Strong-field Nonsequential Double Ionization Research Articles

Internuclear distance dependence of internal-collision induced molecular nonsequential double ionization

ABSTRACT The internuclear distance (R) dependence of the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of parallel aligned diatomic molecules has been investigated. Results show the correlated electron momentum distribution (CEMD) is almost uniformly spread in the four quadrants for R = 4 a.u., while for larger R it is mainly located in the first and third quadrants. Classifying NSDI events into recollision and internal-collision processes demonstrates the CEMD of internal-collision induced NSDI is strongly dependent on R, which changes from a uniform distribution to a back-to-back emission pattern, and finally to a side-by-side emission pattern as R increases. Back analyzing of the classical trajectories shows it originates from the R dependent time delay between double ionization and collision times. When R increases, more and more internal-collision induced NSDI events occur immediately after collision, resulting in the enhanced dominance of the electron emission in the same hemisphere.

Revisiting the recollisional excitation-tunneling process in strong-field nonsequential double ionization of helium

We revisit the excitation-tunneling process in nonsequential double ionization (NSDI) of helium in an 800-nm laser field. The correlated two-electron momentum distributions are calculated by using the improved quantitative rescattering (QRS) model, in which the lowering of the threshold energy due to the presence of an electric field at the instant of recollision is taken into account. In the framework of the QRS model, the correlated two-electron momentum distributions for excitation-tunneling in NSDI can be factorized as a product of the returning-electron wave packet (RWP) and the field-free differential cross section (DCS) for electron impact excitation of the parent ion multiplied by the tunneling ionization rate of electrons in the excited states. The RWPs, which describe the momentum distribution of the returning electrons, are obtained within the strong-field approximation for high-order above-threshold ionization. The DCSs for electron impact excitation of ${\mathrm{He}}^{+}$ are calculated using the state-of-the-art many-electron $R$-matrix theory, and the tunneling ionization rates for electrons in the excited states are evaluated by solving the time-dependent Schr\"odinger equation. The calculated correlated two-electron momentum distribution shows that the fourfold symmetry with regard to the parallel momentum components is broken. This is in contradiction to the prevalent view that the correlation pattern for excitation-tunneling in NSDI is symmetric with respect to the coordinate axes. By including the recollisional ($e,2e$) process, the predicted correlated two-electron momentum distributions are found to be in good qualitative agreement with experiment.

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.

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.

Intensity-dependent recollision dynamics in strong-field nonsequential double ionization

Using the three-dimensional classical ensemble model, we systematically investigate the strong-field nonsequential double ionization (NSDI) of He atom by intense linearly polarized laser pulses at different intensities for 750 nm and 1500 nm in wavelength. In the intensity range of 0.4−0.8 PW/cm<sup>2</sup> considered in this work, for 750 nm wavelength the correlated electron pairs are always distributed mainly near the diagonal but for 1500 nm wavelength, with increasing laser intensity the population of electron pairs moves from the diagonal to the two axes, forming a near-axis V-shaped structure at 0.8 PW/cm<sup>2</sup>. The analysis indicates that for 750 nm with increasing laser intensity the contribution from the single-return events to NSDI decreases sharply and the contribution from the multiple-return events increases. For 1500 nm wavelength when the laser intensity increases, the contributions from one-, two- and three-return trajectories decrease and the contributions of other trajectories increase. It is because most of ionized electrons have a non-zero initial transverse momentum. After the excursion of the ionized electron, when it returns to the parent ion at the first time there is a distance in the transverse direction between the free electron and the parent ion, which hinders the recollision and NSDI from occurring. The transverse deviation can be significantly reduced by the Coulomb attraction from the parent ion to the free electron when it returns back to the parent ion in the longitudinal direction. Higher intensity results in larger returning velocity for the free electron. The free electron faster passes by the parent ion and the Coulomb attraction has less time to pull the free electron to the parent ion. For each return the compensation of the Coulomb attraction for the transverse deviation for high intensity is weaker than for low intensity. Thus for higher intensities more returns are required to compensate for the transverse deviation. Moreover, numerical results show the recollision distance in NSDI is smaller for the longer wavelength and higher intensity. It is attributed to the larger returning velocity of the free electron at the longer wavelength and higher intensity, which can more easily overcome the strong Coulomb repulsion between the two electrons and achieve a smaller recollision distance. Finally, electron correlation behaviors for those trajectories where recollision occurs with different return times are studied.

Attosecond control of correlated electron dynamics in strong-field nonsequential double ionization by parallel two-color pulses

We theoretically investigate the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of Ar by the parallel two-color pulses consisting of 800- and 400-nm laser fields with the semiclassical ensemble model. Our calculations show that the momentum distributions of Ar2+ in the direction parallel to the polarization of laser field exhibit the single- or double-hump structure, depending on the relative phase of the two-color fields. Back analysis of the NSDI trajectories reveals that recollision of returning electron is well confined in a time window of several attoseconds, and the position of which can be controlled with attosecond precision by changing the relative phase of the two-color fields. Thus, the recollision energy is accurately controlled with the two-color fields. As a consequence, the time delay between the double ionization and recollision changes with the relative phase, resulting in the relative-phase-dependent ion momentum distributions. More interestingly, the different peaks of ion momentum spectra result from the NSDI events with different time delays between double ionization and recollision. Thus, the corresponding correlated electron dynamics for different peaks in the ion momentum distributions can be directly determined in the two-color fields.

Multiple recollisions in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields.

With the three-dimensional (3D) classical ensemble method, we theoretically investigate the recollision dynamics in strong-field nonsequential double ionization (NSDI) of Ar by counter-rotating two-color circularly polarized laser fields. With the analysis of the NSDI trajectories, we find that not only multiple-recollision but also single-recollision processes occur in the double ionization events. Furthermore, the multiple-recollision and single-recollision processes both undergo the recollision-induced excitation with subsequent ionization (RESI) and recollision-induced ionization (RII). The angle between the momentum and the force of the laser field at the recollision moment can affect the times of the recollision.

Attosecond interference in strong-field nonsequential double ionization

Kinetic-energy spectra of a single electron from strong-field nonsequential double ionization are investigated in a high-intensity regime with a quantum mechanical model. We find interference fringes with large energy spacings, which increases with the electron kinetic energy. These interference fringes originate from the electronic wave packets born in the recollision by the returning electronic wave packets from the ``short'' and the ``long'' quantum paths. Since the recollision happens in a fraction of a near-infrared (NIR) optical cycle, i.e., in an attosecond time interval, the resulting interference fringes exhibit energy spacings much larger than the NIR photon energy. The comparison of the quantum mechanical results with a classical collision model suggests a near-equal energy sharing between two electrons during the recollision process at very high intensities, in contrast to the extremely unequal energy sharing at low intensities.

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.

Universal time delay in the recollision impact ionization pathway of strong-field nonsequential double ionization

With the semiclassical ensemble model, we investigated the correlated electron dynamics in the recollision impact ionization (RII) pathway of strong-field nonsequential double ionization (NSDI) at different laser wavelengths. Our results show that there is a remarkable time delay (about 400 attoseconds) between double ionization and recollision for a considerable part of the RII events. This type of event is responsible for the valley structure in the correlated electron momentum spectra along the laser polarization direction. More interestingly, our results show that this time delay is independent of the wavelength. This universal time delay is of crucial importance for the comprehensive understanding of the correlated electron dynamics in NSDI.

Coulomb-repulsion-assisted double ionization from doubly excited states of argon

We report a combined experimental and theoretical study to elucidate nonsequential double-ionization dynamics of argon atoms at laser intensities near and below the recollision-induced ionization threshold. Three-dimensional momentum measurements of two electrons arising from strong-field nonsequential double ionization are achieved with a custom-built electron-electron-ion coincidence apparatus, showing laser intensity-dependent Coulomb repulsion effect between the two outgoing electrons. Furthermore, a previously predicted feature of double ionization from doubly excited states is confirmed in the distributions of sum of two-electron momenta. A classical ensemble simulation suggests that Coulomb-repulsion-assisted double ionization from doubly excited states is at play at low laser intensity. This mechanism can explain the dependence of Coulomb repulsion effect on the laser intensity, as well as the transition from side-by-side to back-to-back dominant emission along the laser polarization direction.

Nonsequential double ionization of Xe by mid-infrared laser pulses

With the three-dimensional semiclassical ensemble model, we studied the correlated electron dynamics in strong-field nonsequential double ionization of Xe by mid-infrared laser pulses over a wide range of laser intensities. Numerical results show that the correlated electron momentum distribution exhibits the strong back-to-back pattern at the lower laser intensity. It evolves into the side-by-side behavior as the laser intensity increases and presents the experimentally observed crosslike shape at high laser intensity. Different from the case of near-infrared region where recollision mainly occurs at the first returning, at the mid-infrared region recollision dominantly occurs at the later returnings. The windows of initial transverse velocity for the various multiple-returning recollision trajectories are different and are unambiguously determined by this semiclassical ensemble model.

Correlated electron dynamics in strong-field double ionization

In intense laser-atom/molecule interaction, there are many new phenomena involving multielectron effects. As one of the most important strong-field process, strong-field double ionization of atoms and molecules, especially the strong-field nonsequential double ionization (NSDI), exhibits highly correlated behaviors, providing a clean way to study electron correlation in nature. We review the microscopic electron dynamics of NSDI revealed by recent experimental studies based on the COLTRIMS and the related theory contributions. We summarized the laser intensity-dependent microscopic electron dynamics of NSDI. At low laser intensities, NSDI is dominated by the recollision-excitation with subsequent field ionization, and the time delay between the final ionizations of the two electrons could results in the experimental observed back-to-back emission of the electron pairs. As the laser intensity increases, recollision induced direct ionization dominates NSDI and two electrons ionized almost simultaneously after recollision. In this process the final-state ion-electron attraction and electron repulsion significantly affect the details of the electron correlation pattern. As the laser intensity further increases, the role of final-state ion-electron and electron-electron interactions becomes less important, and the asymmetric energy sharing at recollision is prevalent which accounts for the strange V-like shape in the correlated electron momentum spectra at very high laser intensity. We also introduced the control of the correlated electron dynamics. It has been theoretically predicted that the electron pairs can be controlled to exhibit correlated or anticorrelated behavior with the two-color field, which has been proved by experiment. We also review the progress on strong-field sequential double ionization (SDI). Recent experiments have observed many phenomena which conflicted with the predictions of the previous theoretical models of SDI. Here we introduced a recent developed model of strong-field SDI, which successfully explained the new experimental results and predicted many interesting results.

State-resolved three-dimensional electron-momentum correlation in nonsequential double ionization of benzene

We report state-resolved electron-momentum correlation measurement of strong-field nonsequential double ionization in benzene. With a novel coincidence detection apparatus, highly efficient triple coincidence (electron-electron dication) and quadruple coincidence (electron-electron-cation-cation) are used to resolve the final ionic states and to characterize three-dimensional (3D) electron-momentum correlation. The primary states associated with dissociative and nondissociative dications are assigned. A 3D momentum anticorrelation is observed for the electrons in coincidence with dissociative benzene dication states whereas such a correlation is absent for nondissociative dication states.

Multiple recollisions in strong-field nonsequential double ionization

With the three-dimensional classical ensemble model, we revisited the recollision dynamics in strong-field nonsequential double ionization (NSDI) by linearly polarized laser pulses. Back analysis of the NSDI trajectories shows that a significant part of the double ionization events undergo a multiple-recollision process. Similar to the previously revealed single recollision induced NSDI, the multiple recollisions induced NSDI also occurs through doubly excited states at low laser intensities. Further, we find that the contribution of multiple recollisions in NSDI decreases with the increasing laser intensity and wavelength.

The contribution of the delayed ionization in strong-field nonsequential double ionization.

With the classical ensemble model, we have investigated the pulse-duration dependence of nonsequential double ionization (NSDI) over a wide range of laser intensity. The correlated electron momentum distributions are distinctly different for the few-cycle and multiple cycle pulses, which agree well with the previous experiments. Based on this agreement, we analyzed the underlying process for the pulse-duration dependence of the electron correlation by tracing the classical trajectories. Counterintuitively, our analysis shows that the recollision-induced excited states of NSDI could resist ionization in the strong laser field for a time much longer than one optical cycle even at very high intensities. For the multiple-cycle pulses, NSDI events with such a long time delay have significant contribution to the total NSDI yields, which is responsible for the pulse-duration dependence of the observed correlated patterns in the electron momentum distributions.

Suppression of Recollision-Excitation Ionization in Nonsequential Double Ionization of Molecules by Mid-Infrared Laser Pulses

The electron dynamics in strong field non-sequential double ionization of nitrogen molecules is investigated with the three-dimensional (3D) classical ensemble model. The numerical results show that the longitudinal momentum spectrum of the doubly charged ions evolves from a wide single-hump structure at the near-infrared (NIR) regime into a double-hump structure when the wavelength enters the mid-infrared (MIR) regime. Back analysis reveals that in the MIR regime, the recollision excitation with subsequent ionization (RESI) is strongly suppressed with increasing wavelength, which results in the double-hump structure of the ions momentum spectra. This double-hump structure becomes more pronounced as the wavelength further increases because the contribution of the RESI further decreases.

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.

Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization

With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we found a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides a profound understanding of electronic correlations and complicated multiphoton phenomena and is expected to be a new tool for broad applications, such as quantum coherent control.

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 investigated 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 recollision 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.