Recoil-ion momentum distributions for two-photon double ionization of He and Ne by 44 eV free-electron laser radiation

Control of concerted back-to-back double ionization dynamics in helium

Double ionization (DI) is a fundamental process that despite its apparent simplicity provides rich opportunities for probing and controlling the electronic motion. Even for the simplest multielectron atom, helium, new DI mechanisms are still being found. To first order in the field strength, a strong external field doubly ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion). The ejection into opposite directions (back-to-back motion) cannot be described to first order, making it a challenging target for control. Here, we address this challenge and optimize the field with the objective of back-to-back double ionization using a (1 + 1)-dimensional model. The optimization is performed using four different control procedures: (1) short-time control, (2) derivative-free optimization of basis expansions of the field, (3) the Krotov method, and (4) control of the classical equations of motion. All four procedures lead to fields with dominant back-to-back motion. All the fields obtained exploit essentially the same two-step mechanism leading to back-to-back motion: first, the electrons are displaced by the field into the same direction. Second, after the field turns off, the nuclear attraction and the electron-electron repulsion combine to generate the final motion into opposite directions for each electron. By performing quasi-classical calculations, we confirm that this mechanism is essentially classical.

Measuring the frequency chirp of extreme-ultraviolet free-electron laser pulses by transient absorption spectroscopy

High-intensity ultrashort pulses at extreme ultraviolet (XUV) and x-ray photon energies, delivered by state-of-the-art free-electron lasers (FELs), are revolutionizing the field of ultrafast spectroscopy. For crossing the next frontiers of research, precise, reliable and practical photonic tools for the spectro-temporal characterization of the pulses are becoming steadily more important. Here, we experimentally demonstrate a technique for the direct measurement of the frequency chirp of extreme-ultraviolet free-electron laser pulses based on fundamental nonlinear optics. It is implemented in XUV-only pump-probe transient-absorption geometry and provides in-situ information on the time-energy structure of FEL pulses. Using a rate-equation model for the time-dependent absorbance changes of an ionized neon target, we show how the frequency chirp can be directly extracted and quantified from measured data. Since the method does not rely on an additional external field, we expect a widespread implementation at FELs benefiting multiple science fields by in-situ on-target measurement and optimization of FEL-pulse properties.

Free-electron laser pulses generated from self-amplification of spontaneous emission scheme vary from one another in their characteristics. Here the authors demonstrate a transient absorption spectroscopy method to characterize the frequency chirp of the FEL pulses.

Photon-recoil imaging: Expanding the view of nonlinear x-ray physics

Addressing the ultrafast coherent evolution of electronic wave functions has long been a goal of nonlinear x-ray physics. A first step toward this goal is the investigation of stimulated x-ray Raman scattering (SXRS) using intense pulses from an x-ray free-electron laser. Earlier SXRS experiments relied on signal amplification during pulse propagation through dense resonant media. By contrast, our method reveals the fundamental process in which photons from the primary radiation source directly interact with a single atom. We introduce an experimental protocol in which scattered neutral atoms rather than scattered photons are detected. We present SXRS measurements at the neon K edge and a quantitative theoretical analysis. The method should become a powerful tool in the exploration of nonlinear x-ray physics.

Virtual Sequential Picture for Nonsequential Two-Photon Double Ionization of Helium

By using a model based on the second-order time-dependent perturbation theory, we show that the nonsequential two-photon double ionization of He can be understood in a virtual sequential picture: to excite the final double continuum state |k_{1},k_{2}⟩ by absorbing two photons from the ground state |1s^{2},^{1}S_{0}⟩, the single continuum states |1s,k_{1}⟩ and |1s,k_{2}⟩ serve as the dominant intermediate states. This virtual sequential picture is verified by the perfect agreement of the total ionization cross section, respectively, calculated by this model and by the sophisticated numerical solution to the full-dimensional time-dependent Schrödinger equation. This model, without the consideration of the electron correlation in the final double continuum state, works well for a wide range of laser parameters extending from the nonsequential to the sequential regime. The present Letter demonstrates that the electron correlation in the final double continuum state is not important in evaluating the total cross section, while it is indispensable for an accurate computation of a triply differential cross section. In addition, the virtual sequential picture bridges the sequential and nonsequential two-photon double ionization and reveals connections and distinctions between them.

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses

We study the breakup of H2+ exposed to superintense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes.

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.

Time-dependent theory of angular correlations in sequential double ionization

In this work, we emphasize the importance of the bound-state dynamics to the two-electron ejection in double ionization processes. The conclusions of the present study are pertinent to all excitation or decay processes that proceed via well-defined intermediate states. A general strong-field time-dependent density matrix theory is established and applied to the case of neon, allowing us to analyze the role of the ionizing field in the interpretation of reported angular patterns [M. Kurka et al., J. Phys. B 42, 141002 (2009); A. S. Kheifets, J. Phys. B 42, 134016 (2009)] and in the dynamic ionic alignment. The present analysis reveals that short-pulse coherent excitation of the neon ionic doublet 2P(1/2,3/2) leads to quantum beats in the two-electron angular correlation patterns.

Enhanced nonlinear double excitation of He in intense extreme ultraviolet laser fields

Nonlinear, three-photon double excitation of He in intense extreme ultraviolet free-electron laser fields (∼24.1  eV, ∼5  TW/cm2) is presented. Resonances to the doubly excited states converging to the He+ N=3 level are revealed by the shot-by-shot photoelectron spectroscopy and identified by theoretical calculations based on the time-dependent Schrödinger equation for the two-electron atom under a laser field. It is shown that the three-photon double excitation is enhanced by intermediate Rydberg states below the first ionization threshold, giving a greater contribution to the photoionization yields than the two-photon process by more than 1 order of magnitude.

Nonsequential two-photon double ionization of atoms: identifying the mechanism

We develop an approximate model for the process of direct (nonsequential) two-photon double ionization of atoms. Employing the model, we calculate (generalized) total cross sections as well as energy-resolved differential cross sections of helium for photon energies ranging from 39 to 54 eV. A comparison with results of ab initio calculations reveals that the agreement is at a quantitative level. We thus demonstrate that this complex ionization process can be described by the simple model, providing insight into the underlying physical mechanism. Finally, we use the model to calculate generalized cross sections for the two-photon double ionization of neon in the nonsequential regime.

Multiphoton double ionization of Ar in intense extreme ultraviolet laser fields studied by shot-by-shot photoelectron spectroscopy

Photoelectron spectroscopy has been performed to study the multiphoton double ionization of Ar in an intense extreme ultraviolet laser field (hν ∼ 21  eV, ∼ 5  TW/cm²), by using a free electron laser (FEL). Three distinct peaks identified in the observed photoelectron spectra clearly show that the double ionization proceeds sequentially via the formation of Ar(+): Ar+hν→Ar (+) + e⁻ and Ar²(+) + 2hν→Ar(+) + e⁻. Shot-by-shot recording of the photoelectron spectra allows simultaneous monitoring of FEL spectrum and the multiphoton process for each FEL pulse, revealing that the two-photon ionization from Ar(+) is significantly enhanced by intermediate resonances in Ar(+).

Two-photon inner-shell ionization in the extreme ultraviolet

We have observed the simultaneous inner-shell absorption of two extreme-ultraviolet photons by a Xe atom in an experiment performed at the short-wavelength free electron laser facility FLASH. Photoelectron spectroscopy permitted us to unambiguously identify a feature resulting from the ionization of a single electron of the 4d subshell of Xe by two photons each of energy (93±1)  eV. The feature's intensity has a quadratic dependence on the pulse energy. The results are discussed and interpreted within the framework of recent results of ion spectroscopy experiments of Xe obtained at ultrahigh irradiance in the extreme-ultraviolet regime.

Stabilization of helium in intense xuv laser fields

We investigate the impact of electron-electron correlation on the ionization dynamics of helium in intense, high-frequency laser fields by solving the time-dependent Schrödinger equation from first principles. Although we observe a decrease in the total ionization yield at high field strengths, the hallmark of atomic stabilization, the repulsion between the electrons has a detrimental effect on the degree of stabilization, in particular for short pulses. Investigation of the ion channel yields reveals that the double ionization process is less prone to two-electron effects, and consequently exhibits the most distinct signature of stabilization. We also find that commonly used one-dimensional models tend to overestimate the effect of correlation.

Few-photon multiple ionization of N2 by extreme ultraviolet free-electron laser radiation

Few-photon multiple ionization of N2 was studied differentially in a reaction microscope using 44 eV, approximately 25 fs, intense ( approximately 10(13) W/cm(2)) photon pulses from FLASH. Sequential ionization is observed to dominate. For various intermediate charge states N(2)(n+0 we find a considerable excess of photons absorbed compared to the minimum number that would energetically be required. Photoionization of aligned N(2)(n+) ions, produced by photon absorption in sequential steps, is explored and few-photon absorption pathways are traced by inspecting kinetic energy releases and fragment-ion angular distributions.