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Project supported by the National Natural Science Foundation of China (Grant Nos. 11774131 and 91850114).
We investigate the intensity effect of ultrashort assisting infrared laser pulse on the single-XUV-photon double ionization of helium atoms by solving full six-dimensional time-dependent Schrödinger equation with implement of finite element discrete variable representation. The studies of joint energy distributions and joint angular distributions of the two photoelectrons reveal the competition for ionized probabilities between the photoelectrons with odd parity and photoelectrons with even parity in single-XUV-photon double ionization process in the presence of weak infrared laser field, and such a competition can be modulated by changing the intensity of the weak assisting-IR laser pulses. The emission angles of the two photoelectrons can be adjusted by changing the laser parameters as well. We depict how the assisting-IR laser field enhances and/or enables the back-to-back and side-by-side emission of photoelectrons created in double ionization process.
Investigations of double ionization (DI) of helium atoms with extreme ultraviolet (XUV) laser field[1] have been launched both experimentally[2–4] and theoretically[5–7] for more than two decades. Recently, the experimental advances in generation of XUV light from free-electron lasers[8–10] and the application of the high-order harmonic generation[11] provide opportunities to observe single and multiple ionization of atoms and molecules experimentally.[3,12,13] Hasegawa et al.[14] firstly performed an experiment to measure the two-photon DI cross section of helium exposed to XUV pulses with a photon energy of 42 eV.
In particular, major theoretical researches have been focused on calculations of the triply differential cross sections (TDCSs) for the DI of helium, such as TDCSs calculated by Huetz et al.[15] based on the Wannier theory,[16] TDCSs obtained from time-dependent close-coupling simulations by Palacios et al.,[17] and the convergent close-coupling calculations by Kheifets and Bray.[18] All these works were found to be in good agreement with the angular distribution in the absolute TDCSs measured by Bräuning et al.[18] Besides the quantum mechanics methods, classical and semi-classical methods have a lot of applications and achievements in the investigations of sequential and non-sequential DI,[19,20] as well as the frustrated DI, etc.[21]
Recent progress in experimental physics has performed the pump-probe scheme with the combined infrared (IR) and XUV laser fields for investigating electron dynamics in ultrashort time scales, such as above-threshold ionization (ATI),[22–24] streaking camera,[25] high-order harmonic generation,[26,27] and nonsequential double ionization (NSDI)[28,29] as well. The enhancement of emission of fast photoelectrons and sensitive influences on the photoelectron energy distribution caused by the additional IR laser field were reported by Hu.[30] Also, the IR pulse’s promotion of side-by-side and back-to-back emission has been illustrated by using the finite-element discrete-variable-representation (FE-DVR) method for numerically solving the time-dependent Schröinger equation (TDSE) in full dimensionality.[31–33] In addition, the selection rules,[5,34] comprehensive numerical studies as well as the joint angular distributions (JADs) of the emitted electrons with different energy sharing have been learned.[35]
In a previous work,[36] Liu et al. studied the DI process of helium in IR-assisted XUV laser field by use of the FE-DVR method for numerically solving the TDSE in full dimensionality. It has been found that the assistant IR pulse can promote the side-by-side emission and enables back-to-back emission. Also, we analyzed the dependence of JADs on the IR’s intensity and the dependence of mutual photoelectron angular distributions (MADs) on the energy sharing of the emitted electrons. More recently, Jin et al.[37] investigated the role of IR and XUV laser field respectively, in which the NSDI process was described as an ATI followed by a laser-assisted collision.
An emission geometry for co-planar emission has been described in Ref. [36], in which the two emitted electrons are ejected with angles θi relative to the polarization directions of XUV and IR pulses, and the emission types are distinguished as back-to-back, side-by-side, conic, and symmetric emissions. Investigations of these emission patterns allow researchers to investigate the dynamics of DI process more precisely. The electron emission type in sequential and nonsequential two-photon DI process has been discussed by calculating the JAD at equal energy sharing. Jin et al.[38] showed the contributions of forward and backward collisions to the NSDI probability of the side-by-side and back-to-back patterns.
Here, we carry out calculations of probability density in joint energy distribution (JED) and JAD for the photoelectrons ejected during the ionization of helium atoms by an intense XUV pulse in the presence of a weak IR laser pulse, and discuss how the emission pattern varies with the increasing intensity of the assisting IR laser field. Also, we study the dependence of MADs for photoelectrons with different parities on energy sharing, and find that the emission pattern is similar with that revealed by the JADs for DI where the assistant IR laser pulse is at lower intensity and the photoelectrons are at equal energy sharing.
The rest of this paper is organized as follows: Theoretical methods for the numerical solution of the full-dimensional TDSE for the two emitted electrons during the ionization are presented in Section
The motion of two-electron atoms driven by the laser-assisted XUV laser field is described by the TDSE in atomic units,
The Hamiltonian of the system is
For the two-electron system exposed to the XUV and IR laser field, the wave function is expanded in terms of the bipolar spherical harmonic[35,36,39]
![](cpb_29_7_073202/cpb_29_7_073202_ieqn1.gif)
![](cpb_29_7_073202/cpb_29_7_073202_ieqn2.gif)
Then the DI probability for double ionization corresponding to the final state with momenta k1 and k2 can be given by projecting the final wave function to the asymptotic two-electron wave functions for a long time after the termination of the pulses. For the purpose of removing spurious contribution caused by nonorthogonality of the approximate asymptotic wave function and the initial state, we rewrite the final wave function with exclusion of the overlap between the initial state and the final state.
Finally, we evaluate the correlated energy distribution by integrating over all angles,
![](cpb_29_7_073202/cpb_29_7_073202_ieqn3.gif)
![](cpb_29_7_073202/cpb_29_7_073202_ieqn4.gif)
Our previous studies have focused on the modifications of the JED and JAD of photoelectrons caused by a weak assisting-IR laser field during the DI of helium in an intense XUV pulse. It is worth pointing out that the certain effective numbers of absorbed/emitted IR photons can be represented by each stripe in the JED of the sideband pattern.
In the following, we analyze the effect of intensity of the assisting-IR laser field on the electron dynamics by calculations of JED and JAD of the photoelectrons. For the sake of simplicity, we suppose that the XUV pulse and IR pulse have an overlapping cosine-squared temporal profile with identical phases φXUV = φIR = 0°. We set the IR and XUV pulses with pulse length as 2.6 fs and 0.46 fs, respectively. The peak intensity of the XUV laser field is chosen at 1013 W/cm2, and the central photon energies of the XUV laser and IR field are supposed to be ℏωXUV = 89 eV and ℏωIR = 1.61 eV, respectively.
We first consider the JED for the DI of helium with XUV pulse of central energy 89 eV alone (i.e., without the assisting-IR field) in Fig.
To display these sidebands obviously, the JEDs at different laser intensities are shown in a decomposed manner according to even and odd numbers of absorbed/emitted IR photons [see Figs.
We turn our attention now to examine the intensity effect of assistant IR laser pulses on DI of helium by investigating the JADs of the two ionized electrons at equal energy sharing, where the XUV laser pulses are taken to have central photon energy of 89 eV and a peak intensity of 1013 W/cm2. The results for odd- and even-parity photoelectrons are displayed separately for the double ionization at three different peak intensities: IIR = 1010 W/cm2 [Figs.
As illustrated in Figs.
The second change is that the positions of the main peaks change with increased peak density of the IR laser field. For the case of odd-parity, the four main peaks are distributed along the line of θ1 + θ2 = 360°, and the separation between the main peaks becomes larger as the intensity of the IR field increases. In particular, when the intensity of the IR laser field is taken as 1012 W/cm2, the symmetric emission is fading to compete with back-to-back emission.
The structure of the JADs for the even-parity electrons changes drastically as the intensity of the IR laser field increases. We can see that the dominant emission pattern changes gradually from the ‘back-to-back’ (as shown in Fig.
To further investigate the electronic dynamics of the laser-assisted single-XUV-photon DI of helium, we study the MADs at different energy sharings. The results are shown in Fig.
The detailed discussion of Figs.
In summary, we have investigated the DI process of helium atoms by moderate strong intensity XUV radiation, and explored the electronic dynamics for the IR laser-assisted single-XUV-photon DI process of helium atoms using an numerical calculation of the TDSE in its full dimensionality. It is found that the probability densities in the JEDs and JADs for the odd-parity photoelectrons and even-parity photoelectrons represent opposite changes with increasing intensity of the assisting-IR laser pulses. The JEDs show competition between odd and even parities of photoelectrons. The JADs at equal energy sharing are also studied for photoelectrons with different parities to investigate the influence of assisting-IR laser pulses. The double ionization by XUV laser pulse only used mainly has symmetric emission pattern of the two photoelectrons. The assisting laser field can enable the back-to-back emission pattern for even parity photoelectrons, and split the symmetric emission. The MADs for the photoelectrons with different parities at different energy sharings demonstrate that both back-to-back and side-by-side emissions exist. With the vector superposition scheme, we depict and demonstrate how the modification to MADs is produced in the case of assisted-IR single-XUV-photon DI.
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