Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

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.

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.

Role of Nuclear Coulomb Attraction in Nonsequential Double Ionization of Argon Atom

The microscopic recollision dynamics in strong-field nonsequential double ionization of Ar atoms is in- vestigated using three-dimensional classical ensembles. By adjusting the nuclear Coulomb potential, we can excellently reproduce the experimental results both within the laser intensity regimes well above the reeollision threshold and well below the recollision threshold quantitatively. More importantly, our trajectory analysis clearly reveals the particular electronic dynamics in recollision process： the momentum of the recolliding electron encounters a sudden change both in magnitude and in direction when it approaches the nucleus closely, which show that the nuclear Coulomb attraction plays a key role in the recollision process of nonsequential double ionization of Ar atoms.

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.

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.

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.

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.

Influence of relative phase on the nonsequential double ionization process of CO_(2) molecules by counter-rotating two-color circularly polarized laser fields

We investigate the nonsequential double ionization(NSDI) of linear triatomic molecules by the counter-rotating two-color circularly polarized(CRTC) laser fields with a classical ensemble method. The results of the simulation reveal that NSDI yield strongly connected with the relative phase. The trajectory tracking method shows that the return time of the electron is controlled by the relative phase. In addition, when we change the CRTC laser wavelengths, the relative phase of the maximum and minimum yield of NSDI also changes. This shows that the influence of the Coulomb potential in the triatomic molecules on the electron return process cannot be ignored. This work will effectively promote the electronic dynamics study of NSDI for the triatomic molecule.

Scaling law in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields

Nonsequential double ionization(NSDI) of noble gas atoms in counter-rotating two-color circularly polarized(CRTC) laser fields is investigated. A scaling law is concluded by qualitatively and quantitatively comparing the momentum distributions of two electrons from NSDI in CRTC laser fields for different atoms with different parameters. The scaling law indicates that the momentum distributions from an atom driven by CRTC laser frequency ω1, ω2, and laser intensity I are the same as that from another atom irradiated by CRTC laser frequency kω1, kω2, and laser intensity k3I. This study can provide an avenue in the research of two-color laser field ionization.

Carrier-envelope-phase effect in nonsequential double ionization of Ar atoms by few-cycle laser pulses

A classical ensemble method is used to investigate nonsequential double ionization（NSDI） of Ar atoms irradiated by linearly polarized few-cycle laser pulses. The correlated-electron momentum distribution（CMD） exhibits a strong dependence on the carrier-envelope phase（CEP）. When the pulse duration is four cycles, the CMD shows a cross-like structure, which is consistent with experimental results. The CEP dependence is more notable when the laser pulse duration is decreased to two cycles and a special L-shaped structure appears in CMD. Recollision time of returning electrons greatly depends on CEP, which plays a significant role in accounting for the appearance of this structure.

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.

Electron dynamics of molecular frustrated double ionization driven by strong laser fields

We theoretically investigate the frustrated double ionization(FDI)of molecules with different alignment-dependence using a three-dimensional classical ensemble method.The numerical results show that the FDI probability decreases with increasing wavelength,which is similar to the wavelength dependence of the FDI probability of atoms.Tracing the classical trajectories reveals that the contributions to molecular FDI from single-recollision and multiple-recollision mechanisms are equal in the short wavelength regime.In the long wavelength regime,the single-recollision FDI channel dominates in FDI.The nature in which molecular FDI occurs is identified and explained.

Relative phase-dependent two-electron emission dynamics with two-color circularly polarized laser fields

With the semiclassical ensemble model, we explore the relative phase-dependent nonsequential double ionization (NSDI) of Mg by counter-rotating two-color circularly polarized (TCCP) laser pulses. The yield of Mg2+ sensitively depends on the relative phase Δφ and the intensity of TCCP laser fields. At Δφ=1.5π, the yield of Mg2+ exhibits a pronounced peak in the 0.05 PW/cm2 laser field. This behavior results from the increase of the initial transverse velocity compensating for the drift velocity with the decreasing angle by analyzing the angular distributions of the electron pairs in four relative phases. By changing the relative phases, we find that the recollision excitation with subsequent ionization and the recollision-impact ionization mechanisms can be controlled with TCCP laser fields.