S. L. Haan

Nonsequential double ionization as a completely classical photoelectric effect.

We introduce a unified and simplified theory of atomic double ionization. Our results show that at high laser intensities (I>/=10(14) W/cm(2)) purely classical correlation is strong enough to account for all of the main features observed in experiments to date.

Comparing classical and quantum simulations of strong-field double-ionization.

We compare quantum mechanical and fully classical treatments of electron dynamics accompanying strong field double ionization. The major features seen in quantum mechanical simulations, including the double-ionization jets, are reproduced when using a classical ensemble of two-particle trajectories.

Recollision dynamics and time delay in strong-field double ionization.

Three-dimensional classical ensembles are employed to study recollision dynamics in double ionization of atoms by 780-nm intense lasers. After recollision one electron typically remains bound to the atom for a portion of a laser cycle, during which time the nucleus strongly influences its direction of motion. The electron then escapes over a suppressed barrier, with its final momentum depending critically on the laser phase at escape. The other electron remains unbound after collision, and typically drifts out in a momentum hemisphere opposite from its motion just after the collision. Several example trajectories at intensity 0.4 PW/cm(2) with various time delays between recollision and ionization are presented.

A split-domain algorithm for time-dependent multi-electron wave functions

A computational technique for studying the time-development of two-electron systems is presented, with particular attention given to photoionization or photodetachment of two-electron, one-dimensional model atoms. The technique is based on a partitioning of the spatial wave function into inner and outer parts. The electron-electron interaction is fully accounted for in the inner part, but neglected in the outer part, where the electrons are typically far apart. The time development of the inner part is calculated using a full numerical grid, but the time-development of the outer part is accomplished using canonical basis states. The use of canonical basis states allows the study of atom-laser dynamics for much longer laser pulse durations and lower laser frequencies than would be possible using standard grid techniques.

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 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.

Anticorrelated electrons from weak recollisions in nonsequential 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.

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.

The role of correlation in non-sequential double ionization

We present the results of recent numerical studies of double ionization and correlation in a two-electron model atom. We briefly review basic features of our model and describe the invariant measure of correlation that we find convenient. Our results help to illuminate the dynamics of the double-ionization process. We focus on the well-known “knee” sone. We show that the spatial probability distribution of the two-electron system exhibits jets of double ionization which occur each half cycle. We note a competing process of rapid sequential ionization. We also examine the dependence of these processes on the strength of the electron-electron repulsion, and we find that the size of the jets is particularly sensitive to it in the vicinity of the knee.

Classical modeling of non-sequential double ionization: Recollision, time-delayed ionization, drift, and possible reattachment

We employ 3d classical ensembles to study Non-Sequential Double Ionization (NSDI) of atoms by strong laser fields at visible and infrared wavelengths. We consider in particular the wavelength dependence of final electron drift directions and the net momentum spectra parallel to the laser polarization. We find that as the wavelength is increased the spectrum transitions from a singlet to a doublet, then to a triplet, and finally back to a doublet. We also show that electrons that escape the central potential-energy well during the pulse may nonetheless be bound to the nucleus after laser turnoff.

A completely classical photoelectric effect

Completely classical analysis of the strong-field two-electron photoelectric effect, or non-sequential double ionization (NSDI), gives surprisingly full reproduction of major experimental points. We find that tunnelling is not required for NSDI and that relative phasings of ejected electron jitter motions are intuitively related to ion recoil momentum.