Nonsequential Double Ionization 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.

Simulations of the correlated momentum distributions for nonsequential double ionization of neon in elliptically polarized laser fields

We use the improved quantitative rescattering (QRS) model to simulate the experimentally measured correlated two-electron momentum distributions (CMDs) for nonsequential double ionization (NSDI) of Ne exposed to intense elliptically polarized laser pulses with a central wavelength of 788 nm at a peak intensity of 5 ×1014 W cm−2 for the ellipticities ranging from 0 to 0.25 (Kang et al 2018 Phys. Rev. A 97 063403). Only the CMDs for recollision direct ionization are calculated and the contribution from recollision excitation with subsequent ionization is ignored. With the assumption that recollisions occur after the zero crossing of the electric field along the major polarization, the QRS model successfully reproduces the experimentally observed asymmetry pattern of electron pairs in the CMDs for NSDI of Ne under elliptical polarization. By reducing the peak intensity claimed in experiment by about 30%, good agreement is achieved between the present results and the experimental measurements.

The modeling non-sequential double ionization of helium atom under high-intensity femtosecond laser pulses with shielding charge approximation

In this study, we successfully extracted the ‘knee structure’ for non-sequential double ionization (NSDI) in the helium atom. To achieve this, for the first time, we solved the time-dependent Schrödinger equation in three dimensions for the helium atom, utilizing the shielding charge approximation. Our findings corroborate prior observations by Wang et al [Wang and Eberly, Phys. Rev. Lett. 105, 083001 (2010)], demonstrating that NSDI occurs within a narrower time window in circular polarization compared to linear polarization. As a result, the yield of linear polarization was higher than that of circular polarization, aligning with the previously reported results. Notably, in the case of circular polarization, the time window further narrows with increasing intensity, attributed to a decrease in the time-of-flight.

Control of Frustrated Nonsequential Double Ionization Channels With the Carrier-Envelope Phase of Elliptically Polarized Laser Pulses

Abstract Using a classical approach, we theoretically investigate the frustrated double ionization (FDI) of Ar atoms under elliptically polarized (EP) laser fields. The FDI yield is calculated as a function of laser intensity with different carrier-envelope phases (CEPs), and, similar to the carrier-envelope phase (CEP) dependence of nonsequential double ionization (NSDI), several knee-shaped structures appear. Moreover, both recollision and direct ionization trajectories are observed in FDI events for the “knee” structure regime. The footprints of which channel leads to FDI are encoded in the photoelectron momentum distributions. FDI events related to recollision excitation with subsequent ionization channels and recollision impact ionization channels can be controlled by CEP in EP laser fields.

Manipulating polarization effect in nonsequential double ionization.

We report on a theoretical study of nonsequential double ionization (NSDI) of magnesium atoms by using combined linearly and circularly polarized fields. By employing a concise model including the dynamic ionic dipole potential, we show that the polarization effects can be controlled by tuning the subcycle waveform of the electric field of the two-color pulses. We demonstrate that the influence of the dipole potential on NSDI depends on the symmetry of two-color laser fields by tracing back the electron trajectories. Furthermore, we propose a method allowing for manipulating the returning trajectories with the initial direction of the tunneled electrons almost unchanged.

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 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.

Precollision effect on the double ionization of an Ar atom driven by a two-color counter-rotating circularly polarized laser pulse

The double ionization process of an Ar atom driven by a two-color counter-rotating circularly polarized (TCCP) laser pulse is theoretically investigated. Classical trajectory analysis reveals that a significant portion of Nonsequential Double Ionization (NSDI) events occurs through precollision, rather than the well-known recollision mechanism. In the precollision-induced Nonsequential Double Ionization (PCDI) process, the two electrons exhibit a tendency for back-to-back emission, resulting in a lower electronic correlation effect, and the ion recoil momentum concentrated in the zero momentum region. On the other hand, in the recollision-induced Nonsequential Double Ionization (RCDI) process, the two electrons tend to emit in the same direction, leading to a higher electronic correlation effect, and the ion recoil momentum is situated far from the zero momentum region. Moreover, both PCDI and RCDI strongly depend on the parameters of the driving laser pulse. Therefore, the primary mechanism of double ionization can be experimentally probed by observing the corresponding ion recoil momentum.

Nonsequential double ionization channels control of CO2 molecules with counter-rotating two-color circularly polarized laser field by laser wavelength

Abstract Using the classical ensemble model, we investigate the effect of laser wavelength on the electron dynamics process of nonsequential double ionization (NSDI) for linear triatomic molecules driven by a counter-rotating two-color circularly polarized laser field. Based on the delay time between recollision and final double ionization, two particular ionization channels are separated: recollision-impact ionization (RII) and recollision-induced excitation with subsequent ionization (RESI). Numerical results show that with the increase of the laser wavelength, the triangle structure of the ion momentum distribution becomes more obvious, which indicates that the electron–electron correlation of NSDI is enhanced. In addition, we find that the ratio of the RESI channel gradually decreases with the increase of the laser wavelength, while the ratio of the RII channel is opposite. However, the dominant channel is still RESI. It means that the two ionization channels can be controlled effectively by changing the laser wavelength.

High-order harmonic generation, attosecond pulse, and non-sequential double ionization in the helium atom under high-intensity femtosecond laser pulses

High-order harmonic generation (HHG), attosecond pulse train (APT), isolated attosecond pulse (IAP), and non-sequential double ionization (NSDI) in the Helium atom under intense femtosecond laser pulses are computed using the time-dependent Schrodinger equation (TDSE) in one dimension (1D). By taking into account the electron–electron and electron-nucleus interactions, as well as determining the Helium atom’s ground state wave function through the imaginary time propagation (ITP) method, we are able to observe the widely recognized ‘knee structure’ in the ionization probability of the Helium atom as a function of intensity within an ionization boundary condition model. The results are in good agreement with the experimental data reported by (Walker et al (1994) Phys. Rev. Lett. 73, 1227).

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.

The optimized field amplitude ratio for nonsequential double ionization by counter-rotating two-color circularly polarized fields

With a classical trajectory Monte Carlo model, we systematically study the laser intensity and field amplitude ratio dependence of nonsequential double ionization by counter-rotating two-color circularly polarized fields (800 and 1600[Formula: see text]nm). The results show that the optimized field amplitude ratio changes with the laser intensity, which is attributed to the shift of the most probable amplitude ratio of electron returning with the laser intensity. Moreover, the laser intensity-dependent double ionization probability curve shows a remarkable dip in the transition region between the nonsequential and sequential channels. It can be well explained by the reduction of the probability of electron returning with the increase of the laser intensity.

Determination of ionic polarizability by nonsequential double ionization

Determination of ionic polarizability by nonsequential double ionization

Nonsequential double ionization of atoms driven by few-cycle counter-rotating two-color circularly polarized laser fields

Using a classical ensemble model, we investigated the dependence of nonsequential double ionization (NSDI) on the relative phase driven by few-cycle counter-rotating two-color circularly polarized (TCCP) laser fields, which consist of 1600-nm laser pulse and 800-nm laser pulse. The numerical results reveal that NSDI probability is strongly dependent on the relative phase of counter-rotating TCCP fields, which shows a sin-like behavior of period 2π. The inversion analysis shows that the returning probability of the first electron is very sensitive to the relative phase of counter-rotating TCCP fields, resulting in dependence of NSDI probability on the relative phase. Furthermore, the dynamic behavior of two electrons can be regulated by adjusting the relative phase, leading to the sensitive dependence of momentum distribution of Ar2+ ions on the relative phase of counter-rotating TCCP fields. In addition, our results show that the traveling electron can be controlled to return to the parent ion core from a relatively single direction, which leave an imprint on the momentum distribution of Ar2+ ions.

Controlling multiple returnings in non-sequential double ionization with orthogonal two-color laser pulses

With the three-dimensional semi-classical ensemble model, we studied the non-sequential double ionization by orthogonal two-color laser pulses. Our calculations show that the proportion of events experiencing multiple returnings, the sum of the final energies of two electrons, and the ion momentum distribution depend on the relative phase of the two-color fields, exhibiting oscillatory behavior with a period of π. Back analysis of these trajectories reveals that we can control the recollision energy of the electron by changing the relative phase of the two-color laser pulse. As a consequence, the trajectories of multiple-returning ions change with the relative phase, resulting in relative-phase-dependent ion momentum distributions. The result shows that the momentum distribution of the ions in the trajectories of multiple returnings is clearly wider than that for the case of single returning. For the multiple-returning events, the binary recollision leads to a smaller scattering angle of the first electron.

Pulse length effects in long wavelength driven non-sequential double ionization

Pulse length effects in long wavelength driven non-sequential double ionization

Pulse length effects in long wavelength driven non-sequential double ionization

We present a joint experimental and theoretical study of non-sequential double ionization (NSDI) in argon driven by a 3100 nm laser source. The correlated photoelectron momentum distribution (PMD) shows a strong dependence on the pulse duration, and the evolution of the PMD can be explained by an envelope-induced intensity effect. Determined by the time difference between tunneling and rescattering, the laser vector potential at the ionization time of the bound electron will be influenced by the pulse duration, leading to different drift momenta. Such a mechanism is extracted through a classical trajectory Monte Carlo-based model and it can be further confirmed by quantum mechanical simulations. This work sheds light on the importance of the pulse duration in NSDI and improves our understanding of the strong field tunnel-recollision dynamics under mid-IR laser fields.

Searching for optimal THz generation through calculations of the asymmetry of photoelectron momentum distributions by an improved strong-field-approximation method

From the solution of the time-dependent Schr\"odinger equation (TDSE), it has been shown that in a two-color laser pulse the relative phase that optimizes terahertz (THz) radiation also optimizes the asymmetry of the angular distribution of photoelectrons. Here, we show that a second-order strong-field approximation can accurately calculate the asymmetry of photoelectrons and thus can locate the phase delay that optimizes THz generation, doing so four orders of magnitude faster than TDSE calculations. We further trace that this is possible because THz emission originates from a free-free radiative transition between the rescattered electron and the target ion, similar to other electron-ion collisions in the laser field, e.g., high-harmonic generation and nonsequential double ionization. Our results pave the way to locate the optimal phase delay for any typical laser pulses for maximal THz generation in the laboratory.

Nonsequential double ionization of atoms driven by spatially inhomogeneous laser fields

<sec>Using a three-dimensional classical ensemble method, we investigate the nonsequential double ionization (NSDI) of xenon atoms from the near infrared wavelength to the mid-infrared wavelength in spatially inhomogeneous laser fields, and compare the results with those from spatially homogeneous laser fields. The results show that the NSDI probability curves from spatially inhomogeneous laser field and spatially homogeneous laser field at short wavelength are similar to each other. With the laser wavelength increasing, NSDI at the high intensities is more and more suppressed for spatially inhomogeneous laser field.</sec><sec>Compared with the result from the spatially homogeneous laser field, the final emission angle of two electrons from the NSDI exhibits a very strongly correlated characteristic in the spatially inhomogeneous field, especially at a longer laser wavelength, the final emission angles of two electrons are almost both concentrated around <inline-formula><tex-math id="M2">\begin{document}${0^\circ }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230548_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230548_M2.png"/></alternatives></inline-formula>, meaning that the two electrons are always emitted into the same direction parallelly. Moreover, effective recollision of the NSDI is always dominated by first return of the first electron from the near infrared to the mid-infrared inhomogeneous laser fields, however, the transition from the first return dominance to the second return dominance occurs in the spatially homogeneous laser fields. Further, we reveal the more details of the ultrafast dynamics of the correlated electrons in the spatially inhomogeneous laser field by back-tracing the classical trajectories of NSDI.</sec>

Controlling nonsequential double ionization mechanisms of argon atoms by parallel two-color laser pulses

Controlling nonsequential double ionization mechanisms of argon atoms by parallel two-color laser pulses