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We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.

The biharmonic ( ω , 2 ω ) photoionization of atomic inner-shell electrons opens up new perspectives for studying nonlinear light–atom interactions at intensities in the transition regime from weak to strong-field physics. In particular, the control of the frequency and polarization of biharmonic beams enables one to carve the photoelectron angular distribution and to enhance the resolution of ionization measurements by the (simultaneous) absorption of photons. Apart from its quite obvious polarization dependence, the photoelectron angular distributions are sensitive also to the (relative) intensity, the phase difference and the temporal structure of the incoming beam components, both at resonant and nonresonant frequencies. Here, we describe and analyze several characteristic features of biharmonic ionization in the framework of second-order perturbation theory and (so-called) ionization pathways , as they are readily derived from the interaction of inner-shell electrons with the electric-dipole field of the incident beam. We show how the photoelectron angular distribution and elliptical dichroism can be shaped in rather an unprecedented way by just tuning the properties of the biharmonic field. Since such fields are nowadays accessible from high-harmonic sources or free-electron lasers, these and further investigations might help extract photoionization amplitudes or the phase difference of incoming beams.

Coulomb excitation of hydrogen atoms by vortex protons is theoretically investigated within the framework of the non-relativistic first–Born approximation and the density matrix approach. Special attention is paid to the magnetic sublevel population of excited atoms and, consequently, to the angular distribution of the fluorescence radiation. We argue that both these properties are sensitive to the projection of the orbital angular momentum (OAM), carried by the projectile ions. In order to illustrate the OAM–effect, detailed calculations have been performed for the 1 s → 2 p excitation and the subsequent 2 p → 1 s radiative decay of a hydrogen target, interacting with incident Laguerre–Gaussian vortex protons. The calculation results suggest that Coulomb excitation can be employed for the diagnostics of vortex ion beam at accelerator and storage ring facilities.

In this paper, we aim to investigate angle-resolved linear polarization of the L α 1 ( 3 d 5 / 2 → 2 p 3 / 2 ) , L α 2 ( 3 d 3 / 2 → 2 p 3 / 2 ) , and L ℓ ( 3 s 1 / 2 → 2 p 3 / 2 ) characteristic lines following innershell 2 p 3 / 2 photoionization of selected neutral atoms with closed subshells by unpolarized or linearly polarized ionizing light within the framework of the density-matrix theory. To this aim, a relativistic single-configuration Dirac–Hartree–Fock approximation and the electric dipole approximation of the radiation fields are used to calculate the 2 p 3 / 2 photoionization amplitudes of those atoms, the alignment parameter of the photoionized 2 p 3 / 2 - 1 hole state, and thus the angle-resolved linear polarization of the characteristic lines. It is found that the angle-resolved linear polarization of the L α 1 , 2 and L ℓ lines behaves very differently for different polarization cases of the ionizing light under consideration. In addition, at given ionizing photon energies the L α 1 line is found to be the least linearly polarized for all different ionizing polarization cases, whereas the linear polarization of both the L α 2 and L ℓ lines is much stronger and, actually, rather close to each other despite always having opposite polarization signs. As the nuclear charge and the ionizing photon energy increase, moreover, each of these lines becomes more and more linearly polarized, respectively. Graphical abstract Linear polarization of the L α 1 (top panels), L α 2 (middle), and L ℓ (bottom) lines following innershell 2 p 3 / 2 photoionization of Ba (black solid lines), Yb (red dashed lines), Hg (blue dotted lines), and Rn (green dash–dotted lines) atoms by linearly polarized ionizing γ light with P γ = 1 , as functions of the emission angle θ 0 . Results are given for two different ionizing photon energies of 1.1 (left panels) and 4.0 (right) times their respective 2 p 3 / 2 ionization thresholds.

Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N =126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency. It is challenging to explore properties of heavy elements as they can only be produced artificially. Here, the authors demonstrate a high resolution spectroscopy method, studying the properties of actinium, which can be extended to the study of other elements located at the end of the periodic table.

Within the framework of the density matrix theory, the angular distribution of the characteristic magnetic-quadrupole line 1 s 2 p 3 P 2 → 1 s 2 1 S 0 following electron-impact excitation of heliumlike thallium ions with nuclear spin I = 1 / 2 has been investigated by using the multiconfigurational Dirac–Hartree–Fock method and the relativistic distorted-wave theory. Special attention has been paid to exploring the question of how the angular distribution of the characteristic line is affected by the multipole interference between the dominant magnetic-quadrupole and hyperfine-induced electric-dipole decay channels of its hyperfine-structure-resolved component 1 s 2 p 3 P 2 , F = 3 / 2 → 1 s 2 1 S 0 , F 0 = 1 / 2 . To this aim, detailed calculations are performed for spin-1/2 81 187 Tl 79 + and 81 207 Tl 79 + ions with (relatively) large nuclear magnetic dipole moment. It is found that the hyperfine-induced multipole interference contributes to making the angular distribution of the magnetic-quadrupole line 1 s 2 p 3 P 2 → 1 s 2 1 S 0 less anisotropic for all the impact electron energies considered, although at any given impact energy its angular emission pattern remains always qualitatively consistent with each other for both the two cases without and with the interference contribution included. Moreover, for the case with the interference considered the angular distribution of the magnetic-quadrupole line is found to be sensitive to the nuclear magnetic dipole moment of the spin-1/2 ions, especially at low impact electron energies. Graphic Abstract

We study the Compton scattering of x-rays off electrons that are driven by a relativistically intense short optical laser pulse. The frequency spectrum of the laser-assisted Compton radiation shows a broad plateau in the vicinity of the laser-free Compton line due to a nonlinear mixing between x-ray and laser photons. Special emphasis is placed on how the shape of the short assisting laser pulse affects the spectrum of the scattered x-rays. In particular, we observe sharp peak structures in the plateau region, whose number and locations are highly sensitive to the laser pulse shape. These structures are interpreted as spectral caustics by using a semiclassical analysis of the laser-assisted QED matrix element, relating the caustic peak locations to the laser-driven electron motion.

A most general density-matrix formalism is presented to investigate linear polarization of characteristic lines following electron-impact excitation of atoms or ions with arbitrary nuclear spin, which can account for depolarization of energy levels and multipole mixing of radiation fields. It is then applied to the linear polarization of the Kα1 line radiated from heliumlike ions with nuclear spin I=1/2. As an example, detailed calculations are performed for 81207Tl79+ ions using the multi-configurational Dirac-Fock method and relativistic distorted-wave theory. It is found that the effect of the hyperfine interaction on the linear polarization depends dominantly on impact electron energy. For low impact energies close to the excitation threshold, the hyperfine interaction results in an enhancement of the linear polarization, especially for those photons emitted perpendicularly to the impact electron beam. In contrast, such a hyperfine-induced effect diminishes quickly with increasing impact energy and vanishes at medium and high energies, which is very different from the results for the case of radiative electron capture (Surzhykov et al 2013 Phys. Rev. A 87 052507). The present study is experimentally accessible at both electron-beam ion traps and ion storage rings and, thus, accurate Kα1 polarization measurements at low energies can be utilized to probe the hyperfine interaction in highly charged few-electron ions.

Atomic cascades refer—first and foremost—to the stepwise de-excitation of excited atoms owing to the emission of electrons or photons. Apart from dedicated experiments at storage rings and synchrotrons, such cascades frequently occur in astro and plasma physics, material research, surface science and at various places elsewhere. In addition, moreover, “atomic cascades” have been found a useful concept for modeling atomic behavior under different conditions, for instance, when dealing with the photoabsorption of matter, the generation of synthesized spectra, or for determining a rather wide class of (plasma) rate coefficients. We here compile and discuss several atomic cascades (schemes) that help predict cross sections, rate coefficients, electron and photon spectra, or ion distributions. We also demonstrate how readily these schemes have been implemented within JAC, the Jena Atomic Calculator. Emphasis is placed on the classification of atomic cascades and their (quite) natural breakdown into cascade computations , to deal with the electronic structure and transition amplitudes of atoms and ions, as well as the cascade simulation of those properties and spectra, that are experimentally accessible. As an example, we show and discuss the computation of dielectronic recombination plasma rate coefficients for beryllium-like gold ions. The concept of atomic cascades and its implementation into JAC can be applied for most ions across the periodic table and will facilitate the modeling and interpretation of many forthcoming observations. Graphical abstract

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K –shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1 s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent K α fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.