Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

Intensity dependence in nonsequential double ionization of helium

Using the quantitative rescattering model, we simulate the correlated two-electron momentum distributions for nonsequential double ionization of helium by 800 nm laser pulses at intensities in the range of (2 - 15) × 10¹⁴ W/cm². The experimentally observed V-shaped structure at high intensities [A. Rudenko et al., Phys. Rev. Lett. 99, 263003 (2007)] is attributed to the strong forward scattering in laser-induced recollision excitation and the asymmetric momentum distribution of electrons that are tunneling-ionized from the excited states. The final-state electron repulsion also plays an important role in forming the V-shaped structure.

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 correlated-electron emission in nonsequential double ionization of Ar atoms

Emission of the two electrons released from nonsequential double ionization of argon atoms is anticorrelated at lower laser intensities but is correlated at higher laser intensities. Such a transition is caused by the momentum change of recollision-induced-ionization (RII) electrons. At lower laser intensities, the Coulomb repulsion between the two RII electrons dominates the motion of electrons and pushes them leaving the laser field back-to-back. At higher laser intensities, the drift momentum obtained from the laser field dominates the motion of electrons and drives them leaving the laser field side-by-side.

Boosting photoabsorption by attosecond control of electron correlation

Electron correlation plays an essential role in a wide range of fundamentally important many-body phenomena in modern physics and chemistry. An example is the importance of electron-electron correlation in multiple ionization of multielectron atoms and molecules exposed to intense laser pulses. Manipulating the dynamic electron correlation in such photoinduced processes is a crucial step toward the coherent control of chemical reactions and photobiological processes. The generation of an attosecond extreme ultraviolet (EUV) pulse may enable such controls. Here, we show for the first time, from full-dimensional ab initio calculations of double ionization of helium in intense laser pulses (λ = 780 nm), that the electron-electron interactions can be instantaneously tuned using a time-delayed attosecond EUV pulse. Consequently, the probability of producing energetic electrons from excessive photoabsorption can be enhanced by an order of magnitude, by the attosecond control of electron-electron correlation.

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.

The effect of molecular alignment on correlated electron dynamics in nonsequential double ionization

The electron-electron correlation in nonsequential double ionization (NSDI) from aligned molecules by linearly polarized 800 nm laser pulses has been investigated with the three-dimensional classical ensemble model. The result shows that for the perpendicular alignment the two electrons involved in NSDI more likely exit the molecule into the opposite hemispheres as compared to the parallel alignment, which agrees well with the experimental result [Phys. Rev. Lett. 95, 203003 (2005)]. This alignment effect is qualitatively explained based on the suppressed potential barriers which are different for parallel molecules and perpendicular molecules. Additionally, the intensity dependence of the alignment effect is also explored.

Time-resolved quantum dynamics of double ionization in strong laser fields

Quantum calculations of a (1+1)-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two-electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1D coordinates for the electrons. The time-resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration and reveal the relative importance of sequential and nonsequential double ionization, even when ionization takes place during the same field cycle.

In-plane theory of nonsequential triple ionization

We describe first-principles in-plane calculations of nonsequential triple ionization of atoms in a linearly polarized intense laser pulse. In a fully classically correlated description, all three electrons respond dynamically to the nuclear attraction, the pairwise e-e repulsions, and the laser force throughout the duration of a 780 nm laser pulse. Nonsequential ejection is shown to occur in a multielectron, possibly multicycle and multidimensional, rescattering sequence that is coordinated by a number of sharp transverse recollimation impacts.

Classical effects of laser pulse duration on strong-field double ionization

We use classical electron ensembles and the aligned-electron approximation to examine the effect of laser pulse duration on the dynamics of strong-field double ionization. We cover the range of intensities 10(14)-10(16) W/cm2 for the laser wavelength 780 nm. The classical scenario suggests that the highest rate of recollision occurs early in the pulse and promotes double-ionization production in few-cycle pulses. In addition, the purely classical ensemble calculation predicts an exponentially decreasing recollision rate with each subsequent half cycle. We confirm the exponential behavior by trajectory back analysis.

Speed-up collisions in strong-field double ionization

We compare quantum and classical models of double ionization (DI) for aligned-electron helium in strong laser fields, considering specifically the role of recollision processes in which the returning electron travels in the direction of the laser force. Quantum studies show that for the knee region in our model a small but persistent portion of the total DI occurs through these speed-up collisions.We show that classical modeling displays similar collisions and reveals that with-the-force doubly ionizing collisions typically involve two-particle trajectories in which both electrons can be said to have been bound or very nearly bound at the zero of the laser field just before the collision. Trajectories leading to the with-the-force doubly ionizing collisions can be classified into two categories-direct excitation, in which there is no unambiguous single ionization before the doubly ionizing collision, and recapture, in which an ionized electron returns to the core and is recaptured prior to the speed-up collision. Comparison of the classical and quantum situations for our laser parameters yields evidence that for our parameters the quantum system favors the direct-excitation pathway over the reattachment pathway.

Different rescattering trajectories related to different total electron momenta in nonsequential double ionization

We extend earlier work on two-electron photo-ionization to analyze electron momentum. We provide theoretical evidence distinguishing two categories of e-e trajectory associated with the correlation that develops when an "outer" electron returns to the nucleus in the presence of a high-intensity optical-wavelength laser field. We use the method of back-analysis to connect these two categories of trajectory with NSDI events having either nearly zero (Z) or substantially non-zero (NZ) total electron momentum.

Rescattering double ionization of D2 and H2 by intense laser pulses

We have measured momentum spectra and branching ratios of charged ionic fragments emitted in the double ionization of D2 (and H2) molecules by short intense laser pulses. We find high-energy coincident D+ (and H+) ion pairs with kinetic energy releases between 8 and 19 eV which appear for linearly polarized light but are absent for circularly polarized light. The dependence on the polarization, the energy distributions of the ions, and the dependence on laser intensity of yield ratios lead us to interpret these ion pairs as due to a rescattering mechanism for the double ionization. A quantitative model is presented which accounts for the major features of the data.

Electron-electron momentum exchange in strong field double ionization

We have investigated the momentum balance between the two electrons from strong field double ionization of argon at 780 nm and 1.9 x 10(14) W/cm(2). Experimental data show that perpendicular to the laser polarization direction the electrons emerge preferentially in opposite directions. Results of model calculations are found to agree well with the data and reveal a dominant role of the Coulomb correlation between the two outgoing electrons in this kinematical geometry. Differences between the experimental observations and the theoretical results for the ion momentum distribution indicate the importance of the further effects during the three-body breakup.

Rescattering of ultralow-energy electrons for single ionization of Ne in the tunneling regime

Electron emission for single ionization of Ne by 25 fs, 1.0 PW/cm(2) laser pulses at 800 nm has been investigated in a kinematically complete experiment using a "reaction microscope." Mapping the complete final state momentum space with high resolution, a distinct local minimum is observed at P(e parallel )=0, where P(e parallel ) is the electron momentum parallel to the laser polarization. Whereas tunneling theory predicts a maximum at zero momentum, our findings are in good agreement with recent semiclassical predictions which were interpreted to be due to "recollision."

S-matrix analysis of coincident measurement of two-electron energy distribution for double ionization of He in an intense laser field

Analyses of two mechanisms of double ionization of He in an intense femtosecond laser pulse are made within the S-matrix theory. Their contributions are compared with each other and with the recent data of coincidence measurements for two-electron energy distributions. It is found that the correlated energy-sharing mechanism reproduces the data remarkably well and also confirms the so-called "excessive production" of hot electrons in the process. In contrast, the shakeoff mechanism is found to fail completely to account for either the strength or the trend of the data and is therefore ruled out.

Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling

Vector momentum distributions of two electrons created in double ionization of Ar by 25 fs, 0.25 PW/cm(2) laser pulses at 795 nm have been measured using a "reaction microscope." At this intensity, where nonsequential ionization dominates, distinct correlation patterns are observed in the two-electron momentum distributions. A kinematical analysis of these spectra within the classical "recollision model" revealed an (e,2e)-like process and excitation with subsequent tunneling of the second electron as two different ionization mechanisms. This allows a qualitative separation of the two mechanisms demonstrating that excitation-tunneling is the dominant contribution to the total double ionization yield.

Strong-field double ionization of rare gases

We have studied the double ionization of helium and other rare gases using an electron-ion coincidence technique. With this scheme, the electron energy spectrum correlated to the creation of a doubly charged ion may be compiled. In all cases, the observed double ionization electron distributions are similar and enhanced at high energies, while the single ionization spectra exhibit distinct differences.

Phase-space analysis of double ionization

We use the Wigner transformation to study the electronic center-of-mass motion in phase-space for double ionization in a strong laser field. The rescattering mechanism is clearly visible in the evolution of the fully correlated two-electron system. In a mean-field calculation, on the other hand, the signatures of rescattering are missing. Some properties of the Wigner function in two-particle systems are reported.

Electron energy spectra from intense laser double ionization of helium

The double ionization of helium in the strong-field limit has been studied using an electron-ion coincidence technique. The observed double ionization electron energy spectra differ significantly from the single ionization distributions. This gives new support to the rescattering model of double ionization and explicitly reveals the role of backward electron emission following the e-2e ionizing collision.

Atomic dynamics in single and multi-photon double ionization: An experimental comparison

We have used a multi-particle imaging technique (COLTRIMS) to observe the double ionization of rare gas atoms by multi-photon absorption of 800 nm (1.5 eV) femto-second laser pulses and by single photon absorption (synchrotron radiation). Both processes are mediated by electron correlation. We discuss similarities and differences in the three-body final state momentum distributions.

Routes to nonsequential double ionization

A method is proposed for the calculation of the S matrix for many-electron processes in intense-laser atom physics, in close analogy to the strong-field approximation for one-electron processes. Given a scenario of how some process evolves, corresponding approximations to the classical action are made which allow for the evaluation of the quantum-mechanical S matrix. The method is applied to the distribution of the total electronic momentum in nonsequential double ionization, and the results are compared to recent measurements. Good agreement is obtained for neon for a rescattering scenario. There is no comparable agreement for helium and argon, and possible alternative scenarios are discussed.

Correlated electron emission in multiphoton double ionization

Electronic correlations govern the dynamics of many phenomena in nature, such as chemical reactions and solid state effects, including superconductivity. Such correlation effects can be most clearly investigated in processes involving single atoms. In particular, the emission of two electrons from an atom--induced by the impact of a single photon, a charged particle or by a short laser pulse--has become the standard process for studies of dynamical electron correlations. Atoms and molecules exposed to laser fields that are comparable in intensity to the nuclear fields have extremely high probabilities for double ionization; this has been attributed to electron-electron interaction. Here we report a strong correlation between the magnitude and the direction of the momentum of two electrons that are emitted from an argon atom, driven by a femtosecond laser pulse (at 38 TW cm(-2)). Increasing the laser intensity causes the momentum correlation between the electrons to be lost, implying that a transition in the laser-atom coupling mechanism takes place.