Attosecond correlated dynamics of two electrons passing through a transition state

Modulation of electron correlation dynamics in atomic non-sequential double ionization by counter-rotating two-color circularly polarized laser fields

We investigate the ultrafast electron correlation effects during non-sequential double ionization (NSDI) of argon subjected to a combined femtosecond field composed of counter-rotating two-color circularly polarized (TCCP) pulse laser using a 3D classical ensemble model (CEM). Our simulation results reveal that manipulation of the carrier-envelope phase (CEP) of the external driving field modulates the dynamical behavior of the two electrons, resulting in a notable sensitivity of their momentum distribution to the relative phase of two components of the counter-rotating TCCP field. Through inversion analysis, we uncover the capability to direct electrons toward a single direction, thereby facilitating focused ion-electron collisions on the attosecond timescale. Furthermore, we observe that adjusting the CEP exerts a substantial influence on the NSDI ionization process, modifying the relative contributions of the recollision-induced ionization (RII) mechanism and recollision excitation with subsequent ionization (RESI) mechanism.

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.

Electron correlation and recollision dynamics in nonsequential double ionization by counter-rotating two-color elliptically polarized laser fields

Nonsequential double ionization (NSDI) of Argon atoms by counter-rotating two-color elliptically polarized (TCEP) fields is investigated with a three-dimensional classical ensemble model. Different from two-color circularly polarized fields, the combined electric field in TCEP pulses has no symmetry and the ionized electron mainly returns to the parent ion from one direction. Thus the electron momentum distributions show strong asymmetry. Numerical results show with the increase of the relative phase between the two elliptical fields, the return angle of the travelling electron, i.e., the angle between the return direction of the electron and the +x direction, gradually decreases. Moreover, the dominant behavior of electron pairs evolves from anti-correlation to correlation with the relative phase increasing. This provides an avenue to control the return angle and electron correlation behavior by the relative phase between the two elliptical fields.

Magnetic-Field Effect as a Tool to Investigate Electron Correlation in Strong-Field Ionization

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory Monte Carlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

Electron angular correlation in nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields

Electron correlation in nonsequential double ionization (NSDI) of molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that the two electrons from NSDI of molecules in counter-rotating TCCP fields show strong angular correlation and the angular correlation behavior sensitively depends on the internuclear distance. With the internuclear distance increasing, the dominant behavior of electron pairs evolves from correlation to anti-correlation. It leaves a clear imprint on the ion momentum distributions, which exhibit an inverted Y-shape distribution at a small internuclear distance and a triangle-shape distribution at a large internuclear distance. Back analysis indicates that the asymmetric electron energy sharing by soft recollision and longer time delay of double ionization are responsible for more anti-correlated emissions at large internuclear distances.

8 fs laser pulses from a compact gas-filled multi-pass cell

Compression of 42 fs, 0.29 mJ pulses from a Ti:Sapphire amplifier down to 8 fs (approximately 3 optical cycles) is demonstrated by means of spectral broadening in a compact multi-pass cell filled with argon. The efficiency of the nonlinear pulse compression is limited to 45 % mostly by losses in the mirrors of the cell. The experimental results are supported by 3-dimensional numerical simulations of the nonlinear pulse propagation in the cell that allow us to study spatio-spectral properties of the pulses after spectral broadening.

Laser-Induced Electron Transfer in the Dissociative Multiple Ionization of Argon Dimers

We report on an experimental and theoretical study of the ionization-fragmentation dynamics of argon dimers in intense few-cycle laser pulses with a tagged carrier-envelope phase. We find that a field-driven electron transfer process from one argon atom across the system boundary to the other argon atom triggers subcycle electron-electron interaction dynamics in the neighboring atom. This attosecond electron-transfer process between distant entities and its implications manifests itself as a distinct phase-shift between the measured asymmetry of electron emission curves of the Ar^{+}+Ar^{2+} and Ar^{2+}+Ar^{2+} fragmentation channels. This letter discloses a strong-field route to controlling the dynamics in molecular compounds through the excitation of electronic dynamics on a distant molecule by driving intermolecular electron-transfer processes.

Relative phase effect of nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields

Relative phase effect of nonsequential double ionization (NSDI) of aligned molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results show that NSDI yield in counter-rotating TCCP fields sensitively depends on the relative phase of the two components, which exhibits a sin-like behavior with the period of π/2. NSDI yield achieves its maximum at the relative phase π/8 and minimum at 3π/8. Back analysis indicates the recollision time and the return angle of the electron strongly depend on the relative phase of the two components, which results in the dominant emission direction of the electrons, is different for different relative phases. This indicates that the recollision process can be steered by changing the relative phase of the two components in counter-rotating TCCP laser fields. Meantime, it provides an avenue to obtain information about the recollision time and the return angle in the recollision process from the electron momentum distribution.

Fingerprints of slingshot non-sequential double ionization on two-electron probability distributions

We study double ionization of He driven by near-single-cycle laser pulses at low intensities at 400 nm. Using a three-dimensional semiclassical model, we identify the pathways that prevail non-sequential double ionization (NSDI). We focus mostly on the delayed pathway, where one electron ionizes with a time-delay after recollision. We have recently shown that the mechanism that prevails the delayed pathway depends on intensity. For low intensities slingshot-NSDI is the dominant mechanism. Here, we identify the differences in two-electron probability distributions of the prevailing NSDI pathways. This allows us to identify properties of the two-electron escape and thus gain significant insight into slingshot-NSDI. Interestingly, we find that an observable fingerpint of slingshot-NSDI is the two electrons escaping with large and roughly equal energies.

Nonsequential double ionization by co-rotating two-color circularly polarized laser fields

Nonsequential double ionization (NSDI) of Ar in co-rotating two-color circularly polarized (TCCP) laser fields is investigated with a three-dimensional classical ensemble model. Our numerical results indicate that co-rotating TCCP fields can induce NSDI by recollision process, while the yield is an order of magnitude lower than counter-rotating case. NSDI yield in co-rotating TCCP fields strongly depends on field ratio of the two colors and achieves its maximum at a ratio of 2.4. In co-rotating TCCP fields, the short recollision trajectory with traveling time smaller than one cycle is dominant. Moreover, the recollision time in co-rotating TCCP laser fields depends on the field ratio, which is mapped to the electron momentum distribution. This provides anavenue to obtain information about recollision time and access the subcycle dynamics of the recollision process.

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.

Slingshot Nonsequential Double Ionization as a Gate to Anticorrelated Two-Electron Escape

At intensities below the recollision threshold, we show that recollision-induced excitation with one electron escaping fast after recollision and the other electron escaping with a time delay via a Coulomb slingshot motion is one of the most important mechanisms of nonsequential double ionization (NSDI), for strongly driven He at 400 nm. Slingshot NSDI is a general mechanism present for a wide range of low intensities and pulse durations. Anticorrelated two-electron escape is its striking hallmark. This mechanism offers an alternative explanation of anticorrelated two-electron escape obtained in previous studies.

Intensity-dependent two-electron emission dynamics in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields

Nonsequential double ionization of helium in counter-rotating two-color circularly polarized laser fields is investigated with a three-dimensional classical ensemble model. At moderate intensity, the momentum distribution of the two electrons shows a maximum in the middle of each side of the triangle of the negative vector potential. At high intensity, the momentum distribution exhibits a double-triangle structure, which is attributed to the different values of the laser intensity where the two electrons are released after recollision. At low intensity, the momentum distribution shows a shift deviating from the middle of the side of the triangle of the negative vector potential. This is because the first electrons are emitted within a narrow time window after the field maximum. In addition, at low intensity, double-recollision events and NSDI originating from doubly excited states induced by recollision are prevalent.

Anomalous ellipticity dependence in nonsequential double ionization of ArXe

Using a three-dimensional classical ensemble method, we present a theoretical study of nonsequential double ionization of ArXe dimer aligned along the minor axis of the elliptically polarized laser pulse. Numerical results show that NSDI probability firstly increases and then decreases with the laser ellipticity increasing, which is different from atoms. Moreover, the correlated electron momentum spectra from elliptical polarization are always asymmetric, and the asymmetry is enhanced as the ellipticity increases. Analysis backward in time indicates that in NSDI of ArXe aligned along the minor axis the recollision occurs via a semi-elliptical trajectory.

Controlling nonsequential double ionization of Ne with parallel-polarized two-color laser pulses

We measure the recoil-ion momentum distributions from nonsequential double ionization of Ne by two-color laser pulses consisting of a strong 800-nm field and a weak 400-nm field with parallel polarizations. The ion momentum spectra show pronounced asymmetries in the emission direction, which depend sensitively on the relative phase of the two-color components. Moreover, the peak of the doubly charged ion momentum distribution shifts gradually with the relative phase. The shifted range is much larger than the maximal vector potential of the 400-nm laser field. Those features are well recaptured by a semiclassical model. Through analyzing the correlated electron dynamics, we found that the energy sharing between the two electrons is extremely unequal at the instant of recollison. We further show that the shift of the ion momentum corresponds to the change of the recollision time in the two-color laser field. By tuning the relative phase of the two-color components, the recollision time is controlled with attosecond precision.

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.

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.

Non-sequential double ionization with near-single cycle laser pulses

A three-dimensional semiclassical model is used to study double ionization of Ar when driven by a near-infrared and near-single-cycle laser pulse for intensities ranging from 0.85 × 10¹⁴ W/cm² to 5 × 10¹⁴ W/cm². Asymmetry parameters, distributions of the sum of the two electron momentum components along the direction of the polarization of the laser field and correlated electron momenta are computed as a function of the intensity and of the carrier envelope phase. A very good agreement is found with recently obtained results in kinematically complete experiments employing near-single-cycle laser pulses. Moreover, the contribution of the direct and delayed pathways of double ionization is investigated for the above observables. Finally, an experimentally obtained anti-correlation momentum pattern at higher intensities is reproduced with the three-dimensional semiclassical model and shown to be due to a transition from strong to soft recollisions with increasing intensity.

Nonsequential double ionization of Mg from a doubly excited complex driven by circularly polarized laser field

With the classical ensemble method, the correlated-electron dynamics of Mg atom from a doubly excited, transition Coulomb complex in few-cycle circularly polarized (CP) laser field at low laser intensity is theoretically investigated. The low energy transfer during the recollision process indicates that the two electrons cannot release directly, but it can pass through a doubly excited state, and then escape with the ionization time difference. The numerical results show that the feature of the sequential double ionization (SDI) can be observed in the nonsequential double ionization (NSDI) process. The SDI-like results demonstrate that the intermediate state has lost any memory of its formation dynamics. The distribution of the angle between the two release directions of the two electrons also depends on the ionization time difference. Finally, the influence of e-e Coulomb repulsion is discussed.

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.

Close to transform-limited, few-cycle 12 µJ pulses at 400 kHz for applications in ultrafast spectroscopy

Non-collinear optical parametric amplification has become the leading technology for amplifying few-cycle carrier-envelope phase (CEP) stable pulses to high energy at extreme repetition rates. In this work, a parametric amplifier system devoted to ultrafast photoionization experiments with coincidence detection is reported. The amplifier delivers CEP-stable few-cycle pulses with an average power of 5 W, and operates at repetition rates between 400 and 800 kHz. Close to transform-limited compression of the few-cycle pulses is achieved with minimized spatio-temporal distortions. Potential limitations introduced by spatio-temporal couplings to applications in attosecond science are analyzed. In particular, it is shown that pulse front tilt resulting from non-collinear amplification can considerably reduce the asymmetry in stereo above threshold ionization (stereo-ATI) experiments.

Origin of double-line structure in nonsequential double ionization by few-cycle laser pulses

We investigate nonsequential double ionization (NSDI) of molecules by few-cycle laser pulses at the laser intensity of 1.2-1.5 × 10(14) W/cm(2) using the classical ensemble model. The same double-line structure as the lower intensity (1.0 × 10(14) W/cm(2)) is also observed in the correlated electron momentum spectra for 1.2-1.4 × 10(14) W/cm(2). However, in contrast to the lower intensity where NSDI proceeds only through the recollision-induced double excitation with subsequent ionization (RDESI) mechanism, here, the recollision-induced excitation with subsequent ionization (RESI) mechanism has a more significant contribution to NSDI. This indicates that RDESI is not necessary for the formation of the double-line structure and RESI can give rise to the same type of structure independently. Furthermore, we explore the ultrafast dynamics underlying the formation of the double-line structure in RESI.

Transition of recollision trajectories from linear to elliptical polarization

Using a classical ensemble method, we revisit the topic of recollision and nonsequential double ionization with elliptically polarized laser fields. We focus on how the recollision mechanism transitions from short trajectories with linear polarization to long trajectories with elliptical polarization. We propose how this transition can be observed by meansuring the carrier-envelop-phase dependence of the correlated electron momentum spectra using currently available few-cycle laser pulses.

Channel-resolved above-threshold double ionization of acetylene

We experimentally investigate the channel-resolved above-threshold double ionization (ATDI) of acetylene in the multiphoton regime using an ultraviolet femtosecond laser pulse centered at 395 nm by measuring all the ejected electrons and ions in coincidence. As compared to the sequential process, diagonal lines in the electron-electron joint energy spectrum are observed for the nonsequential ATDI owing to the correlative sharing of the absorbed multiphoton energies. We demonstrate that the distinct channel-resolved sequential and nonsequential ATDI spectra can clearly reveal the photon-induced acetylene-vinylidene isomerization via proton migration on the cation or dication states.

Interaction effects on dynamical localization in driven helium

Dynamical localization prevents driven atomic systems from fast fragmentation by hampering the excitation process. We present numerical simulations within a collinear model of microwave-driven helium Rydberg atoms and prove that dynamical localization survives the impact of electron-electron interaction, even for doubly excited states in the presence of fast autoionization. We conclude that the effect of electron-electron repulsion on localization can be described by an appropriate rescaling of the atomic level density and of the external field with the strength of the interaction.

Subcycle control of electron-electron correlation in double ionization

Double ionization of neon with orthogonally polarized two-color (OTC) laser fields is investigated using coincidence momentum imaging. We show that the two-electron emission dynamics in nonsequential double ionization can be controlled by tuning the subcycle shape of the electric field of the OTC pulses. We demonstrate experimentally switching from correlated to anticorrelated two-electron emission, and control over the directionality of the two-electron emission. Simulations based on a semiclassical trajectory model qualitatively explain the experimental results by a subcycle dependence of the electron recollision time on the OTC field shape.

Ionization of excited atoms by intense single-cycle THz pulses

We have employed intense, single-cycle THz pulses to explore strong-field ionization of low-lying Na Rydberg states in the low-frequency limit. At the largest fields used, F≃430  kV/cm, electrons with energies up to 60 eV are created. The field ionization threshold is greater than expected for adiabatic "over-the-barrier" ionization and is found to scale as n-3. In addition, for a given field amplitude, higher energy electrons are produced during the ionization of the most tightly bound states. These observations can be attributed to the suppression of scattering from the nonhydrogenic ion core, the long times required for Rydberg electrons to escape over the barrier in the field-dressed Coulomb potential, and the failure, in the single-cycle limit, of the standard prediction for electron energy transfer in an oscillating field. The latter, in particular, holds important implications for future strong-field experiments involving the interaction of ground-state atoms and molecules with true single-cycle laser fields.

Strong-field double ionization through sequential release from double excitation with subsequent Coulomb scattering

We perform a triple coincidence study on differential momentum distributions of strong-field double ionization of Ar atoms in linearly polarized fields (795 nm, 45 fs, 7×10(13)  W/cm2). Using a three-dimensional two-electron atomic-ensemble semiclassical model including the tunneling effect for both electrons, we retrieve differential momentum distributions and achieve a good agreement with the measurement. Ionization dynamics of the correlated electrons for the side-by-side and back-to-back emission is analyzed separately. According to the semiclassical model, we find that the doubly excited states are largely populated after the laser-assisted recollision and large amounts of double ionization dominantly takes place through sequential ionization of doubly excited states at such a low laser intensity. Compared with the Coulomb-free and Coulomb-corrected sequential tunneling models, we verify that electrons can obtain an energy as large as ∼6.5U p through Coulomb scattering in the combined laser and doubly charged ionic fields.

Observation of electron energy discretization in strong field double ionization

We report on the observation of discrete structures in the electron energy distribution for strong field double ionization of argon at 394 nm. The experimental conditions were chosen in order to ensure a nonsequential ejection of both electrons with an intermediate rescattering step. We have found discrete above-threshold ionization like peaks in the sum energy of both electrons, as predicted by all quantum mechanical calculations. More surprisingly, however, is the observation of two above-threshold ionization combs in the energy distribution of the individual electrons.

Contribution of recollision ionization to the cross-shaped structure in nonsequential double ionization

With the three-dimensional classical ensemble model, we investigate the correlated electron emission in nonsequential double ionization (NSDI) of argon atoms by few-cycle laser pulses. Our calculations well reproduce the experimentally observed cross-shaped structure in the correlated two-electron momentum spectrum [ Nature Commun. 3, 813 (2012)]. By tracing these NSDI trajectories, we find that besides the process of recollision-induced excitation with subsequent ionization just before the next field maximum, the recollision ionization also significantly contributes to the cross-shaped structure.