Strong-field Double Ionization Research Articles

Classical Simulations Including Electron Correlations for Sequential Double Ionization

With a classical ensemble model that includes electron correlations during the whole ionization process, we investigate strong-field sequential double ionization of Ar by elliptically polarized pulses at the quantitative level. The experimentally observed intensity-dependent three-band or four-band structures in the ion momentum distributions are well reproduced with this classical model. More importantly, the experimentally measured ionization time of the second electrons by A. N. Pfeiffer et al. [Nature Phys. 7, 428 (2011)], which cannot be predicted by the standard independent-electron model, is quantitatively reproduced by this fully classical correlated model. The success of our work encourages classical descriptions and interpretations of the complex multielectron effects in strong-field ionization where nonperturbative quantum approaches are currently not feasible.

Strong-Field Ionization Rate Depends on the Sign of the Magnetic Quantum Number

We report the first experimental observation of the dependence of strong-field ionization rate on the sign of the magnetic quantum number. We measure the strong-field sequential double ionization yield of argon by two time-delayed near-circularly polarized laser pulses. It is found that double-ionization yield is enhanced more than 3 times if two lasers have the opposite helicities. Analysis shows that the single ionization of both the neutral and ion prefer the same sign of the magnetic quantum number. A qualitative and intuitive model is proposed to help understand this phenomenon.

Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization

With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we found a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides a profound understanding of electronic correlations and complicated multiphoton phenomena and is expected to be a new tool for broad applications, such as quantum coherent control.

Role of Nuclear Coulomb Attraction in Nonsequential Double Ionization of Argon Atom

The microscopic recollision dynamics in strong-field nonsequential double ionization of Ar atoms is investigated using three-dimensional classical ensembles. By adjusting the nuclear Coulomb potential, we can excellently reproduce the experimental results both within the laser intensity regimes well above the recollision threshold and well below the recollision threshold quantitatively. More importantly, our trajectory analysis clearly reveals the particular electronic dynamics in recollision process: the momentum of the recolliding electron encounters a sudden change both in magnitude and in direction when it approaches the nucleus closely, which show that the nuclear Coulomb attraction plays a key role in the recollision process of nonsequential double ionization of Ar atoms.

Breakdown of the independent electron approximation in sequential double ionization

Correlated electron emission in strong field double ionization is dominated by recollision of the first ionized electron with its parent ion. With laser pulses that are close-to-circularly polarized, recollision may be greatly modified or avoided and the electrons are usually assumed to be field ionized without mutual interaction. Here, we present coincidence momentum measurements of the doubly charged ion and the two electrons, which are in disagreement with the independent electron assumption for close-to-circularly polarized fields. These experiments demonstrate that recollision is not the only mechanism that can lead to correlated electron emission in strong field double ionization.

Direct versus delayed pathways in strong-field non-sequential double ionization

We report full-dimensionality quantum and classical calculations of the double ionization (DI) of laser-driven helium at 390 nm. Good agreement between the quantum and classical results is observed. We identify the relative importance of the two main non-sequential DI pathways: the direct—with an almost simultaneous ejection of both electrons—and the delayed. We find that the delayed pathway prevails at small intensities independently of total electron energy, but at high intensities the direct pathway predominates up to a certain upper limit in total energy, which increases with intensity. An explanation of this increase with intensity is provided.

Timing the release in sequential double ionization

The timing of electron release in strong-field double ionization poses great challenges both for conceptual definition and for conducting experimental measurements. Here we present coincidence momentum measurements of the doubly charged ion and of the two electrons arising from double ionization of argon using elliptically polarized laser pulses. Based on a semi-classical model, the ionization times are calculated from the measured electron momenta across a large intensity range. This paper discusses how this method provides timings on a coarse and on a fine scale, similar to the hour and the minute hand of a clock. We found that the ionization time of the first electron is in good agreement with the simulation, whereas the ionization of the second electron occurs significantly earlier than predicted. An ‘attoclock’ that measures the relative release time of electrons during double ionization is now presented. The technique enables investigation of the subtle differences between sequential and non-sequential ionization when elliptically polarized light is used to excite two electrons from argon atoms.

Quantitative rescattering theory of correlated two-electron momentum spectra for strong-field nonsequential double ionization of helium

We study the correlated two-electron momentum spectra of the nonsequential double ionization (NSDI) of an atom in an intense laser field based on the recently developed quantitative rescattering (QRS) theory. According to the rescattering model, an electron that was released earlier in the laser pulse may return to collide again with the target ion. NSDI can occur directly if this electron knocks out another electron in a process similar to the ($e,2e$) process or indirectly by first exciting the target ion to an excited state which is later ionized by the laser field. Using QRS, we obtain the returning electron wave packet. By multiplying this wave packet with standard field-free ($e,2e$) differential cross sections, or with inelastic electron-impact excitation cross sections and the subsequent tunneling ionization, we obtain the correlated two-electron momentum spectra. The calculated spectra agree mostly with the experimental data. However, experimental data show additional features that cannot be accounted for by these two mechanisms only, and other mechanisms for NSDI are suggested. The contributions of these mechanisms to the longitudinal ion momentum distributions are also analyzed. The present quantum mechanical QRS calculation verifies the validity of rescattering model for the NSDI processes at the most fundamental and detailed level.

Elliptical Polarization and Probability of Double Ionization

The degree of elliptical polarization of intense short laser pulses is shown to be related to the timing of strong-field nonsequential double ionization. Higher ellipticity is predicted to force the initiation of double ionization into a narrower time window, and this "pins" the ionizing field strength in an unexpected way, leading to the first experimentally testable formula for double ionization probability as a function of ellipticity.

Nonsequential double ionization of triatomic molecules in strong laser fields

In this paper, we extend strong-field double ionization from diatomic molecules to triatomic molecules. Strong-field double ionization of CO${}_{2}$ is studied here with both linear and circular polarizations. A clear nonsequential signature is seen in doubly ionized CO${}_{2}$. We also compare nonsequential double ionization behaviors of CO${}_{2}$ to those of the well-studied diatomic molecules, and the difference is attributed to the detailed electronic structures in molecules.

Exploration of strong-field multiphoton double ionization, rescattering, and electron angular distribution of He atoms in intense long-wavelength laser fields: The coupled coherent-state approach

This work was partially supported by the Chemical Sciences, Geosciences and Biosciences Division of the Office of Basic Energy Sciences, Office of Sciences, US Department of Energy and by the US National Science Foundation. J.G. would also like to acknowledge the partial support of the Chinese Scholarship Council (CSC). J.G. and X.L. were partially supported by the National Natural Science Foundation of China under Grant No. 10974068.

Strong-field double ionization at the transition to below the recollision threshold

We investigate the strong-field double ionization using a semiclassical model, in which the recollision-induced excitation-tunneling (RIET) effect has been taken into account with the Wentzel-Kramers-Brillouin (WKB) approach. When the laser intensity is below the recollision threshold, we find that both RIET and multiple recollisions become significant and can produce the anticorrelated (back-to-back) electron pair. Distinct footprints left by these two mechanisms on the correlated momentum spectra have been identified. As another signature of the transition to below the recollision threshold regime, we find that the V-shaped (or fingerlike) structure in the correlated momentum spectra fades away. Our model calculations have been compared with a recent experiment on argon atoms.

Monte Carlo Wave Packet Theory of Dissociative Double Ionization

Nuclear dynamics in strong-field double ionization processes is predicted using a stochastic Monte Carlo wave packet technique. Using input from electronic structure calculations and strong-field electron dynamics the description allows for field-dressed dynamics within a given molecule as well as transitions between several different charge states. The description is computationally efficient and applicable to a wide range of systems. As a proof of principle, theoretical nuclear kinetic energy release spectra for H2 (D2) in strong near-infrared laser pulses of 40 fs duration are compared to experiments and very good agreement is obtained.

Strong field double ionization of H 2: Insights from nonlinear dynamics

The uncorrelated (“sequential”) and correlated (“nonsequential”) double ionization of the H 2 molecule in strong laser pulses is investigated using tools of nonlinear dynamics. We focus on the phase-space dynamics of this system, specifically by finding the dynamical structures that regulate these ionization processes. The emerging picture complements the recollision scenario by clarifying the distinct roles played by the recolliding and core electrons. Our analysis leads to verifiable predictions of the intensities where qualitative changes in ionization occur. We also show how these findings depend on the internuclear distance.

Effects of Elliptical Polarization on Strong-Field Short-Pulse Double Ionization

We predict new end-of-pulse behavior in high-field atomic double ionization. Calculations of atomic electron trajectories in short intense laser pulses confirm our analysis of elliptical polarization. We exhibit a four-band structure in ion momentum distributions under various ellipticities, and predict that sequential and nonsequential double ionization can be cleanly distinguished under elliptical polarization.

Strong field double ionization: what is under the ‘knee’?

Both uncorrelated (‘sequential’) and correlated (‘nonsequential’) processes contribute to the double ionization of the helium atom in strong laser pulses. The double ionization probability has a characteristic ‘knee’ shape as a function of the intensity of the pulse. We investigate the phase-space dynamics of this system, specifically by finding the dynamical structures that regulate the ionization processes. The emerging picture complements the recollision scenario by clarifying the distinct roles played by the recolliding and core electrons. Our analysis leads to verifiable predictions of the intensities where qualitative changes in ionization occur, leading to the hallmark ‘knee’ shape.

Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory

Time-dependent (TD) density functional theory (TDDFT) promises a numerically tractable account of many-body electron dynamics provided good simple approximations are developed for the exchange-correlation (XC) potential functional (XCPF). The theory is usually applied within the adiabatic XCPF approximation, appropriate for slowly varying TD driving fields. As the frequency and strength of these fields grows, it is widely held that memory effects kick in and the eligibility of the adiabatic XCPF approximation deteriorates irreversibly. We point out, however, that when a finite system of electrons in its ground-state is gradually exposed to a very a high-frequency and eventually ultra-strong homogeneous electric field, the adiabatic XCPF approximation is in fact rigorously applicable. This result shows that adiabatic XCPF has a larger scope of applicability than previously suspected and in this sense is compliant with recent numerical findings by Thiele et al. [M. Thiele, E.K.U. Gross, S. Kümmel, Phys. Rev. Lett. 100 (2008) 153004] of negligible memory effects in strong-field double ionization.

Classical Trajectory Diagnosis of a Fingerlike Pattern in the Correlated Electron Momentum Distribution in Strong Field Double Ionization of Helium

With a semiclassical quasistatic model, we identify the distinct roles of nuclear Coulomb attraction, final-state electron repulsion, and the electron-field interaction in forming the fingerlike (or V-shaped) pattern in the correlated electron momentum distribution for helium double ionization in intense laser field [Phys. Rev. Lett. 99, 263002;Phys.Rev.Lett.99, 263003 (2007)]. The underlying microscopic trajectory configurations responsible for asymmetric electron energy sharing after electron-electron collision have been uncovered, and the corresponding subcycle dynamics is analyzed. The correlation pattern is found to be sensitive to the transverse momentum of correlated electrons.

Recoil collisions as a portal to field-assisted ionization at near-uv frequencies in the strong-field double ionization of helium

We explore the dependence of the double ionization of the He atom on the frequency of a strong laser field while keeping the ponderomotive energy constant. As we increase the frequency we find that the remarkable ``fingerlike'' structure for high momenta recently found for $\ensuremath{\omega}=0.055\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ persists for higher frequencies. At the same time, at $\ensuremath{\omega}=0.187\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, a new X-shaped structure emerges for small momenta that prevails in the correlated momenta distribution. The role of this structure as a signature of the frequency dependence of nonsequential double ionization is discussed.

Intensity-dependent transitions between different pathways of strong-field double ionization

Momentum distributions of ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ar}}^{2+}$ ions created by linearly polarized $795\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, $25\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ laser pulses have been traced at intensities from ${10}^{14}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ using a ``reaction microscope.'' Apart from the transition from nonsequential to sequential ionization, characterized by significant changes in longitudinal momentum distributions developing from a double hump, over a triple-peak structure to a narrow single Gaussian observed for both ions, for ${\mathrm{Ar}}^{2+}$ we find a similar behavior but reversed in its intensity dependence in the purely nonsequential regime, pointing to contributions of recollision excitation plus subsequent field ionization, or to the role of ``Z trajectories'' recently predicted within classical calculations.