Process Of Two-photon Double Ionization Research Articles

Non-dipole effects on angular distribution of photoelectrons in sequential two-photon double ionization of Ar atom and K<sup>+</sup> ion

Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.

Temporal coherent control of resonant two-photon double ionization of the hydrogen molecule via doubly excited states

We use time-delayed, counter-rotating, circularly polarized few-cycle attosecond nonoverlapping pulses to study the temporal coherent control of the resonant process of two-photon double ionization (TPDI) of hydrogen molecule via doubly excited states for pulse propagation direction along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$ either parallel or perpendicular to the molecular axis $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\parallel}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a pulse carrier frequency of 36 eV resonantly populating the ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$ doubly excited state as well as other $^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}$ doubly excited states, we find that the indirect ionization pathway through these doubly excited states changes the character of the kinematical vortex-shaped momentum distribution produced by the two direct ionization pathways from fourfold to twofold rotational symmetry. This result is similar to what found in TPDI of the He atom involving $^{1}P_{\ifmmode\pm\else\textpm\fi{}1}^{o}$ doubly excited states [Ngoko Djiokap and Starace, J. Opt. 19, 124003 (2017)]; however, angular distributions exhibiting a quantum beat effect between the ground state and a doubly excited state seen for the He atom are observed here for its molecular counterpart with an anomaly in shape and magnitude, not in frequency. The sixfold differential probability integrated over the azimuthal angle of the photoelectron pair shows that this anomaly is due to autoionization decays and quantum beats between doubly excited states. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\perp}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a broadband pulse carrier frequency of 30 eV populating the ${Q}_{1}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(1)$, ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, and ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(2)$ doubly excited states, the momentum distribution is shown to exhibit dynamical electron vortices with four spiral arms, which originates from the interplay between the $^{1}\mathrm{\ensuremath{\Delta}}_{g}^{+}$, $^{1}\mathrm{\ensuremath{\Pi}}_{g}^{+}$, and $^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ dynamical ionization amplitudes. Our treatment within either the adiabatic-nuclei approximation or fixed-nuclei approximation shows that the latter provides a very good account for this correlated process.

Universality of the Dynamic Characteristic Relationship of Electron Correlation in the Two-Photon Double Ionization Process of a Helium-Like SystemSupported by the National Natural Science Foundation of China (Grant Nos. 91850209, 11774129, and 11774411), and the National Key Research and Development Program of China (Grant Nos. 2019YFA0307700 and 2016YFA0401100).

Universality of the dynamic characteristic relationship between the characteristic time t c and the two-electron Coulomb interaction energy of the ground state in the two-photon double ionization process is investigated via changing the parameters of the two-electron atomic system and the corresponding laser conditions. The numerical results show that the product keeps constant around 4.1 in the cases of changing the nucleus charge, the electron charge, the electron mass, and changing simultaneously the nucleus charge and the electron charge. These results demonstrate that the dynamic characteristic relationship in the two-photon double ionization process is universal. This work sheds more light on the dynamic characteristic relationship in ultrafast processes and may find its application in measurements of attosecond pulses.

The probe of electron correlation along the He isoelectronic sequence by intense and short laser pulses

The two-photon double ionization process along the He isoelectronic sequence (He − Ne8+) is investigated by solving the full-dimensional time-dependent Schrödinger equation in an intense laser field. The ionization is triggered from the ground state of each system with photons of energy higher than its second ionization potential, in which case the sequential two-electron ejection is allowed. The results of the total two-photon double ionization probability and the energy distribution of ejected electrons demonstrate the important effect of the nuclear charge Z on the dynamics of the interaction between the two ejected electrons.

Direct and Sequential Two-Photon Double Ionization of Two-Electron Quantum Dots.

In this work we study the double ionization yields and kinetic energy spectra of a two-electron spherical quantum dot (QD) exposed in laser fields. The theoretical description is based on an ab initio nonperturbative configuration interaction theory capable of describing the two-electron QD dynamics in THz and mid-IR ultrashort laser fields. The QD's confinement potential is approximated to have a Gaussian-like spatial dependence. We have found that significant variations of the two-electron kinetic energy patterns and two-photon double ionization yields occur as we vary the QD's size. For a given laser pulse, the double ionization yield increases by orders of magnitude when the dot size is reduced. The size of the QD determines the sequential or direct character of the two-photon double ionization process. Provided that it is energetically allowed, the sequential two-photon double ionization process, requiring minimal interelectronic correlations, becomes dominant over the direct one. In the sequential regime, the corresponding two-electron kinetic energy spectrum changes from a broadened single-peaked to a doubly peaked one. Moreover, we also have identified features in the spectrum that are distinctively different than those in its atomic counterpart.

Two-photon double ionization of metastable1,3S1s2shelium

We investigate the process of two-photon double ionization (TPDI) of the metastable helium ${}^{1,3}S$ $1s2s$ states. The process has been simulated within a fully $ab$ $initio$ numerical framework, solving the time-dependent Schr\"odinger equation in full dimensionality for the two interacting electrons, in a $B$-spline-based methodology. The presence of doubly excited (autoionizing) states in the direct TPDI regime causes resonance-enhanced multiphoton ionization, and we demonstrate this effect by accessing the ${}^{1,3}P$ $2s2p$ doubly excited states. Fully converged theoretical calculations are presented, and a well-defined cross section is extracted for the direct TPDI process and compared in the context of its analogous process in the helium ground state. In addition, the resonance-enhanced two-photon double-ionization mechanism is explored, and we discuss how this process differs from both direct and sequential ionization processes.

Numerical study of two-photon ionization of helium using anab initionumerical framework

Few-photon-induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schr\"odinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold ($~54.4$ eV) versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process caused by the bandwidth of the applied field.

(2γ,2e) total and differential cross-section calculations for helium with ħω = 40–50 eV

We consider two-photon double ionization of helium and analyse the electron dynamics in the region where the process is direct (39.49 eV < ħω < 54.42 eV). The fundamental process of two-photon double ionization (TPDI) is far from being well understood. In order to gain physical insight into the dynamics involved in TPDI, we investigate the electron energy distributions for ħω = 46 eV and ħω = 50 eV, angular distributions are also analysed. The theoretical approach is based on the resolution of the time-dependent Schrodinger equation (TDSE), using a spectral approach. At the end of the pulse the TPDI probability is extracted from the total wavefunction using two different approaches. The first one neglects the electron interaction in the double continuum while the second one includes electron correlation effects. At ħω ≈ 45 eV the electrons are preferably emitted back-to-back with equal energy. At ħω = 50 eV the excess energy is likely to be transfered to one of the electron, while the electrons are emitted in opposite or same directions.