and the final double ionization.The numerical results indicate that the ion momentum distribution is changed and the triangle structure is more obvious with the decrease of the relative phase.We also demonstrate that the RESI process always dominates in the whole double ionization process and the ratio of RESI and RII channels can be influenced by the relative phase.

Nonsequential double ionization of the aligned hydrogen molecule in strong field

This paper studies the nonsequential double ionization （NSDI） process of diatomic molecules aligned parallel and perpendicular to an intense linearly polarized laser field by using a three-dimensional semiclassical model. With this model, it achieves insight into the ion momentum distribution under the combined influence of a two-centre Coulomb potential and an intense laser field, and this result shows the significant influence of molecular alignment on the ratio between double and single ionization rate. Careful investigations show that the NSDI process for different alignment molecules has a close relation to the laser intensity and the different bounding electron distribution has a significant influence on the final ion momentum distribution.

Quantitative rescattering theory for nonsequential double ionization

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.

Double ionization of helium interacting with elliptically polarized laser pulse by classical ensemble simulations

This paper uses the classical ensemble method to study the double ionization of a 2-dimensional （2D） model helium atom interacting with an elliptically polarized laser pulse. The classical ensemble calculation demonstrates that the ratio of double to single ionization decreases with the increasing ellipticity of the driving field. The classical scenario shows that there are hardly any e--e recollisions with the circularly polarized laser pulse. The double ionization probability is studied for linearly and circularly polarized laser pulses. The classical numerical results are consistent with the semiclassical rescattering mechanism and in agreement with the experimental results and the quantum calculations qualitatively.

Nonsequential double ionization of diatomic molecules by elliptically polarized laser pulses

Using the classical ensemble method, we investigate nonsequential double ionization （NSDI） of diatomic molecules by elliptically polarized laser pulses. The results show that the ellipticity of the laser field has a strong suppression effect on NSDI probabilities both in parallel and perpendicular alignments. The double ionization （DI） channel is commonly dominated by NSDI, and the NSDI channel changes with ellipticity. As ellipticity increases, more and more NSDIs occur through recollision excitation with subsequent field ionization （RESI）. Moreover, like the case of linear polarization, the two electrons involved in NSDI for perpendicularly aligned molecules are more likely to emit into the opposite hemispheres as compared to the case of parallel alignment. Additionally, this alignment effect increases as ellipticity increases.

Effect of electron excitation in nonsequential double ionization by intense laser fields

We study the double ionization process of atoms in intense laser fields. The momentum distributions of the correlated electrons are calculated. Contrary to the general expectation, we show an increasing proportion of the electrons ionized via excitation with the increasing laser intensity. These electrons generally have small energy thus they concentratedly distribute on the central region of the momentum diagram. Consequently, the central part of the momentum diagram becomes more notable in higher intensity laser fields. Further study suggests that this phenomenon is general in double ionization.

Exploration of strong-field double ionization of C3H6 with the structures of propene and cyclopropane in intense laser fields

By using classical ensemble method, we investigate the double ionization of C3H6 molecule with different structures （propene and cyclopropane） in intense laser fields. The numerical results show that the non-sequential double ionization occurs in propene molecule rather than cyclopropane molecule in 1200 nm laser field. To further explain this interesting phenomenon, the momentum distribution of double ionized electrons is presented and the result presents the ＂finger-like＂ structure at about 30 TW/cm^2 of propene molecule, and this structure is more obvious than that in cyclopropane molecule. The above phenomena are also demonstrated by analysing the energy distributions of double-ionized electrons versus time. Moreover, we also investigated the angular distribution at the end of pulse, which is different between propene and cyclopropane.

Multiple recollisions in nonsequential double ionization below the recollision-ionization threshold

By using the three-dimensional classical ensemble model,the recollision dynamics in nonsequential double ionization(NSDI)of Ar by 780-nm laser pulses at(6-1.2)×10^(14)W/cm^(2) was extensively studied.We revealed the picture of multiplerecollision in the double ionization events at the laser intensity region below the recollision-ionization threshold.Via tracing the NSDI trajectories,it was found that the contribution of these multiple-recollision events increases as the laser intensity decreases.In this low intensity region,many multiple-recollision induced NSDI trajectories occur through the doubly excited states.The decay speed of the doubly excited state decreases with the decreasing laser intensity.