Quantum effects in double ionization of argon below the threshold intensity

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.

Strong Polarization of a J=1/2 to 1/2 Transition Arising from Unexpectedly Large Quantum Interference

We experimentally show that the 1s^{2}2s^{2}2p_{1/2}-1s2s^{2}2p_{1/2}^{2} transition in Pb^{77+} emitted in dielectronic recombination of Pb^{78+} is strongly polarized, although it is an intrinsically unpolarized J=1/2 to 1/2 transition. This unanticipated polarization is shown to be due to quantum interference with radiative recombination. The interference effect has been studied on an asymmetric resonance profile but has never been studied on polarization. In this Letter, we show that the effect on polarization can arise from a different cross term than that responsible for asymmetry, resulting in unexpectedly large polarization even for a nearly symmetric resonance suggesting a small interference.

Ellipticity dependence of anticorrelation in the nonsequential double ionization of Ar

Within the framework of the improved quantitative rescattering (QRS) model, we simulate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization (NSDI) of Ar by elliptically polarized laser pulses with a wavelength of 788 nm at an intensity of 0.7 × 10¹⁴ W/cm² for the ellipticities ranging from 0 to 0.3. Only the CMDs for recollision excitation with subsequent ionization (RESI) are calculated and the contribution from recollision direct ionization is neglected. According to the QRS model, the CMD for RESI can be factorized as a product of the parallel momentum distribution (PMD) for the first released electron after recollision and the PMD for the second electron ionized from an excited state of the parent ion. The PMD for the first electron is obtained from the laser-free differential cross sections for electron impact excitation of Ar⁺ calculated using state-of-the-art many-electron R-matrix theory while that for the second electron is evaluated by solving the time-dependent Schrödinger equation. The results show that the CMDs for all the ellipticities considered here exhibit distinct anticorrelated back-to-back emission of the electrons along the major polarization direction, and the anticorrelation is more pronounced with increasing ellipticity. It is found that anticorrelation is attributed to the pattern of the PMD for the second electron ionized from the excited state that, in turn, is caused by the delayed recollision time with respect to the instant of the external field crossing. Our work shows that both the ionization potential of the excited parent ion and the laser intensity play important roles in the process.

Entanglement of orbital angular momentum in non-sequential double ionization

Entanglement has a capacity to enhance imaging procedures, but this remains unexplored for attosecond imaging. Here, we elucidate that possibility, addressing orbital angular momentum (OAM) entanglement in ultrafast processes. In the correlated process non-sequential double ionization (NSDI) we demonstrate robust photoelectron entanglement. In contrast to commonly considered continuous variables, the discrete OAM allows for a simpler interpretation, computation, and measurement of entanglement. The logarithmic negativity reveals that the entanglement is robust to incoherence and an entanglement witness minimizes the number of measurements to detect the entanglement, both quantities are related to OAM coherence terms. We quantify the entanglement for a range of targets and field parameters to find the most entangled photoelectron pairs. This methodology provides a general way to use OAM to quantify and measure entanglement, well-suited to attosecond processes, and can be exploited to enhance imaging capabilities through correlated measurements, or for generation of OAM-entangled electrons.

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.

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.

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.

Nonsequential double ionization of alkaline-earth metal atoms by intense mid-infrared femtosecond pulses

A systematic study of nonsequential double ionization (NSDI) of alkaline-earth metal atoms with mid-infrared femtosecond pulses is reported. We find that the measured NSDI yield shows a strong target dependence and it is more suppressed for alkaline-earth metal with higher ionization potential. The observation is attributed to the differences in the recollision induced excitation and ionization cross sections of alkaline-earth metals. This work indicates that NSDI of alkaline-earth metals can be generally understood within recollision picture and sheds light on ultrafast control of electron correlation and dynamics of ionic excited states during NSDI of atoms with complex structures.

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.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

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.

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.

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.

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.

Controlling Below-Threshold Nonsequential Double Ionization via Quantum Interference

We show through simulation that quantum interference in nonsequential double ionization can be used to control the recollision excitation with subsequent ionization (RESI) mechanism. This includes the shape, localization, and symmetry of RESI electron-momentum distributions, which may be shifted from a correlated to an anticorrelated distribution or vice versa, far below the direct ionization threshold intensity. As a testing ground, we reproduce recent experimental results by employing specific coherent superpositions of excitation channels. We examine two types of interference, from electron indistinguishability and intracycle events, and from different excitation channels. These effects survive focal averaging and transverse-momentum integration.