Nonsequential Double Ionization Process Research Articles

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

Abstract 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 was theoretically studied. And the dynamics in two typical collision pathways, recollision-impact-ionization (RII) and recollision-excitation 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 relative amplitude of 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 of the NSDI process.

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 0.5π and 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.

Nonsequential double ionization of Ar atoms in counter-rotating two-color elliptically polarized laser fields

Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated by using the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Unlike counter-rotating two-color circularly polarized laser field, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first quadrant and the third quadrant to anti-correlation behavior mainly located in the second quadrant and fourth quadrant. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI process. In addition, further analysis finds that the shape of the trajectory becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more populations move to the second quadrant and the fourth quadrant as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.

The nonsequential double ionization of Ar atoms with different initial angular momenta irradiated by a circularly polarized laser pulse

The non-sequential double ionization process of Ar atoms with different initial angular momenta in the 500 nm circularly polarized field is investigated with a classical ensemble model. The numerical results show that, under the circularly polarized laser pulse, the double ionization yield as a function of the laser intensity for Ar atoms with different initial angular momenta exhibit an obvious Knee structure. The ionization yield in the counter-rotating case where the electronic initial rotation direction is opposite to the vector potential of the laser field, significantly higher than that in the co-rotating case where the electronic initial rotation direction is consistent with the vector potential of the laser field. Based on the classical trajectory analysis, it is found that this ionization difference comes from the angle between the direction of the electronic momentum and the force of the laser field at the single ionization instant. The angle in the counter-rotating case is greater than that in the co-rotating case, and the counter-rotating electrons are more likely to return to the parent ion for recollision. Besides, the recollision intants of Ar atoms with the different initial angular momenta are mapped to the electron momentum spectrum. This may provide a method to obtain the electron’s recollision instant of Ar atoms with different initial angular momenta.

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.

Intensity dependence of ionic-state-resolved electron-electron correlation in strong-field double ionization

In this paper, we theoretically investigate the nonsequential double ionization (NSDI) process of Ne induced by linearly polarized laser field using strong field approximation theory. It is found that, with increasing laser intensity, the correlated electron momentum distributions (CEMDs) corresponding to multiple-return-collision process, which is believed to predominate in NSDI process at high intensity, exhibit a dependence on the wave function of the intermediate ionic state. This observation indicates that the information of the intermediate ionic state in NSDI process can be extracted from CEMD at specific laser intensity.

Ionic-state-resolved electron–electron correlation in strong-field double ionization

In this paper, we theoretically investigate the nonsequential double ionization (NSDI) process of Ne induced by 400 nm linearly polarized laser field with a intensity above the recollision threshold using the S-matrix theory. It is unexpected to find that, significantly different from the results for wavelength longer than 800 nm, both the electron momentum correlated distribution and the longitudinal momentum distribution of Ne2+ exhibit a strong dependence on the wave function of the intermediate ionic state from which the second electron is ionized. This observation provides a potential way to extract the information about the ionic-state wave function based on NSDI process.

Phase delay effect of nonsequential double ionization of Ar atoms in a 45°cross-linearly-polarized two-color laser field

We theoretically investigate the nonsequential double ionization (NSDI) of Ar atoms by a three-dimensional (3D) classical ensemble method in a 45∘ cross-linearly-polarized two-color (CTC) laser field. Our results show that the phase delay of the synthesized two-color laser field can influence the NSDI process. By tracing the classical trajectories of the NSDI process, we find that the single-recollision (SR) and the double-recollision (DR) both occur. Whether the recollision processes happen once or twice, the NSDI predominantly experience the recollision-induced excitation with subsequent ionization (RESI) channel. And the phase delay of the CTC pulse could influence the probability of the double ionization and the energy transfer in NSDI process. This provides a method to obtain the information about the dynamics of the recollision process.

Influence of relative phase on the nonsequential double ionization process of CO2 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.

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.

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.

Controlling electron collision by counterrotating circular two-color laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 61475168, 11674231, and 61575124).

Electron collision as well as its controlling lies in the core of study on nonsequential double ionization (NSDI). A single collision occurred in a convergent time is important to disclose the essential features of the electron correlation. However, it is difficult to form such a collision. By using counterrotating circular two-color (CRTC) laser fields, we show that a single electron collision can be achieved in a convergent time and a net electron correlation is set up within the sub-femtosecond time scale in the NSDI process of Ar atoms. The proposed method is also valid for other atoms, provided that one chooses the frequency and intensity of the CRTC field according to a scaling law.

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.

Effect of elliptical polarizations on nonsequential double ionization in two-color elliptically polarized laser fields**Project supported by the National Natural Science Foundation of China (Grant No. 61575077) and the Natural Science Foundation of Jilin Province, China (Grant No. 20180101225JC).

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.

Nonsequential double ionization of helium in IR+XUV two-color laser fields II: collision-excitation ionization process

We recently investigated the collision-ionization mechanism of the nonsequential double-ionization (NSDI) process in IR+XUV two-color laser fields [(2016) Phys. Rev. A 93 043417]. Here, we extend this work to study the collision-excitation-ionization (CEI) mechanism of the NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the extreme ultraviolet (XUV) photon energy is smaller than the ionization threshold of the He+ ion, and the momentum spectrum shows complex interference patterns and symmetrical structures. By channel analysis, we find that, as the energy carried by the recollision electron is not enough to excite the bound electron, the bound electron will absorb XUV photons during their collision; as a result, both forward and backward collisions make a comparable contribution to the NSDI processes. However, it is found that, as the energy carried by the recollision electron is large enough to excite the bound electron, the bound electron does not absorb any XUV photon and it is excited only by sharing the energy carried by the recollision electron, hence the forward collision plays a dominant role in the NSDI processes. Moreover, we find that the interference patterns of the NSDI spectra can be reconstructed by the spectra of two above-threshold ionization (ATI) processes, which may be used to analyze the structure of the two separate ATI spectra by NSDI processes.

Laser-Induced Inelastic Diffraction from Strong-Field Double Ionization.

In this Letter, we propose a novel laser-induced inelastic diffraction (LIID) scheme based on the intense-field-driven atomic nonsequential double ionization (NSDI) process and demonstrate that, with this LIID approach, the doubly differential cross sections (DDCSs) of the target ions, e.g., Ar^{+} and Xe^{+}, can be accurately extracted from the two-dimensional photoelectron momentum distributions in the NSDI process of the corresponding atoms. The extracted DDCSs exhibit a strong dependence on both the target and the laser intensity, in good agreement with calculated DDCSs from the scattering of free electrons. The LIID scheme may be extended to molecular systems and provides a promising approach for imaging of the gas-phase molecular dynamics induced by a strong laser field with unprecedented spatial and temporal resolution.

INVESTIGATING THE MULTIPLE RECOLLISION OF THE NONSEQUENTIAL DOUBLE IONIZATION PROCESS

<p>We systematically investigate the contribution of recollision dynamics to the nonsequential double ionization process (NSDI) of Ar atom for a wide range of laser intensity. The result shows that the first- and second-recollision scenarios have significant contribution to the NSDI events. Moreover, we figure out that the impact of double-recollision trajectories decreases as the laser intensity increases. Besides, many details of multiple recollisions are also investigated in this paper.</p>

INVESTIGATING THE MULTIPLE RECOLLISION OF THE NONSEQUENTIAL DOUBLE IONIZATION PROCESS

<p>We systematically investigate the contribution of recollision dynamics to the nonsequential double ionization process (NSDI) of Ar atom for a wide range of laser intensity. The result shows that the first- and second-recollision scenarios have significant contribution to the NSDI events. Moreover, we figure out that the impact of double-recollision trajectories decreases as the laser intensity increases. Besides, many details of multiple recollisions are also investigated in this paper.</p>

Classical trajectory analysis of Mg in a circularly polarized laser field

The nonsequential double ionization (NSDI) of Mg atoms is investigated in a circularly polarized laser field using the classical ensemble method. We demonstrate the time evolution of the two-electron energy distribution, the time evolution of the repulsion energy distribution between two electrons in the double ionization process and the time of evolution of the distance distribution between the nucleus and two electrons. The theoretical results indicate that a single recollision leads to the NSDI process. Moreover, we also look into the elliptical trajectories to illustrate the difference in the return process of the first ionized electron. The dependence of the electron momentum distribution on the angle between the momentum and the force of laser field at the time of the first electron is also investigated and the results show that the angle plays a key role in the electron recollision time.

Nonsequential double ionization of Ne subject to few-cycle femtosecond laser pulses

We investigate experimentally and theoretically the evolution of Ne2+ ion momentum distributions from Nonsequential Double Ionization (NSDI) in few-cycle laser pulses with respect to the Carrier Envelope Phase (CEP). The distributions depend strongly on the CEP and exhibit an asymmetric double-hump structure at some CEPs. A semiclassical calculation can reproduce the experimental observations qualitatively, where the rescattering scenario is identified as the main mechanism of double ionization. Analysis based on this semiclassical model reveals that double ionization happens a little later than the collision. Depending on the time difference between the ionization moment and the collision moment, we can distinguish two ionization pathways involved, i.e., Recollision Impact Ionization (RII) (with time difference below 0.1 optical cycle) and Recollision-Excitation and Subsequent Ionization (RESI) (with time difference above 0.1 optical cycle) pathways. The asymmetric pattern results from both RII and RESI: RII leads to the asymmetric double-hump structure, while RESI contributes to the low momentum part and makes the dip of the double-hump structure shallower. Furthermore, Ne2+ ion momentum distributions from RII depend strongly on the CEP and the distributions from RESI seem to be not very sensitive to the CEP. To shed more light on physical mechanism of the asymmetric momentum distribution, the momentum distributions from two ionized electrons are presented at the collision moment, the ionization moment and the moment right after laser field ends for each pathway, respectively. The comparison unravels that the asymmetry comes from the asymmetric acceleration from the laser electric field after the double ionization moments. To demonstrate the significant role of long range Coulomb potential in NSDI process, we replace the Coulomb potential with a short-range model potential in the calculation and the results show appreciable distinctions from the case of Coulomb potential. It is clarified that the Coulomb potential raises the yields of RESI process, which, in turn, makes the dip shallower.