Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

Experimental advances with laser intensities above1 TW/cm(2), with pulse durations between roughly 50 and 5 fs, have led to the discovery of new atomic effects that include examples of startlingly high electron correlation. These phenomena have presented an unexpected theoretical challenge as they lie outside the domains of both of the nominally applicable theories, namely, straightforward perturbative radiation theory and quasistatic tunneling theory. The two liberated electrons present a new few-body collective effect. When they are not released independently, one by one, the term nonsequential double ionization has been adopted. Theoretical avenues of attack have emerged in two categories, which are strikingly different. They can be labeled as "all-at-once" and "step-by-step" approaches. Although different, even conceptually opposite in some ways, both approaches have been successful in confronting substantial parts of the experimental data. These approaches are examined and compared with their results in addressing key experimental data obtained over the past decade.

Theories of photoelectron correlation in laser-driven multiple atomic ionization

In the context of strong field-matter interaction, an increasing number of phenomena has been found to be not understood within the single-active-electron approximation. For such phenomena, electron-electron correlation plays an important role in the underlying dynamics. In this review, we will provide a broad overview of electron-electron correlation and examine two distinct cases of its manifestation in strong field physics. In the first example, we examine nonsequential double and multiple ionization of atoms, discussing the experimental manifestation of the electron correlation and the theoretical models that have been developed to describe the effect. The second case examines the interaction of larger systems with intense laser fields, for which multielectron effects have to be invoked for an accurate description of the dynamics.

Electron-electron correlation in strong laser fields

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagiellonski, 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 Schr\"odinger 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 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 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 SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between Electron Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization (RESI); (ii) time-dependent treatment in the single active electron (SAE) approximation of "large" molecules and targets which are themselves undergoing dynamics during the HHG or ATI process. 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.a#13; a#13; a#13; We dedicate this work to the memory of Bertrand Carre, who passed away in March 2018 at the age o

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Symphony on strong field approximation

We have investigated the correlated electron dynamics in nonsequential double ionization (NSDI) of helium by the orthogonally polarized two-color pulses that consisted of an 800-nm and a 400-nm laser fields using the classical ensemble model. Depending on the relative phase of the two-color field, the electron momentum distributions along the polarization direction of the 800-nm field exhibit a surprisingly strong anticorrelated or correlated behavior. Back analysis reveals that recollisions eventually leading to NSDI are concentrated in a time window as short as several hundreds attoseconds with this scheme. By changing the relative phase of the two-color field, the revisit time of recolliding electron wave packet has been controlled with attosecond precision, which is responsible for the various correlated behaviors of the two electrons. Our results reveal that the orthogonally polarized two-color field can serve as a powerful tool to control the correlated electron dynamics in NSDI.

Correlated electron dynamics in nonsequential double ionization by orthogonal two-color laser pulses

The production of high-momentum electrons in double ionization of helium by near-infrared lasers is investigated using three-dimensional classical ensembles The nucleus' role is examined by systematically adjusting the nuclear potential The primary source of the high-energy electrons is found to be backscattering off the nucleus at recollision Recollision excitation with backscattering of the unbound electron is found to be especially important It is shown that recollision excitation with ionization before the next field maximum can lead to a correlated electron pair

Recollision excitation, electron correlation, and the production of high-momentum electrons in double ionization.

The production of anticorrelated (back-to-back) electrons in double ionization of atoms by lasers at 483 or 800 nm is examined with 3D classical ensembles, for situations in which the energy available at recollision is less than the binding energy. Recollision excitation typically leads to unequal electron energies. The more energetic electron most often drifts into the backward direction, whereas the other electron may be more likely to drift into the forward direction. That electron often ionizes late in the first laser maximum after recollision or early in the second maximum.

https://iopscience.iop.org/article/10.1088/0953-4075/41/21/211002/pdf

Anticorrelated electrons from weak recollisions in nonsequential double ionization

Longitudinal momentum spectra and electron drift directions are considered for several laser wavelengths in non-sequential double ionization of helium using three-dimensional classical ensembles. In this model, the familiar doublet for wavelength 800 nm and intensities of order 5 × 1014 W cm−2 becomes a triplet for wavelength 1314 nm, then a doublet for 2017 nm. The results are explained based on whether the post-ionization impulse from the laser results in backward drift for one or both electrons.

https://iopscience.iop.org/article/10.1088/0953-4075/42/13/134009/pdf

Electron drift directions in strong-field double ionization of atoms

Longitudinal momentum spectra and electron drift directions are considered for several laser wavelengths in Non-Sequential Double Ionization of helium using three dimensional classical ensembles. In this model, the familiar doublet for wavelength 800 nm and intensities of order 0.5 PW/cm^2, becomes a triplet for wavelength 1314 nm, then a doublet with plateau for 2017 nm. The results are explained based on whether the post-ionization impulse from the laser results in backward drift for one or both electrons.

Electron Drift Directions in Strong-Field Double Ionization of Atoms

Fully classical three-dimensional ensembles are examined under conditions of nonsequential double ionization and are shown to have trajectories in which both electrons apparently ionize only to have one electron bound to the nucleus after the laser pulse. These trajectories feature recollision excitation with subsequent over-the-barrier ionization at about the laser maximum. The ``ionized'' electron oscillates in the laser field but has small enough drift velocity to be recaptured at laser turnoff. Whether recapture can occur is shown to have extreme sensitivity to conditions at ionization.

Z. S. Smith

Papers

Recollision excitation, electron correlation, and the production of high-momentum electrons in double ionization.

Anticorrelated electrons from weak recollisions in nonsequential double ionization

Electron drift directions in strong-field double ionization of atoms

Electron Drift Directions in Strong-Field Double Ionization of Atoms

Frustrated nonsequential double ionization: A classical model