Probing electron correlation via attosecond xuv pulses in the two-photon double ionization of helium

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.

Time-dependent optimized coupled-cluster method for multielectron dynamics. IV. Approximate consideration of the triple excitation amplitudes

We present a cost-effective treatment of the triple excitation amplitudes in the time-dependent optimized coupled-cluster (TD-OCC) framework called TD-OCCDT(4) for studying intense laser-driven multielectron dynamics. It considers triple excitation amplitudes correct up to the fourth-order in many-body perturbation theory and achieves a computational scaling of O(N⁷), with N being the number of active orbital functions. This method is applied to the electron dynamics in Ne and Ar atoms exposed to an intense near-infrared laser pulse with various intensities. We benchmark our results against the TD complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and TD Hartree-Fock (TDHF) methods to understand how this approximate scheme performs in describing nonperturbatively nonlinear phenomena, such as field-induced ionization and high-harmonic generation. We find that the TD-OCCDT(4) method performs equally well as the TD-OCCDT method, almost perfectly reproducing the results of the fully correlated TD-CASSCF with a more favorable computational scaling.

Simulation of a hydrogen atom in a laser field using the time-dependent variational principle

The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrödinger equation in one and three dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.

Two-Electron Interference in Strong-Field Ionization of He by a Short Intense Extreme Ultraviolet Laser Pulse

Double ionization of helium by a single intense (above 10^{18}  W/cm^{2}) linearly polarized extreme ultraviolet laser pulse is studied by numerically solving the full-dimensional time-dependent Schrödinger equation. For the laser intensities well beyond the perturbative limit, novel gridlike interference fringes are found in the correlated energy spectrum of the two photoelectrons. The interference can be traced to the multitude of two-electron wave packets emitted at different ionization times. A semianalytical model for the dressed two-photon double ionization is shown to qualitatively account for the interference patterns in the joint energy spectrum. Similar signatures of interferences between transient induced time-delayed ionization bursts are expected for other atomic and molecular multielectron systems.

Disentangling Strong-Field Multielectron Dynamics with Angular Streaking

The study into the interaction between a strong laser field and atoms/molecules has led to significant advances in developing spectroscopic tools in the attosecond time-domain and methods for controlling chemical reactions. There has been great interest in understanding the complex electronic and nuclear dynamics of molecules in strong laser fields. However, it is still a formidable challenge to fully model such dynamics. Conventional experimental tools such as photoelectron spectroscopy encounter difficulties in revealing the involved states because the electron spectra are largely dictated by the property of the laser field. Here, with strong field angular streaking technique, we measure the angle-dependent ionization yields that directly reflect the symmetry of the ionizing orbitals of methyl iodide and thus reveal the ionization/dissociation dynamics. Moreover, kinematically complete measurements of momentum vectors of all fragments in dissociative double ionization processes allow access to electron-momentum correlations that reveal correlated multielectron dynamics.

Attosecond Electron Correlation Dynamics in Double Ionization of Benzene Probed with Two-Electron Angular Streaking

With a novel three-dimensional electron-electron coincidence imaging technique and two-electron angular streaking method, we show that the emission time delay between two electrons can be measured from tens of attoseconds to more than 1 fs. Surprisingly, in benzene, the double ionization rate decays as the time delay between the first and second electron emission increases during the first 500 as. This is further supported by the decay of the Coulomb repulsion in the direction perpendicular to the laser polarization. This result reveals that laser-induced electron correlation plays a major role in strong field double ionization of benzene driven by a nearly circularly polarized field.

Correlated Electron Dynamics at Surfaces Investigated via He^{2+} Ion Neutralization

The neutralization of a single He^{2+} ion near a Ir surface leads to the emission of an electron pair. Via coincidence spectroscopy we give evidence that a sizable amount of these electron pairs originate from a correlated single step neutralization of the ion involving a total of four electrons from the metal. These correlated electron pairs cannot be explained in the common picture of two consecutive and independent neutralization steps. We infer a characteristic time scale for the correlated electron dynamics in the metal of 40-400  as.

Criterion for Distinguishing Sequential from Nonsequential Contributions to the Double Ionization of Helium in Ultrashort Extreme-Ultraviolet Pulses

We quantify sequential and nonsequential contributions in two-photon double ionization of helium atoms by intense ultrashort extreme-ultraviolet pulses with central photon energies ℏω_{ctr} near the sequential double-ionization threshold. If the spectrum of such pulses overlaps both the sequential (ℏω>54.4 eV) and nonsequential (ℏω<54.4 eV) double-ionization regimes, the sequential and nonsequential double-ionization mechanisms are difficult to distinguish. By tracking the double-ionization asymmetry in joint photoelectron angular distributions, we introduce the two-electron forward-backward-emission asymmetry as a measure that allows the distinction of sequential and nonsequential contributions. Specifically, for ℏω_{ctr}=50 eV pulses with a sine-squared temporal profile, we find that the sequential double-ionization contribution is the largest at a pulse length of 650 as, due to competing temporal and spectral constraints. In addition, we validate a simple heuristic expression for the sequential double-ionization contribution in comparison with ab initio calculations.

Note: An improved 3D imaging system for electron-electron coincidence measurements

We demonstrate an improved imaging system that can achieve highly efficient 3D detection of two electrons in coincidence. The imaging system is based on a fast frame complementary metal-oxide semiconductor camera and a high-speed waveform digitizer. We have shown previously that this detection system is capable of 3D detection of ions and electrons with good temporal and spatial resolution. Here, we show that with a new timing analysis algorithm, this system can achieve an unprecedented dead-time (<0.7 ns) and dead-space (<1 mm) when detecting two electrons. A true zero dead-time detection is also demonstrated.

Nonlinear Dichroism in Back-to-Back Double Ionization of He by an Intense Elliptically Polarized Few-Cycle Extreme Ultraviolet Pulse

Control of double ionization of He by means of the polarization and carrier-envelope phase (CEP) of an intense, few-cycle extreme ultraviolet (XUV) pulse is demonstrated numerically by solving the six-dimensional two-electron, time-dependent Schrödinger equation for He interacting with an elliptically polarized XUV pulse. Guided by perturbation theory (PT), we predict the existence of a nonlinear dichroic effect (∝I^{3/2}) that is sensitive to the CEP, ellipticity, peak intensity I, and temporal duration of the pulse. This dichroic effect (i.e., the difference of the two-electron angular distributions for opposite helicities of the ionizing XUV pulse) originates from interference of first- and second-order PT amplitudes, allowing one to probe and control S- and D-wave channels of the two-electron continuum. We show that the back-to-back in-plane geometry with unequal energy sharing is an ideal one for observing this dichroic effect that occurs only for an elliptically polarized, few-cycle attosecond pulse.

Application of discrete variable representation to planar H2+ in strong xuv laser fields

We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.

Multielectron transitions induced by neutron impact on helium

We explore excitation and ionization by neutron impact as a novel tool for the investigation of electron-electron correlations in helium. We present single- and double-ionization spectra calculated in accurate numerical ab initio simulations for incoming neutrons with kinetic energies of up to 150 keV. The resulting electron spectra are found to be fundamentally different from photoionization or charged particle impact due to the intrinsic many-body character of the interaction. In particular, doubly excited resonances that are strongly suppressed in electron or photon impact become prominent. The ratio of double to single ionization is found to differ significantly from those of photon and charged-particle impact.

Momentum space analysis of multiphoton double ionization of helium by intense attosecond xuv pulses

We investigate the momentum and energy distributions of the two electrons in multiphoton double ionization of He by intense attosecond xuv pulses, based on a two-dimensional model. Two different patterns of the momentum distributions are identified, corresponding to the uncorrelated and correlated channels, respectively. Our analysis of the electron correlations focuses on two-photon and three-photon double ionization processes for different pulse durations and for different time delays after the pulses. For both two-photon and three-photon cases, a clear correlation valley in energy distributions is found when both electrons are ejected in opposite directions. This is mostly attributed to the electron correlations during the ionization of the first electron. We also find that when two electrons are ejected in the same direction, their Coulomb repulsion has an significant influence on the electron energy distributions during the postionization stage. Finally, in the case of three photon double ionization, we observe that the effects of the Coulomb repulsion become much more complicated, and a new catch-up collision phenomena is observed in the energy distributions.

Two-electron time-delay interference in atomic double ionization by attosecond pulses

A two-color two-photon atomic double ionization experiment using subfemtosecond uv pulses can be designed such that the sequential two-color process dominates and one electron is ejected by each pulse. Nonetheless, ab initio calculations show that, for sufficiently short pulses, a prominent interference pattern in the joint energy distribution of the sequentially ejected electrons can be observed that is due to their indistinguishability and the exchange symmetry of the wave function.