We calculate various differential and double differential characteristics of ionization by a single photon for H$^-$, He and for the two-electron ions with Z=3,4,5 in the region of the so-called quasi-free mechanism (QFM) domination. We employ highly accurate wave functions at the electron-electron coalescence line where coordinates of both ionized electrons coincide. We trace the Z dependence for the double differential distribution. For all considered targets we discuss the dependence of the photoelectron energy distribution on the photon energy. Our calculation demonstrated the rapid decrease of QFM contribution with increase of the difference in energy of two outgoing electrons, and with decrease of the angle between two outgoing momenta. As a general feature, we observe the decrease of QFM contribution with nuclear charge growth.
We calculate the distributions in recoil momenta and their energy distributions for the high energy non-relativistic double photoionization of helium caused by the quasifree mechanism of the process. The distributions obtain local maxima at small values of the recoil momenta. This is in agreement with the earlier predictions and with recently obtained experimental data. We obtained also the angular correlations, which reach the largest value in the "back-to-back" configuration of the photoelectrons. Our analysis is valid in all high energy nonrelativistic region. Particular equations are true …
Above 54.4 eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse VUV and soft X-ray so…
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 "finger-like" structure for high momenta recently found for $ω=0.055$ a.u. \cite{Staudte, Rudenko} persists for higher frequencies. At the same time, at $ω=0.187$ a.u. a new X-shape 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 non-sequential double ionization is discus…
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800 nm) and ultrashort (6 fs) laser pulse. We first focus on intensities corresponding to the tunneling regime and identify the main ionization mechanisms in this regime. We devise a selection of observables, such as, the correlated momenta and the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape where all the main mechanisms have distinct traces. Secondly, we address intensities above but close to the over-the-barrier …
We present the development and performance of a newly built recoil ion momentum spectrometer to study the fragmentation dynamics of ionized molecules. The spectrometer is based on the two-stage Wiley-McLaren geometry and satisfies both time and velocity focusing conditions. An electrostatic lens has been introduced in the drift region to achieve velocity imaging and higher angular collection. The spectrometer is equipped with a 2D position-sensitive detector with multi-hit coincidence electronics. Ionic fragments with kinetic energy ~ 8 eV can be detected with 4π collection. The overall perfor…
Energy and Angular-Momentum Redistribution in Hydrogen Migdal Ionization
School of Physics, Yantai University（烟台大学物理学院）；Department of Physics and Institute of Theoretical Physics, Nanjing Normal University（南京师范大学物理科学与技术学院/理论物理研究所）；College of Science, China University of Petroleum (East China)（中国石油大学（华东）理学院）
The generation of electron vortex states in ionization by intense and short laser pulses is analyzed under the scope of the lowest-order Born approximation. For near infrared laser fields and nonrelativistic intensities of the order of $10^{16}$~W/cm$^2$, we show that one has to modify the nonrelativistic treatment of ionization by accounting for recoil and mass relativistic corrections. By using the corrected quasi-relativistic theory, the requirements for the observation of electron vortex states with non-negligible probability and large topological charge are determined.
We present both full quantum mechanical and semiclassical calculations of above threshold ionization (ATI) of a hydrogen atom in the tunneling regime by a few-cycle linearly polarized infrared laser pulse. As a quantum treatment, we applied the direct integration of the time dependent Schrödinger equation (TDSE). In the semiclassical approximation (SCA), it is assumed that wavepacket propagation in the post-tunneling process can be well described within the classical framework. With these two methods, we analyze the similarities and deviations for ionization of the hydrogen atom. We found that…
Using a three-dimensional quasiclassical technique we explore the double ionization pathways of a diatomic molecule driven by an intense infrared (800nm) ultrashort laser pulse. For intensities corresponding to the tunneling regime, we find that the three main ionization mechanisms have distinct traces when considering the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape. In addition, we find that the previously observed "finger-like" structure in the correlated momenta of the strongly driven He is also present for strongly driven diatomic mo…
Using the cold target recoil ion momentum spectroscopy (COLTRIMS) technique, we have measured the simultaneous projectile and target ionization in collisions of He$^+$ projectiles with a mixture of gaseous H$_2$ and D$_2$ for an incident projectile energy of 650 keV. Motivated by Cooper et al. [Phys. Rev. Lett. 100, 043204 (2008)], we look for differences in the ionization cross section of the two isotopes with the highest resolution and statistical significance. Contributions of the electron-electron and electron-nucleus interactions have been clearly separated kinematically by measuring the …
Fully accounting for non-dipole effects in the electron dynamics, double ionization is studied for He driven by a near-infrared laser field and for Xe driven by a mid-infrared laser field. Using a three-dimensional semiclassical model, the average sum of the electron momenta along the propagation direction of the laser field is computed. This sum is found to be an order of magnitude larger than twice the average electron momentum along the propagation direction of the laser field in single ionization. Moreover, the average sum of the electron momenta in double ionization is found to be maximum…
Detection of nascent O($^3P_j$, $j=2,1,0$) atoms using one-photon resonant excitation to the $3s\,^3S^o_1$ state at $\sim 130$ nm followed by near-threshold ionization, i. e., 1 + 1' resonance enhanced multi-photon ionization (REMPI), has been investigated. The aim was to achieve low ion recoil, improved sensitivity, and reliable angular momentum polarization information, with an as simple as possible laser setup. An efficient 1 + 1' scheme has been found where the VUV light for the first step 1 is generated by difference frequency ($2ω_1 - ω_2$) VUV generation by four wave mixing in Kr gas, a…
We discuss the final stages of double ionization of atoms in a strong linearly polarized laser field within a classical model. We propose that all trajectories leading to non-sequential double ionization pass close to a saddle in phase space which we identify and characterize. The saddle lies in a two degree of freedom subspace of symmetrically escaping electrons. The distribution of longitudinal momenta of ions as calculated within the subspace shows the double hump structure observed in experiments. Including a symmetric bending mode of the electrons allows us to reproduce the transverse ion…
We measure the absolute absorption cross section of molecules using a matter-wave interferometer. A nanostructured density distribution is imprinted onto a dilute molecular beam through quantum interference. As the beam crosses the light field of a probe laser some molecules will absorb a single photon. These absorption events impart a momentum recoil which shifts the position of the molecule relative to the unperturbed beam. Averaging over the shifted and unshifted components within the beam leads to a reduction of the fringe visibility, enabling the absolute absorption cross section to be ex…
We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$\times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicat…
We analyze tunnel ionization of a single atom based on the Wigner function over the classical phase space which inspires improved classical electron trajectories: these start with exit momenta based on the quantum momentum function and correspond very well to the subsequent quantum evolution. We derive an approximate analytic formula to reconstruct the tunnel exit time and exit momentum from electron momentum data that can be measured e.g. with a usual time-of-flight electron detector.
Recent high resolution measurements of the momenta of two electrons emitted from Argon atoms in a strong laser field show a strong preference for the outgoing electrons to have similar momenta and to be ejected in the same direction along the field. We discuss the final stages of this process in a classical model in the spirit of Wanniers approach to double ionization after electron impact. Starting from an intermediate state of high but negative energy the field opens up a channel through which both electrons can escape. Near the threshold for this process Coulomb repulsion favors an escape w…
The effect of the Pauli exclusion principle on double ionization of He atoms by strong, linearly polarized laser pulses is analyzed. We show that correlated electron escape, with electron momenta symmetric with respect to the field polarization axis, is suppressed if atoms are initially prepared in the metastable state 3S. The effect is a consequence of selection rules for the transition to the appropriate outgoing two-electron states. We illustrate the suppression in numerical calculations of electron and ion momentum distributions within a reduced dimensionality model.
We calculate the double differential distributions and distributions in recoil momenta for the high energy non-relativistic double photoionization of helium. We show that the results of recent experiments is the pioneering experimental manifestation of the quasifree mechanism for the double photoionization, predicted long ago in our papers. This mechanism provides a surplus in distribution over the recoil momenta at small values of the latter, corresponding to nearly "back-to-back" emission of the electrons. Also in agreement with previous analysis the surplus is due to the quadrupole terms of…
We present an experimental scheme which combines the well established method of velocity-mapimaging, with a cold trapped metastable neon target. The device is used for obtaining the branching ratios and recoil-ion energy distributions for the penning ionization process in optical collisions of ultracold metastable neon. The potential depth of the highly excited dimer potential is extracted and compared with theoretical calculations. The simplicity to construct, characterize and apply such a device, makes it a unique tool for the low-energy nuclear physics community, enabling opportunities for …
Using a three-dimensional semiclassical model, we study double ionization for strongly-driven He fully accounting for magnetic field effects. For linearly and slightly elliptically polarized laser fields, we show that recollisions and the magnetic field combined act as a gate. This gate favors more transverse - with respect to the electric field - initial momenta of the tunneling electron that are opposite to the propagation direction of the laser field. In the absence of non-dipole effects, the transverse initial momentum is symmetric with respect to zero. We find that this asymmetry in the t…
We present a momentum-resolved study of strong field multiple ionization of ionic targets. Using a deconvolution method we are able to reconstruct the electron momenta from the ion momentum distributions after multiple ionization up to four sequential ionization steps. This technique allows an accurate determination of the saturation intensity as well as of the electron release times during the laser pulse. The measured results are discussed in comparison to typically used models of over-the-barrier ionization and tunnel ionization.
In this work our previous fully differential ionization cross section calculations using the semiclassical, impact parameter method are improved by a new method suitable to calculate impact parameter values corresponding to different momentum transfers. This goal is achieved by two successive steps. First, using the transverse momentum balance different projectile scattering angles are calculated for the binary and recoil peak regions as a function of the transferred momentum. Then, by treating the projectile scattering as a classical potential scattering problem, impact parameters are assigne…
High-precision QED calculations of the ground-state ionization energies are performed for all boronlike ions with the nuclear charge numbers in the range $16 \leqslant Z\leqslant 96$. The rigorous QED calculations are performed within the extended Furry picture and include all many-electron QED effects up to the second order of the perturbation theory. The contributions of the third- and higher-order electron-correlation effects are accounted for within the Breit approximation. The nuclear recoil and nuclear polarization effects are taken into account as well. In comparison with the previous e…
The laser intensity dependence of the recoil energies from the Coulomb explosion of small argon clusters has been investigated by resolving the contributions of the individual charge states to the ion recoil energy spectra. Between $10^{14}$ and $10^{15}$ W/cm$^2$ the high-energy tail of the ion energy spectra changes its shape and develops into the well-known knee feature, which results from the cluster size distribution, laser focal averaging, and ionization saturation. Resolving the contributions of the different charge states to the recoil energies, the experimental data reveal that the ba…
We consider the final stage of triple ionization of atoms in a strong linearly polarized laser field. We propose that for intensities below the saturation value for triple ionization the process is dominated by the simultaneous escape of three electrons from a highly excited intermediate complex. We identify within a classical model two pathways to triple ionization, one with a triangular configuration of electrons and one with a more linear one. Both are saddles in phase space. A stability analysis indicates that the triangular configuration has the larger cross sections and should be the dom…
We formulate a three-dimensional semi-classical model to address triple and double ionization in three-electron atoms driven by intense infrared laser pulses. During time propagation, our model fully accounts for the Coulomb singularities, the magnetic field of the laser pulse and for the motion of the nucleus at the same time as for the motion of the three electrons. The framework we develop is general and can account for multi-electron ionization in strongly-driven atoms with more than three electrons. To avoid unphysical autoionization arising in classical models of three or more electrons,…
We investigate laser induced nonsequential multiple ionization using a simple statistical model in which an electron recollides inelastically with its parent ion. In this collision, it thermalizes with the remaining $N-1$ bound electrons within a time interval $Δt$. Subsequently, all the $N$ electrons leave. We address the question of how the above time delays influence the individual contributions from the orbits in which the first electron, upon return, is accelerated or decelerated by the field, respectively, to the ion momentum distributions. In both cases, the time delays modify the drift…
Electron-electron correlation effects play an instrumental role in our understanding of sequential (SDI) and non-sequential double ionization (NSDI) mechanisms. Here, we present a theoretical study of NSDI driven by plasmonic-enhanced spatial inhomogeneous fields. By numerically solving the time-dependent Schrödinger equation for a linear reduced model of He and a double-electron time-evolution probability analysis, we provide evidence for the enhancement effects in NSDI showing that the double ionization yield at lower laser peak intensities is increased due to the inhomogeneity of the laser …
Accurate molecular imaging via high-order harmonic generation relies on comparing the harmonic emission from a molecule and an adequate reference system. However, an ideal reference atom with the same ionization properties as the molecule does not always exist. We show that for suitably designed, very short laser pulses, a one-to-one mapping between high-order harmonic frequencies and electron momenta in above-threshold ionization exists. Comparing molecular and atomic momentum distributions then provides the electron return amplitude in the molecule for every harmonic frequency. We show that …
Molecules show a much increased multiple ionization rate in a strong laser field as compared to atoms of similar ionization energy. A widely accepted model attributes this to the action of the joint fields of the adjacent ionic core and the laser on its neighbor inside the same molecule. The underlying physical picture for the enhanced ionization is that the up-field atom that gets ionized. However, this is still debated and remains unproven. Here we report an experimental verification of this long-standing prediction. This is accomplished by probing the two-site double ionization of ArXe, whe…
For the description of nonsequential double ionization (NSDI) of rare-gas atoms by a strong linearly polarized laser field, the quantum-mechanical $S$-matrix diagram that incorporates rescattering impact ionization is evaluated in the strong-field approximation. We employ a uniform approximation, which is a generalization of the standard saddle-point approximation. We systematically analyze the manifestations of the electron-electron interaction in the momentum distributions of the ejected electrons: for the interaction, by which the returning electron frees the bound electron, we adopt either…
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800~nm) 27~fs laser pulse. For intensities ranging from the tunneling to the over-the-barrier regime, we identify the double ionization pathways in a unified way as a function of total electron energy. For the tunneling regime, we discuss the differences in the interplay of double ionization (DI) pathways between strongly driven He and strongly driven $N_{2}$. For intermediate intensities in the over-the-barrier regime, we find that both the correlated momenta and the do…
Compton scattering is one of the fundamental interaction processes of light with matter. Already upon its discovery [1] it was described as a billiard-type collision of a photon kicking a quasi-free electron. With decreasing photon energy, the maximum possible momentum transfer becomes so small that the corresponding energy falls below the binding energy of the electron. Then ionization by Compton scattering becomes an intriguing quantum phenomenon. Here we report a kinematically complete experiment on Compton scattering at helium atoms below that threshold. We determine the momentum correlati…
