# Publications by

Jiri Hofbrucker

## 2022

**High-intensity laser experiments with highly charged ions in a Penning trap**

**97**, 084002 (2022)

**Abstract:** We have conceived and built the HILITE (High-Intensity Laser-Ion Trap Experiment) Penning-trap setup for the production, confinement and preparation of pure ensembles of highly charged ions in a defined quantum state as a target for various high-intensity lasers. This enables a broad suite of laser-ion interaction studies at high photon energies and/or intensities, such as non-linear photo-ionisation studies. The setup has now been used to perform experiments at one such laser facility, namely the FLASH Free-Electron Laser at DESY in Hamburg, Germany. We describe the experimental possibilities of the apparatus, the results of the first measurements and future experiments at other laser facilities.

**Photoexcitation of atoms by cylindrically polarized Laguerre-Gaussian beams**

**105**, 033103 (2022)

**Abstract:** We analyze the photoexcitation of atoms with a single valence electron by cylindrically polarized Laguerre-Gaussian beams. Theoretical analysis is performed within the framework of first-order perturbation theory and by expanding the vector potential of the Laguerre-Gaussian beam in terms of its multipole components. For cylindrically polarized Laguerre-Gaussian beams, we show that the (magnetic) sub-components of electric-quadrupole field vary significantly in the beam cross section with beam waist and radial distance from the beam axis. We discuss the influence of varying magnetic multipole components in the beam cross section on the sublevel population of a localized atomic target. In addition, we calculate the total excitation rate of electric-quadrupole transition (4s S-2(1/2) -> 3d D-2(5/2)) in a mesoscopic target of a Ca+ ion. These calculations shows that the total rate of excitation is sensitive to the beam waist and the distance between the center of the target and the beam axis. However, the excitation by a cylindrically polarized Laguerre-Gaussian beam is found more efficient in driving electric-quadrupole transition in the mesoscopic atomic target than the circularly polarized beams.

**Relativistic calculations of two-color two-photon K-shell ionization**

**76**, 18 (2022)

**Abstract:** We investigate the two-color two-photon K-shell ionization of neutral atoms based on the relativistic second-order perturbation theory and independent particle approximation. Analytical expressions for the relativistic and nonrelativistic total cross sections are derived in terms of radial transition amplitudes and Stokes parameters. Particular attention is paid especially to how the two-photon ionization total cross section depends on the energy sharing and polarization of the two incident photons. We construct the nonrelativistic expressions of cross section ratios for different polarization combinations of the two incident photons. The numerical results of total cross section and cross section ratios show that the energy sharing of the two incident photons plays an essential role in two-photon K-shell ionization. Particularly, if the energies of the two incident photons are identical, the total cross section and cross section ratios will reach the minimum or maximum value. Moreover, due to the strong screening effects, we find strong deviations of the cross section ratios near the two-photon ionization threshold of the Ne atom.

## 2021

**Steering of circular dichroism in biharmonic ionization of atoms**

**104**, L031103 (2021)

**Elliptical dichroism in biharmonic ionization of atoms**

**104**, 013102 (2021)

**Abstract:** In multiphoton ionization of atoms, elliptical dichroism may arise in the photoelectron angular distributions due to the interference of the possible ionization pathways. We here consider the interaction of atoms with an elliptically polarized biharmonic $(\omega + 2\omega)$ field which simultaneously allows one- and two-photon ionization of the atoms. The interference between these two ionization pathways introduces contributions to the elliptical dichroism in addition to the dichroism that arises from the two-photon ionization alone. We show that these additional dichroism contributions can lead to a stronger dichroism in comparison to the one arising from two-photon ionization only. We present a relativistic analysis of the corresponding photoelectron angular distributions and discuss individual contributions to the dichroic phenomena. Detailed computations have been performed for biharmonic ionization of neutral helium atoms.

## 2020

**Nonlinear Cooper minimum as a precise tool for understanding multiphoton photoionization**

**1412**, 152017 (2020)

**Abstract:** A new approach to accurately assess multiphoton ionization is suggested. Vanishing of the dominant ionization channel in nonresonant (direct) multiphoton ionization is predicted for a specific incident photon energy. The exact energy position of such nonlinear Cooper minimum can be accurately measured and requires calculations of the complete electronic spectrum. Measurements of various observables at these photon energies are desirable for further evaluation of theoretical calculations at hitherto unreachable accuracy.

**Enhanced polarization transfer to the characteristic L alpha x-ray lines near the nonlinear Cooper minimum of two-photon ionization**

**102**, 042807 (2020)

**Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima**

**8**, 54 (2020)

**Abstract:** Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level resonances are expected, we demonstrate that equally strong variations occur near the nonlinear Cooper minimum. The described phenomena is demonstrated on the example of two-photon ionization of magnesium atom.

**Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation**

**10**, 3617 (2020)

**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 1s 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 Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

**Two-photon ionization of many-electron atoms**

Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät (2020)

**Abstract:** Until recently, the nonlinear interaction between light and matter has been restricted to only low photon energies produced by optical lasers. However, about a decade ago, the rise of free-electron laser facilities revolutionized the field of nonlinear light-matter interaction by delivering intense high-energy light pulses. Today, such lasers are used for research in materials science, chemical technology, biophysical science, solid-state physics as well as fundamental research. It is the new experimental possibilities provided by free-electron lasers that motivated the work presented in this thesis. Two-photon ionization process is one of the simplest nonlinear interactions in which absorption of two photons by an atom (or a molecule) leads to promoting one of its bound electrons to continuum. This work presents studies of two-photon ionization of neutral atoms. After a brief historical introduction to the topic of nonlinear light-matter interaction, the density matrix describing the state of an atom and a photoelectron following two-photon ionization is derived. The density matrix contains the complete information about the overall system consisting of a photoion and a photoelectron. In each successive chapter, part of this density matrix is used to obtain characteristic quantities such as total two-photon ionization cross section, photoelectron angular distributions, ion polarization or even degree of polarization of fluorescence photon produced by subsequent decay of the photoion. Physical properties of these quantities are studied and intriguing phenomena, such as elliptical dichroism, polarization transfer as well as relativistic and screening effects are investigated. In one-photon ionization, the photon energy for which the dominant ionization channel vanishes is called the Cooper minimum. This concept is extended to nonlinear ionization of atoms and the effect of the minimum on all above mentioned quantities is studied. In this work it is shown, that the nonlinear Cooper minimum leads to strong variation in practically all observables of the two-photon ionization process. For example, the polarization transfer from the incident to fluorescence photon can be maximized and so can be the elliptical dichroism in photoelectron angular distributions. Furthermore, it is theorized, that detection of the energy position of the nonlinear Cooper minimum could lead to comparison of experimental measurements and theoretical calculations at hitherto unreachable accuracy.

## 2019

**Fluorescence polarization as a precise tool for understanding nonsequential many-photon ionization**

**100**, 011401 (2019)

**Abstract:** Nonsequential two-photon ionization of inner-shell np subshell of neutral atoms by circularly polarized light is investigated. Detection of subsequent fluorescence as a signature of the process is proposed and the dependence of fluorescence degree of polarization on incident photon beam energy is studied. It is generally expected that the degree of polarization remains approximately constant, except when the beam energy is tuned to an intermediate n′ resonance. However, strong unexpected change in the polarization degree is discovered for nonsequential two-photon ionization at specific incident beam energy due to a zero contribution of the otherwise dominant ionization channel. Polarization degree of the fluorescence depends less on the beam parameters, and its measurements at this specific beam energy, whose position is very sensitive to the details of the employed theory, are highly desirable for evaluation of theoretical calculations of nonlinear ionization at hitherto unreachable accuracy.

## 2018

**Maximum Elliptical Dichroism in Atomic Two-Photon Ionization**

**121**, 053401 (2018)

**Abstract:** Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |ΔED|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.

## 2017

**Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms**

**408**, 125 (2017)

**Abstract:** Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically within the framework of second-order perturbation theory. The non-relativistic results are compared with the relativistic calculations in the dipole and no-pair approximations as well as with the complete relativistic approach. The calculations are performed in both velocity and length gauges. Our results show a significant decrease of the total cross section for heavy atoms as compared to the non-relativistic treatment, which is mainly due to the relativistic wavefunction contraction. The effects of higher multipoles and negative continuum energy states counteract the relativistic contraction contribution, but are generally much weaker. While the effects beyond the dipole approximation are equally important in both gauges, the inclusion of negative continuum energy states visibly contributes to the total cross section only in the velocity gauge.

**Photoelectron distribution of nonresonant two-photon ionization of neutral atoms**

**96**, 013409 (2017)

**Abstract:** Photoelectron angular distributions following the nonresonant two-photon K-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening effects of the inactive electrons can significantly affect the photoelectron distributions and can also lead to a strong elliptical dichroism. Numerical results are presented for the case of two-photon K-shell ionization of neutral Ne, Ge, Xe, and U atoms.

## 2016

**Relativistic calculations of the nonresonant two-photon ionization of neutral atoms**

**94**, 063412 (2016)

**Abstract:** The nonresonant, two-photon, one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section; for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold; for the case of Ne, for example, the cross section drops there by a factor of three.