Correlated Electron Momentum Distribution Research Articles

Electron momentum correlation along laser magnetic field direction as a probe of nondipole effect in strong-field nonsequential double ionization

The electric dipole approximation is commonly adopted in the theoretical investigation of light-atom/molecule interaction, wherein the magnetic component of the driving electromagnetic field is neglected. Our study highlights the significant role of the magnetic field effect in the recollision dynamics of nonsequential double ionization (NSDI) driven by a mid-infrared laser. Due to the magnetic component of the laser field, in the multiple-returning events, the tunneling electron with a large initial momentum along the laser magnetic field direction at some specific tunneling time is inefficient for NSDI. The corresponding footprint is revealed in the correlated electron momentum distribution along the magnetic field direction. Moreover, we show that this effect becomes more obvious with increasing laser wavelength, leading to a notable reduction in the NSDI yield. Our findings provide an alternative perspective for studying the recollision dynamics involving the magnetic field effect.

Nonsequential double ionization of Ar in two-color inhomogeneous laser fields

With the classical ensemble method, we investigate the correlated electron dynamics in nonsequential double ionization (NSDI) of Ar in parallel two-color inhomogeneous laser fields with different inhomogeneity parameter ϵ. Numerical results show that at low laser intensities, the probability of NSDI is higher for two-color laser fields with a higher inhomogeneity parameter ϵ. At high laser intensities, however, the probability of NSDI decreases as ϵ increases. It is also shown that under low laser intensities, the two-color inhomogeneous laser fields drives the NSDI predominantly dominated by the RII channel, and the ratio of the RII channel increases as ϵ increases. More interestingly, an arc-like structure is found in the correlated electron momentum distributions for the two-color inhomogeneous laser fields. The underlying dynamics are revealed by tracing back to classical trajectories.

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.

Manipulating nonsequential double ionization of atoms by parallel polarized three-color laser fields

Nonsequential double ionization (NSDI) of He atoms in a parallel polarized three-color field is investigated by using a three-dimensional classical ensemble model. The driving field is composed of 1600-nm and 800-nm laser pulses with equal intensity. A weak 400-nm laser pulse is used as a controlling field. The results indicate that in the correlated electron momentum distribution and ion momentum distribution, the electron pairs and ions of the first returning recollision (FRR) trajectory, the odd-returning recollision (ORR) trajectory (excluding FRR), and the even-returning recollision (ERR) trajectory are located in different regions separated well from each other. The electron pairs from FRR trajectories mainly distribute around the origin, and those electron pairs from ORR and ERR trajectories respectively cluster in the first quadrant and the third quadrant. With the increase of the phase of the controlling field, the proportion of FRR trajectories in NSDI first increases and then decreases, and the proportions of those trajectories with the returning number more than one first decrease and then increase, which leads to the fact that with the increase of the phase of the controlling field, the anticorrelated emissions first increase and then decrease and correspondingly the ion momentum distribution evolves from a double-hump to a triple-hump and then to a double-hump structure. Moreover, NSDI from multiple-returning recollision trajectories mainly occur through recollision-induced direct ionization (RDI) mechanism, while NSDI from the FRR trajectories mainly occurs through recollision-induced excitation with subsequent ionization (RESI) mechanism. Thus the dominant NSDI ionization mechanism can also be controlled by changing the phase of the controlling field.

Nonsequential double ionization of Ne with elliptically polarized laser pulses

We show through simulation that the improved quantitative rescattering model (QRS) can successfully predict the nonsequential double ionization (NSDI) process by intense elliptically polarized laser pulses. Using the QRS model, we calculate the correlated two-electron and ion momentum distributions of NSDI in Ne exposed to intense elliptically polarized laser pulses with a wavelength of 788 nm at a peak intensity of $5.0\ifmmode\times\else\texttimes\fi{}{10}^{14}$ W/${\mathrm{cm}}^{2}$. We analyze the asymmetry in the doubly charged ion momentum spectra observed by Kang et al. [Phys. Rev. Lett. 120, 223204 (2018)] in going from linearly to elliptically polarized laser pulses. Our model reproduces the experimental data well. Furthermore, we find that the ellipticity-dependent asymmetry arises from the drift velocity along the minor axis of the elliptic polarization. We explain how the correlated electron momentum distributions along the minor axis provide access to the subcycle dynamics of recollision. From these findings, we expect that we can extend the QRS model for NSDI toward more complicated laser fields in the future.

Nonsequential double ionization driven by inhomogeneous laser fields.

With a three-dimensional classical ensemble method, we theoretically investigated the correlated electron dynamics in nonsequential double ionization (NSDI) driven by the spatially inhomogeneous fields. Our results show that NSDI in the spatially inhomogeneous fields is more efficient than that in the spatially homogeneous fields at the low laser intensities, while at the high intensities NSDI is suppressed as compared to the homogeneous fields. More interestingly, our results show that the electron pairs from NSDI exhibit a much stronger angular correlation in the spatially inhomogeneous fields, especially at the higher laser intensities. The correlated electron momentum distribution shows that in the inhomogeneous fields the electron pairs favor to achieve the same final momentum, and the distributions dominantly are clustered in the more compact regions. It is shown that the electron's momentum is focused by the inhomogeneous fields. The underlying dynamics is revealed by back-tracing the classical trajectories.

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.

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.

Controlling non-sequential double ionization with chirped laser pulse

The non-sequential double ionization (NSDI) of He in a chirped few-cycle laser pulse is studied using a full-dimensional semi-classical model. The NSDI probability is found to be very sensitive to the rate of wavelength change. An abrupt jump is found in the probability distribution during the crossover from up- to down-chirped pulse, followed with a further increase of the probability when keep increasing the rate of wavelength change. In the meantime, the correlated electron momentum distribution transfers from anti-correlated to a correlated pattern. Further analysis reveals the underlying mechanism to be the increase of the kinetic energy of returned electron acquired from the chirped pulse in the re-collision process. The dominant NSDI mechanism transfers from recollision-induced excitation with subsequent field ionization (RESI) to electron-impact ionization (EI). Therefore, the chirped laser pulse could be a useful tool for controlling the electron dynamics in NSDI and beyond.

Third-order S-matrix study of electron-electron correlation in nonsequential double ionization

Correlated electron momentum distribution of nonsequential double ionization of a Ne atom in intense laser fields is calculated using a third-order S-matrix formalism which takes into account the interaction between the Coulomb potential of the parent ion and the photoelectrons. Compared to the second-order S-matrix calculation, the correlation distributions of the two processes which take into account the effect of the ionic Coulomb potential on either of the two ionized electrons after their collision tend to be concentrated off the diagonal of the first and third quadrants, which are closer to the experimental observations. Our further analysis shows that this modification to the second-order calculation is due to the fact that, scattering of the emitted electron upon the parent ion will alter the photoelectron angular distribution from concentration in the laser direction to focus in a direction deviating from the laser field. And this will significantly reduce the momentum of the electron in the direction of the laser field. Our results are in accord with previous studies which reveal that electron-nuclear Coulomb interaction, electron-electron collision and the final-state electron repulsion all play significant roles in the formation of the fingerlike structure.

The carrier-envelope phase effect in non-sequential double ionization by few-cycle linearly polarized laser field

Using the two-dimensional classical ensemble method, we investigate the nonsequential double-ionization (NSDI) processes of Ar atom by few-cycle linearly polarized laser field. We demonstrate that the recollision-induced excitation with subsequent ionization (RESI) and the recollision-induced ionization (RII) channels can be effectively controlled by laser intensities. Moreover, the carrier-envelope-phases (CEPs) play a key role in controlling RESI and RII mechanism. The correlated electron momentum distribution is demonstrated for the RII and RESI channels at different CEPs and intensities.

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.

Identification of doubly excited states in nonsequential double ionization of Ar in strong laser fields

We use the semiclassical model to study the intensity dependence of nonsequential double ionization (NSDI) of Ar in short strong laser pulses. The contributions to NSDI through sequential ionization of doubly excited states (SIDE) are identified by tracking the energy trajectories of the two outgoing electrons. The correlated electron momentum distributions are calculated from which the longitudinal momentum distributions of the fast and the slow electrons for the side-by-side and the back-to-back emissions are obtained. The simulated momentum distributions of the fast and the slow electrons for NSDI of Ar by linearly polarized fields with a wavelength of 795 nm at an intensity of 7 × 1013 W cm−2 are in good agreement with the experimental measurements of Liu et al (2014 Phys. Rev. Lett. 112 013003). We demonstrate that the process of double ionization through SIDE dominates NSDI only when the laser intensities are below the recollision threshold; nevertheless, for higher intensities the SIDE process still takes place although the contribution to the NSDI yields decreases rapidly as the intensity increases. It has been found that for SIDE at different intensities, both the correlated electron momentum spectra and the momentum distributions of the fast and the slow electrons remain the same.

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.

Controlling Three-Dimensional Electron–Electron Correlation via Elliptically Polarized Intense Laser Field**Supported by the National Key Program for S&T Research and Development under Grant No 2016YFA0401100, the National Basic Research Program of China under Grant No 2013CB922201, and the National Natural Science Foundation of China under Grant Nos 11504215, 11374197, 11334009 and 11425414.

The three-dimensional electron–electron correlation in an elliptically polarized laser field is investigated based on a semiclassical model. Asymmetry parameter α of the correlated electron momentum distribution is used to quantitatively describe the electron–electron correlation. The dependence of α on ellipticity ε is totally different in three directions. For the z direction (major polarization direction), α first increases and reaches a maximum at , then it decreases quickly. For the y direction in which the laser field is always absent, the ellipticity has a minor effect, and the asymmetry parameter fluctuates around . However, for the x direction (minor polarization direction), α increases monotonously with ellipticity though starts from the same value as in the y direction when . The behavior of α in the x direction actually indicates a transformation from the Coulomb interaction dominated correlation to the laser field dominated correlation. Therefore, our work provides an efficient way to control the three-dimensional electron–electron correlation via an elliptically polarized intense laser field.

Recollision dynamics in nonsequential double ionization of atoms by long-wavelength pulses

Recollision dynamics and electron correlation behavior are investigated for several long laser wavelengths (1200-3000 nm) in nonsequential double ionization (NSDI) of helium using three-dimensional classical ensembles. Numerical results show that for these long wavelengths NSDI events are mainly from the multiple-return trajectory which is different from the case of 800 nm. Moreover, with increasing laser wavelength NSDI events move from the diagonal to the two axes in the correlated electron momentum distributions, and finally form an experimentally observed prominent V-shaped structure [Phys. Rev. X 5, 021034 (2015)] in the first and third quadrants. Back analysis indicates that the asymmetric energy sharing between the two electrons at recollision is responsible for the formation of the prominent V-shaped structure of 3000 nm.

Pulse-duration effect in nonsequential double ionization of Ar atoms

Nonsequential double ionization of Ar atoms in intense few-cycle laser pulses is studied by a classical ensemble method. The laser pulses are of trapezoidal shape with one cycle in both ramp on and ramp off. We obtain the cycle-resolved electron dynamics by increasing the optical cycles in the laser pulse one by one. We find that, at the higher laser intensity, the correlated-electron momentum distribution (CMD) in the three-cycle laser pulse exhibits two predominate structures in the first and third quadrants. They are formed by the electron pairs in which the second electron is knocked out by the returning electron in the second cycle. As the pulse duration increases, more electron pairs accumulate in the second and fourth quadrants of the CMDs. In these electron pairs, the second electron is first excited owing to collision with the returning electron and then is ionized by the laser field. By varying the peak intensity, we show the transition of the CMDs from anticorrelation to correlation in three-cycle laser pulses, which disproves that multiple collisions cause the transition.

Role of Coulomb repulsion in correlated-electron emission from a doubly excited state in nonsequential double ionization of molecules

With the classical ensemble model, we investigate nonsequential double ionization of aligned molecules by few-cycle laser pulses at low intensity, where the two electrons finally are ionized through a transition doubly excited state induced by recollision. The correlated electron momentum distribution of parallel molecules exhibits the line-shaped structure parallel to the diagonal. Our analysis indicates that besides the ionization time difference of two electrons from the doubly excited state, the final-state e-e Coulomb repulsion plays a vital role in the formation of the line-shaped structural momentum distribution. For perpendicular molecules, due to the prominent near half-cycle ionization time difference between the two electrons from the doubly excited state, the momentum distribution shows clear anticorrelation behavior.

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.

Quantum interference in time-delayed nonsequential double ionization

We perform a systematic analysis of quantum interference in nonsequential double ionization focusing on the recollision-excitation with subsequent ionization (RESI) mechanism, employing the strong-field approximation (SFA). We find that interference has a major influence on the shape, localization and symmetry of the correlated electron momentum distributions. In particular, the fourfold symmetry with regard to the parallel momentum components observed in previous SFA studies is broken. Two types of interference are observed and thoroughly analyzed, namely that caused by electron indistinguishability and intra-cycle events, and that stemming from different excitation channels. We find that interference is most prominent around the diagonal and anti-diagonal in the parallel-momentum plane and provide fully analytical expressions for most interference patterns encountered. We also show that this interference can be controlled by an appropriate choice of phase and excited-state geometry. This leads a to myriad of shapes for the RESI distributions including correlated, anti-correlated and ring-shaped.