# Referierte Publikationen

## 2021

**Angular coefficients for symmetry-adapted configuration states in jj-coupling**

**267**, 108086 (2021)

**Abstract:** In atomic structure and collision theory, the efficient spin-angular integration is known to be crucial and often decides, how accurate the properties and behavior of atoms can be predicted numerically. Various methods have been developed in the past to keep the computation (and implementation) of the spin-angular integration feasible for complex shell structures, including open d- and f-shell elements. To support such computations, we here provide a new implementation of the angular coefficients for jjcoupled and symmetry-adapted configuration states that is entirely built upon the quasi-spin formalism. The moduleSpinAngularis based on Julia, a new programming language for scientific computing, and supports a simple access to all (completely) reduced tensors, coefficients of fractional parentage for subshells with j <= 9/2 as well as the re-coupling coefficients from this formalism. Moreover, this module has been worked out for multiple purposes, including 1) the accurate calculation of atomic properties, 2) further studies on spin-angular integration theory, 3) the development of new or existing computer programs as well as 4) the manipulation of reduced matrix elements from this theory. The present implementation will therefore help advance the algebraic evaluation of many-electron (transition) amplitudes and to apply the theory to newly emerging research areas.

**Derivative corrections to the Heisenberg-Euler effective action**

**09**, 070 (2021)

**Abstract:** We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak-and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields.

**Vacuum birefringence at x-ray free-electron lasers**

**23**, 095001 (2021)

**Abstract:** We study the perspectives of measuring the phenomenon of vacuum birefringence predicted by quantum electrodynamics using an x-ray free-electron laser (XFEL) alone. We devise an experimental scheme allowing two consecutive XFEL pulses to collide under a finite angle, and thus act as both pump and probe field for the effect. The signature of vacuum birefringence is encoded in polarization-flipped signal photons to be detected with high-purity x-ray polarimetry. Our findings for idealized scenarios underline that the discovery potential of solely XFEL-based setups can be comparable to those involving optical high-intensity lasers. For currently achievable scenarios, we identify several key details of the x-ray optical ingredients that exert a strong influence on the magnitude of the desired signatures.

**Scaling potential of beam-splitter-based coherent beam combination**

**29**, 27900 (2021)

**Abstract:** The impact of nonlinear refraction and residual absorption on the achievable peakand average power in beam-splitter-based coherent beam combination is analyzed theoretically. While the peak power remains limited only by the aperture size, a fundamental average power limit is given by the thermo-optical and thermo-mechanical properties of the beam splitter material and its coatings. Based on our analysis, 100 kW average power can be obtained with state-of-the-art optics at maintained high beam quality (M-2 <= 1.1) and at only 2% loss of combining efficiency. This result indicates that the power-scaling potential of today\textquotesingle s beam-splitter-based coherent beam combination is far from being depleted. A potential scaling route to megawatt-level average power is discussed for optimized beam splitter geometry.

**Relativistic modified Bessel-Gaussian beam generated from plasma-based beam braiding**

**104**, 021501 (2021)

**Abstract:** We theoretically and numerically demonstrate the generation of a relativistic modified Bessel-Gaussian beam (MBGB) via plasma-based beam braiding. It is realized by injecting several intense Gaussian pulses with well-designed offsets and angles into an underdense plasma channel which acts as a laser-pulse combiner via refractive coupling. The MBGB propagates stably in the plasma channel with a well-controlled orbital angular momentum of large value, exciting a twisted plasma wave. After leaving the plasma, it becomes unguided and survives in vacuum for at least hundreds of femtoseconds. This method is insensitive to the initial laser injection conditions and thus should be robust for experimental implementation. It provides an alternative approach in generating high-quality tunable intense optical vortex beams which are desired for various applications.

**Proton-neutron pairing correlations in the self-conjugate nucleus Sc-42**

**819**, 136439 (2021)

**Abstract:** Collinear laser spectroscopy of the N = Z = 21 self-conjugate nucleus Sc-42 has been performed at the JYFL IGISOL IV facility in order to determine the change in nuclear mean-square charge radius between the I-pi = 0(+) ground state and the I-pi = 7(+) isomer via the measurement of the Sc-42g,Sc-42m isomer shift. New multi-configurational Dirac-Fock calculations for the atomic mass shift and field shift factors have enabled a recalibration of the charge radii of the Sc42-46 isotopes which were measured previously. While consistent with the treatment of proton-neutron, proton-proton and neutron-neutron pairing on an equal footing, the reduction in size for the isomer is observed to be of a significantly larger magnitude than that expected from both shell-model and ab-initio calculations. The measured nuclear magnetic dipole moment and electric quadruple moment, on the other hand, are in good agreement with simple empirical estimates and shell-model calculations.

**Novel Tunnel Magnetoresistive Sensor Functionalities via Oblique-Incidence Deposition**

**13**, 32343 (2021)

**Abstract:** Controlling the magnetic properties of ultrathin films remains one of the main challenges to the further development of tunnel magnetoresistive (TMR) device applications. The magnetic response in such devices is mainly governed by extending the primary TMR trilayer with the use of suitable contact materials. The transfer of magnetic anisotropy to ferromagnetic electrodes consisting of CoFeB layers results in a field-dependent TMR response, which is determined by the magnetic properties of the CoFeB as well as the contact materials. We flexibly apply oblique-incidence deposition (OID) to introduce arbitrary intrinsic in-plane anisotropy profiles into the magnetic layers. The OID-induced anisotropy shapes the magnetic response and eliminates the requirement of additional magnetic contact materials. Functional control is achieved via an adjustable shape anisotropy that is selectively tailored for the ultrathin CoFeB layers. This approach circumvents previous limitations on TMR devices and allows for the design of new sensing functionalities, which can be precisely customized to a specific application, even in the high field regime. The resulting sensors maintain the typical TMR signal strength as well as a superb thermal stability of the tunnel junction, revealing a striking advantage in functional TMR design using anisotropic interfacial roughness.

**Vacuum Birefringence at the Gamma Factory**

**n/a**, 2100137 (2021)

**Abstract:** Abstract The perspectives of studying vacuum birefringence at the Gamma Factory are explored. To this end, the parameter regime which can be reliably analyzed resorting to the leading contribution to the Heisenberg?Euler effective Lagrangian is assessed in detail. It is explicitly shown that?contrary to naive expectations?this approach allows for the accurate theoretical study of quantum vacuum signatures up to fairly large photon energies. The big advantage of this parameter regime is the possibility of studying the phenomenon in experimentally realistic, manifestly inhomogeneous pump and probe field configurations. Thereafter, two specific scenarios giving rise to a vacuum birefringence effect for traversing gamma probe photons are analyzed. In the first scenario the birefringence phenomenon is induced by a quasi-constant static magnetic field. In the second case it is driven by a counter-propagating high-intensity laser field.

**Towards attosecond imaging at the nanoscale using broadband holography-assisted coherent imaging in the extreme ultraviolet**

**4**, 154 (2021)

**Abstract:** The inherently broad bandwidth of attosecond pulses conflicts with the coherence requirements of lensless imaging. Here, broadband holography-assisted coherent imaging is demonstrated with a resolution of less than 35 nm. Nanoscale coherent imaging has emerged as an indispensable modality, allowing to surpass the resolution limit given by classical imaging optics. At the same time, attosecond science has experienced enormous progress and has revealed the ultrafast dynamics in complex materials. Combining attosecond temporal resolution of pump-probe experiments with nanometer spatial resolution would allow studying ultrafast dynamics on the smallest spatio-temporal scales but has not been demonstrated yet. To date, the large bandwidth of attosecond pulses poses a major challenge to high-resolution coherent imaging. Here, we present broadband holography-enhanced coherent imaging, which enables the combination of high-resolution coherent imaging with a large spectral bandwidth. By implementing our method at a high harmonic source, we demonstrate a spatial resolution of 34 nm in combination with a spectral bandwidth of 5.5 eV at a central photon energy of 92 eV. The method is single-shot capable and retrieves the spectrum from the measured diffraction pattern.

**Above-threshold ionization driven by Gaussian laser beams: beyond the electric dipole approximation**

**54**, 144002 (2021)

**Abstract:** Strong-field atomic experiments have recently become sensitive to nondipole (magnetic) interactions. In particular, photoelectrons emitted in above-threshold ionization possess a nonzero momentum along the beam axis as a result of the Lorentz force. Here, we show how this longitudinal momentum can be theoretically calculated based on a nondipole strong-field approximation that accounts not only for the temporal but also the spatial dependence of the laser field in the photoelectron continuum. If the driving laser beam is approximated as a plane wave, the theoretical values differ from known experimental results by a constant offset. We demonstrate that this offset can successfully be removed if a realistic Gaussian beam profile is accounted for in the quantum description of ATI. We also discuss the influence of the size of the beam waist in the focus.

**Connecting Fano Interference and the Jaynes-Cummings Model in Cavity Magnonics**

**7**, 114 (2021)

**Abstract:** We show that Fano interference can be realized in a macroscopic microwave cavity coupled to a spin ensemble at room temperature. Via a formalism developed from the linearized Jaynes-Cummings model of cavity electromagnonics, we show that generalized Fano interference emerges from the photon–magnon interaction at low cooperativity. In this regime, the reflectivity approximates the scattering cross-section derived from the Fano-Anderson model. Although asymmetric lineshapes in this system are often associated with the Fano formalism, we show that whilst Fano interference is actually present, an exact Fano form cannot be achieved from the linear Jaynes-Cummings model. In the Fano model an additional contribution arises, which is attributed to decoherence in other systems, and in this case is due to the resonant nature of the photonic mode. The formalism is experimentally verified and accounts for the asymmetric lineshapes arising from the interaction between magnon and photon channels. As the magnon–photon coupling strength is increased, these channels merge into hybridized magnon–photon modes and the generalized Fano interference picture breaks down. Our results are universally applicable to systems underlying the linearized Jaynes-Cummings Hamiltonian at low cooperativity and connect the microscopic parameters of the quantum optical model to generalized Fano lineshapes.

**Agile spectral tuning of high order harmonics by interference of two driving pulses**

**29**, 22117 (2021)

**Abstract:** In this work, the experimental realization of a tunable high photon flux extreme ultraviolet light source is presented. This is enabled by high harmonic generation of two temporally delayed driving pulses with a wavelength of 1030 nm, resulting in a tuning range of 0.8 eV at the 19th harmonic at 22.8 eV. The implemented approach allows for fast tuning of the spectrum, is highly flexible and is scalable towards full spectral coverage at higher photon energies.

**Ultraviolet dual comb spectroscopy: a roadmap**

**29**, 21859 (2021)

**Abstract:** Dual Comb Spectroscopy proved its versatile capabilities in molecular fingerprinting in different spectral regions, but not yet in the ultraviolet (UV). Unlocking this spectral window would expand fingerprinting to the electronic energy structure of matter. This will access the prime triggers of photochemical reactions with unprecedented spectral resolution. In this research article, we discuss the milestones marking the way to the first UV dual comb spectrometer. We present experimental and simulated studies towards UV dual comb spectroscopy, directly applied to planned absorption measurements of formaldehyde (centered at 343 nm, 3.6 eV) and argon (80 nm, 16 eV). This will enable an unparalleled relative resolution of up to 10-9 - with a table-top UV source surpassing any synchrotron-linked spectrometer by at least two and any grating-based UV spectrometer by up to six orders of magnitude.

**Electron-loss-to-continuum cusp in collisions of U89+ with N-2 and Xe**

**104**, 012809 (2021)

**Abstract:** We study the electron-loss-to-continuum (ELC) cusp experimentally and theoretically by comparing the ionization of U89+ projectiles in collisions with N-2 and Xe targets, at a beam energy of 75.91 MeV/u. The coincidence measurement between the singly ionized projectile and the energy of the emitted electron is used to compare the shape of the ELC cusp at weak and strong perturbations. A significant energy shift for the centroid of the electron cusp is observed for the heavy target of Xe as compared to the light target of N-2. Our results provide a stringent test for fully relativistic calculations of double-differential cross sections performed in the first-order approximation and in the continuum-distorted-wave approach.

**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.

**Single-cycle versus multicycle nonsequential double ionization of argon**

**104**, 013105 (2021)

**Abstract:** Using an improved quantitative rescattering model, we calculate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization of Ar exposed to intense laser pulses with a wavelength of 790 nm at a peak intensity of 1.0×10¹⁴ W/cm². We analyze the drastic variations in the CMDs that were observed by Kübel et al. [New J. Phys. 16, 033008 (2014)] in the transition from near-single-cycle to multicycle driving laser pulses. Our model reproduces their experimental data well. We also find that the transition from near-single-cycle to multicycle driving laser pulses depends strongly on the details of the pulse envelope. Special attention is paid to the mechanisms responsible for the cross-shaped structure observed experimentally with 4 fs pulses. Our analysis reveals that the cross-shaped structure in the carrier-envelope phase-averaged CMD for near-single-cycle pulses can be attributed to strong backward scattering of the recolliding electron as well as the narrow momentum distributions of the tunnel-ionized electrons compared to those for long pulses. This also explains why the cross-shaped distributions collapse to a rather structureless distribution when the pulse duration is increased to 8 fs.

**Role of free-carrier interaction in strong-field excitations in semiconductors**

**104**, 035203 (2021)

**Abstract:** The interaction of laser pulses with condensed matter forms the basis of light-wave-driven electronics potentially enabling tera- and petahertz switching rate applications. Carrier control using near- and midinfrared pulses is appealing for integration into existing platforms. Toward this end, a fundamental understanding of the complexity of phenomena concerning sub-band-gap driven semiconductors such as high harmonic generation, carrier excitation due to multiphoton absorption, and interband tunneling as well as carrier-carrier interactions due to strong acceleration in infrared transients is important. Here, stimulated emission from polycrystalline ZnO thin films for pump wavelengths between 1.2 mu m (1 eV) and 10 mu m (0.12 eV) is observed. Contrary to the expected higher intensity threshold for longer wavelengths, the lowest threshold pump intensity for stimulated emission is obtained for the longest pump wavelength corroborating the importance of collisional excitation upon intraband electron acceleration.

**Vacuum birefringence and diffraction at an x-ray free-electron laser: From analytical estimates to optimal parameters**

**104**, 013006 (2021)

**Abstract:** We study vacuum birefringence and x-ray photon scattering in the head-on collision of x-ray free electron and high-intensity laser pulses. Resorting to analytical approximations for the numbers of attainable signal photons, we analyze the behavior of the phenomenon under the variation of various experimental key-parameters and provide new analytical scalings. Our optimized approximations allow for quantitatively accurate results on the one-percent level. We in particular demonstrate that an appropriate choice of the x-ray focus and pulse duration can significantly improve the signal for given laser parameters, using the experimental parameters to be available at the Helmholtz International Beamline for Extreme Fields at the European XFEL as example. Our results are essential for the identification of the optimal choice of parameters in a discovery experiment of vacuum birefringence at the high-intensity frontier.

**Laser-Driven Anharmonic Oscillator: Ground-State Dissociation of the Helium Hydride Molecular Ion by Midinfrared Pulses**

**127**, 043202 (2021)

**Abstract:** The vibrational motion of molecules represents a fundamental example of an anharmonic oscillator. Using a prototype molecular system, HeH+, we demonstrate that appropriate laser pulses make it possible to drive the nuclear motion in the anharmonic potential of the electronic ground state, increasing its energy above the potential barrier and facilitating dissociation by purely vibrational excitation. We find excellent agreement between the frequency-dependent response of the helium hydride molecular cation to both classical and quantum mechanical simulations, thus removing any ambiguities through electronic excitation. Our results provide access to the rich dynamics of anharmonic quantum oscillator systems and pave the way to state-selective control schemes in ground-state chemistry by the adequate choice of the laser parameters.

**Application of Gamma Attenuation Technique and Artificial Intelligence to Detect Scale Thickness in Pipelines in Which Two-Phase Flows with Different Flow Regimes and Void Fractions Exist**

**13**, 1198 (2021)

**Abstract:** Scale deposits can reduce equipment efficiency in the oil and petrochemical industry. The gamma attenuation technique can be used as a non-invasive effective tool for detecting scale deposits in petroleum pipelines. The goal of this study is to propose a dual-energy gamma attenuation method with radial basis function neural network (RBFNN) to determine scale thickness in petroleum pipelines in which two-phase flows with different symmetrical flow regimes and void fractions exist. The detection system consists of a dual-energy gamma source, with Ba-133 and Cs-137 radioisotopes and two 2.54-cm x 2.54-cm sodium iodide (NaI) detectors to record photons. The first detector related to transmitted photons, and the second one to scattered photons. The transmission detector recorded two signals, which were the counts under photopeak of Ba-133 and Cs-137 with the energy of 356 keV and 662 keV, respectively. The one signal recorded in the scattering detector, total counts, was applied to RBFNN as the inputs, and scale thickness was assigned as the output.

**Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions**

**9**, 20 (2021)

**Abstract:** In this paper, we present an experimental and theoretical study of excitation processes for the heaviest stable helium-like ion, that is, He-like uranium occurring in relativistic collisions with hydrogen and argon targets. In particular, we concentrate on angular distributions of the characteristic K alpha radiation following the K -> L excitation of He-like uranium. We pay special attention to the magnetic sub-level population of the excited 1s2l(j) states, which is directly related to the angular distribution of the characteristic K alpha radiation. We show that the experimental data can be well described by calculations taking into account the excitation by the target nucleus as well as by the target electrons. Moreover, we demonstrate for the first time an important influence of the electron-impact excitation process on the angular distributions of the K alpha radiation produced by excitation of He-like uranium in collisions with different targets.

**Multipass cell for high-power few-cycle compression**

**46**, 2678 (2021)

**Abstract:** A multipass cell for nonlinear compression to few-cycle pulse duration is introduced composing dielectrically enhanced silver mirrors on silicon substrates. Spectral broadening with 388 W output average power and 776 mu J pulse energy is obtained at 82% cell transmission. A high output beam quality (M-2 < 1.2) and a high spatio-spectral homogeneity (97.5%), as well as the compressibility of the output pulses to 6.9 fs duration, are demonstrated. A finite element analysis reveals scalability of this cell to 2 kW average output power.

**Justifying the thin-crystal approximation in spontaneous parametric down-conversion for collinear phase matching**

**103**, 063508 (2021)

**Abstract:** Spatially engineered photons from spontaneous parametric down-conversion (SPDC) are a valuable tool for studying and applying photonic entanglement. An advantage of SPDC is that simple expressions for the two-photon state can be obtained using justified approximations. In particular, the thin-crystal approximation has often been invoked in the engineering of high-dimensional entangled states. Knowledge of the conditions under which the thin-crystal approximation remains valid is essential for the realization of experimental setups. We provide a quantitative guideline on the validity of the thin-crystal approximation in calculating the two-photon spatial state. In particular, we show that the applicability of this regime is related to the focusing parameter (w) over barp = w(p)/root lambda(p) L, where w(p) and lambda(p) are the beam waist and wavelength of the pump beam, respectively, and L is the length of the nonlinear crystal. Additionally, the validity of the thin-crystal regime is investigated concerning the size of a subspace in the Laguerre Gaussian basis, into which the two-photon state can be projected in a given experiment.

**Unification of topological invariants in Dirac models**

**103**, 245146 (2021)

**Abstract:** Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system. For topological materials described by Dirac models, we introduce a wrapping number as a unified approach to obtain the topological invariants in arbitrary dimensions and symmetry classes. Given a unit vector that parametrizes the momentum dependence of the Dirac model, the wrapping number describes the degree of the map from the Brillouin zone torus to the sphere formed by the unit vector that we call the Dirac sphere. This method is gauge-invariant and originates from the intrinsic features of the Dirac model and moreover places all known topological invariants, such as the Chern number, winding number, Pfaffian, etc, on equal footing.

**Curvature bound from gravitational catalysis in thermal backgrounds**

**103**, 125027 (2021)

**Abstract:** We investigate the phenomenon of gravitational catalysis, i.e., curvature-induced chiral symmetry breaking and fermion mass generation, at finite temperature. Using a scale-dependent analysis, we derive a thermal bound on the curvature of local patches of spacetime. This bound quantifies regions in parameter space that remain unaffected by gravitational catalysis and thus are compatible with the existence of light fermions as observed in nature. While finite temperature generically relaxes the curvature bound, we observe a comparatively strong dependence of the phenomenon on the details of the curvature. Our bound can be applied to scenarios of quantum gravity, as any realistic candidate has to accommodate a sufficient number of light fermions. We argue that our bound therefore represents a test for quantum-gravity scenarios: A suitably averaged spacetime in the (trans-)Planckian regime that satisfies our curvature bound does not induce correspondingly large Planckian fermion masses by gravitational catalysis. The temperature dependence derived in this work facilitates to follow the fate of gravitational catalysis during the thermal history of the (quantum) Universe. In an application to the asymptotic-safety scenario of quantum gravity, our bound translates into a temperature-dependent upper bound on the number of fermion flavors.

**Generation of straight and curved hollow plasma channels by laser-generated nonlinear wakefields and studies of ultra-intense laser pulse guiding**

**28**, 063104 (2021)

**Abstract:** We report on a study of highly controllable, quasi-static hollow plasma channels generated by ion motion following a laser–plasma interaction via numerical simulations. These channels are generated by ion motion in a nonlinear wakefield, which has an asymmetry between focusing and defocusing periods. Such plasma channels, driven by a fs duration, 100 TW level laser pulse, have the capability to guide more powerful laser pulses. Moreover, we show that curved plasma channels can be generated in a transverse density gradient plasma and all-optical guiding of a second, significantly more powerful laser pulse in such a curved plasma channel. This mechanism may be useful for creating plasma optics for multi-stage TeV laser plasma accelerators and compact synchrotron radiation sources.

**The effects of laser polarization and wavelength on injection dynamics of a laser wakefield accelerator**

**28**, 063101 (2021)

**Abstract:** Here, we investigate the effects of laser polarization and wavelength on electron injection dynamics in a laser wakefield accelerator. During the ionization process, electrons gain residual momentum and kinetic energy via above threshold ionization, which has a strong dependence on laser polarization. A circularly polarized laser pulse results in a much higher residual momentum and kinetic energy gain for the ionized electrons compared with the linearly polarized case. This residual momentum results in particle injection because of the sensitivity of particle trapping to the initial conditions and enhanced the total injected beam charge in both experiments and particle-in-cell simulations. Due to the strong correlation of above threshold ionization with laser wavelength, in this work we extended the investigation to long wavelength (up to 20 μm) drive pulses using particle-in-cell simulations. Owing to the gain in kinetic energy, it may be expected that the charge trapped would consistently increase for circular polarization with increasing laser wavelength, but this was not observed. Instead, there are oscillations with wavelength in the relative trapped charge between linear and circular polarization cases, which arise because of ionization and heating effects on the plasma. Our studies highlight the complex interplay between several different physical effects, including injection regimes—above threshold ionization assisted injection, wave-breaking injection by carrier-envelope-phase effects and ionization injection—ionization gradient induced laser pulse evolution, and thermal modifications to the wake structure that need considering when extrapolating laser wakefield acceleration to different wavelength regimes.

**Many-Electron QED with Redefined Vacuum Approach**

**13**, 1014 (2021)

**Abstract:** The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

**Signatures of the Carrier Envelope Phase in Nonlinear Thomson Scattering**

**11**, 528 (2021)

**Abstract:** High-energy radiation can be generated by colliding a relativistic electron bunch with a high-intensity laser pulse-a process known as Thomson scattering. In the nonlinear regime the emitted radiation contains harmonics. For a laser pulse whose length is comparable to its wavelength, the carrier envelope phase changes the behavior of the motion of the electron and therefore the radiation spectrum. Here we show theoretically and numerically the dependency of the spectrum on the intensity of the laser and the carrier envelope phase. Additionally, we also discuss what experimental parameters are required to measure the effects for a beamed pulse.

**Approximate Atomic Green Functions**

**26**, 2660 (2021)

**Abstract:** In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on classes of virtual excitations, or so-called excitation schemes, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of Jac, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.

**Polarized QED cascades**

**23**, 053025 (2021)

**Abstract:** By taking the spin and polarization of the electrons, positrons and photons into account in the strong-field QED processes of nonlinear Compton emission and pair production, we find that the growth rate of QED cascades in ultra-intense laser fields can be substantially reduced. While this means that fewer particles are produced, we also found them to be highly polarized. We further find that the high-energy tail of the particle spectra is polarized opposite to that expected from Sokolov–Ternov theory, which cannot be explained by just taking into account spin-asymmetries in the pair production process, but results significantly from ‘spin-straggling’. We employ a kinetic equation approach for the electron, positron and photon distributions, each of them spin/polarization-resolved, with the QED effects of photon emission and pair production modelled by a spin/polarization dependent Boltzmann-type collision operator. For photon-seeded cascades, depending on the photon polarization, we find an excess or a shortage of particle production in the early stages of cascade development, which provides a path towards a controlled experiment. Throughout this paper we focus on rotating electric field configuration, which represent an idealized model and allows for a straightforward interpretation of the observed effects.

**Transverse mode instability and thermal effects in thulium-doped fiber amplifiers under high thermal loads**

**29**, 14963 (2021)

**Abstract:** We experimentally analyze the average-power-scaling capabilities of ultrafast, thulium-doped fiber amplifiers. It has been theoretically predicted that thulium-doped fiber laser systems, with an emission wavelength around 2 mu m, should be able to withstand much higher heat-loads than their Yb-doped counterparts before the onset of transverse mode instability (TMI) is observed. In this work we experimentally verify this theoretical prediction by operating thulium doped fibers at very high heat-load. In separate experiments we analyze the performance of two different large-core, thulium-doped fiber amplifiers. The first experiment aims at operating a short, very-large core, thulium-doped fiber amplifier at extreme heat-load levels of more than 300 W/m. Even at this extreme heat-load level, the onset of TMI is not observed. The second experiment maximizes the extractable average-output power from a large-core, thulium-doped, fiber amplifier. We have achieved a pump-limited average output power of 1.15 kW without the onset of TMI. However, during a longer period of operation at this power level the amplifier performance steadily degraded and TMI could be observed for average powers in excess of 847 W thereafter. This is the first time, to the best of our knowledge, that TMI has been reported in a thulium-doped fiber amplifier.

**Table-top extreme ultraviolet second harmonic generation**

**7**, 2265 (2021)

**Abstract:** The lack of available table-top extreme ultraviolet (XUV) sources with high enough fluxes and coherence properties has limited the availability of nonlinear XUV and x-ray spectroscopies to free-electron lasers ( FELs). Here, we demonstrate second harmonic generation (SHG) on a table-top XUV source by observing SHG near the TiM2,3 edge with a high-harmonic seeded soft x-ray laser. Furthermore, this experiment represents the first SHG experiment in the XUV. First-principles electronic structure calculations suggest the surface specificity and separate the observed signal into its resonant and nonresonant contributions. The realization of XUV-SHG on a table-top source opens up more accessible opportunities for the study of element-specific dynamics in multicomponent systems where surface, interfacial, and bulk-phase asymmetries play a driving role.

**Coherence tomography with broad bandwidth extreme ultraviolet and soft X-ray radiation**

**127**, 55 (2021)

**Abstract:** We present an overview of recent results on optical coherence tomography with the use of extreme ultraviolet and soft X-ray radiation (XCT). XCT is a cross-sectional imaging method that has emerged as a derivative of optical coherence tomography (OCT). In contrast to OCT, which typically uses near-infrared light, XCT utilizes broad bandwidth extreme ultraviolet (XUV) and soft X-ray (SXR) radiation (Fuchs et al in Sci Rep 6:20658, 2016). As in OCT, XCT\textquotesingle s axial resolution only scales with the coherence length of the light source. Thus, an axial resolution down to the nanometer range can be achieved. This is an improvement of up to three orders of magnitude in comparison to OCT. XCT measures the reflected spectrum in a common-path interferometric setup to retrieve the axial structure of nanometer-sized samples. The technique has been demonstrated with broad bandwidth XUV/SXR radiation from synchrotron facilities and recently with compact laboratory-based laser-driven sources. Axial resolutions down to 2.2 nm have been achieved experimentally. XCT has potential applications in three-dimensional imaging of silicon-based semiconductors, lithography masks, and layered structures like XUV mirrors and solar cells.

**High-Repetition Rate Optical Pump-Nuclear Resonance Probe Experiments Identify Transient Molecular Vibrations after Photoexcitation of a Spin Crossover Material**

**12**, 3240 (2021)

**Abstract:** Phonon modes play a vital role in the cooperative phenomenon of light-induced spin transitions in spin crossover (SCO) molecular complexes. Although the cooperative vibrations, which occur over several hundreds of picoseconds to nanoseconds after photoexcitation, are understood to play a crucial role in this phase transition, they have not been precisely identified. Therefore, we have performed a novel optical laser pump-nuclear resonance probe experiment to identify the Fe-projected vibrational density of states (pDOS) during the first few nanoseconds after laser excitation of the mononuclear Fe(II) SCO complex [Fe(PM-BiA)(2)(NCS)(2)]. Evaluation of the so obtained nanosecond-resolved pDOS yields an excitation of similar to 8% of the total volume of the complex from the low-spin to high-spin state. Density functional theory calculations allow simulation of the observed changes in the pDOS and thus identification of the transient inter- and intramolecular vibrational modes at nanosecond time scales.

**Redefined vacuum approach and gauge-invariant subsets in two-photon-exchange diagrams for a closed-shell system with a valence electron**

**103**, 042818 (2021)

**Abstract:** CThe two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In contrast to other methods, the redefined vacuum approach enables the identification of eight gauge-invariant subsets and, thus, efficiently checks the consistency of the obtained results. The gauge invariance of found subsets is demonstrated both analytically (for an arbitrary state) as well as numerically for 2s, 2p(1/2), and 2p(3/2) valence electrons in Li-like ions. Identifying gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, e.g., three-photon exchange, where the fragmentation on simpler subsets is crucial for its successful calculation.

**Quantum vacuum signatures in multicolor laser pulse collisions**

**103**, 076009 (2021)

**Abstract:** Quantum vacuum fluctuations give rise to effective nonlinear interactions between electromagnetic fields. A prominent signature of quantum vacuum nonlinearities driven by macroscopic fields are signal photons differing in characteristic properties such as frequency, propagation direction and polarization from the driving fields. We devise a strategy for the efficient tracing of the various vacuum-fluctuation-mediated interaction processes in order to identify the most prospective signal photon channels. As an example, we study the collision of up to four optical laser pulses and pay attention to sum and difference frequency generation. We demonstrate how this information can be used to enhance the signal photon yield in laser pulse collisions for a given total laser energy.

**Laser spectroscopy of the 2S1/2-2P1/2, 2P3/2 transitions in stored and cooled relativistic C³⁺ ions**

**11**, 9370 (2021)

**Abstract:** The 2S1/2−2P1/2 and 2S1/2−2P3/2 transitions in Li-like carbon ions stored and cooled at a velocity of beta=0.47 in the experimental storage ring (ESR) at the GSI Helmholtz Centre in Darmstadt have been investigated in a laser spectroscopy experiment. Resonance wavelengths were obtained using a new continuous-wave UV laser system and a novel extreme UV (XUV) detection system to detect forward emitted fluorescence photons. The results obtained for the two transitions are compared to existing experimental and theoretical data. A discrepancy found in an earlier laser spectroscopy measurement at the ESR with results from plasma spectroscopy and interferometry has been resolved and agreement between experiment and theory is confirmed.

**Improving the Contrast of Pseudothermal Ghost Images Based on the Measured Signal Distribution of Speckle Fields**

**2021**, 2621 (2021)

**Abstract:** In this study, we examine the quality of microscale ghost images as a function of the measured histographic signal distribution of the speckle fields from a nonuniform pseudothermal light source. This research shows that the distribution of the detected signal level on each pixel of the camera plays a significant role in improving the contrast-to-noise ratio (CNR) of pseudothermal ghost imaging. To our knowledge, the scaling of CNR with different pixel intensity distributions of the speckle fields is observed for the first time in the field of pseudothermal microscale ghost imaging. The experimental observations are in very good agreement with numerical analysis. Based on these findings, we can predict the settings for light sources that will maximize the CNR of microscale ghost images.

**Frustrated double ionization of atoms in circularly polarized laser fields**

**23**, 033041 (2021)

**Abstract:** We theoretically study frustrated double ionization (FDI) of atoms subjected to intense circularly polarized laser pulses using a three-dimensional classical model. We find a \textasciigrave knee\textquotesingle structure of FDI probability as a function of intensity, which is similar to the intensity dependence of nonsequential double ionization probability. The observation of FDI is more favourable when using targets with low ionization potentials and short driving laser wavelengths. This is attributed to the crucial role of recollision therein, which can be experimentally inferred from the photoelectron momentum distribution generated by FDI. This work provides novel physical insights into FDI dynamics with circular polarization.

**Investigation of spatiotemporal output beam profile instabilities from differentially pumped capillaries**

**29**, 6957 (2021)

**Abstract:** Differentially pumped capillaries, i.e., capillaries operated in a pressure gradient environment, are widely used for nonlinear pulse compression. In this work, we show that strong pressure gradients and high gas throughputs can cause spatiotemporal instabilities of the output beam profile. The instabilities occur with a sudden onset as the flow evolves from laminar to turbulent. Based on the experimental and numerical results, we derive guidelines to predict the onset of those instabilities and discuss possible applications in the context of nonlinear flow dynamics. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

**Long-range quasi-non-diffracting Gauss-Bessel beams in a few-cycle laser field**

**29**, 10997 (2021)

**Abstract:** Many applications ranging from nonlinear optics to material processing would benefit from pulsed ultrashort (quasi-)non-diffracting Gauss-Bessel beams (GBBs). Here we demonstrate a straightforward yet efficient method for generating such zeroth- and first-order GBBs using a single reflective spatial light modulator. Even in the sub-8-fs range there are no noticeable consequences for the measured pulse duration. The only effect is a weak coloring of the outer-lying satellite rings of the beams due to the spectrum spanning over more than 300 nm. The obtained beams have diffraction half-angles below 40 mu rad and reach propagation distances in excess of 1.5 m.

**Real-time phase-retrieval and wavefront sensing enabled by an artificial neural network**

**29**, 1 (2021)

**Abstract:** In this manuscript we demonstrate a method to reconstruct the wavefront of focused beams from a measured diffraction pattern behind a diffracting mask in real-time. The phase problem is solved by means of a neural network, which is trained with simulated data and verified with experimental data. The neural network allows live reconstructions within a few milliseconds, which previously with iterative phase retrieval took several seconds, thus allowing the adjustment of complex systems and correction by adaptive optics in real time. The neural network additionally outperforms iterative phase retrieval with high noise diffraction patterns.

**1 kW, 10 mJ, 120 fs coherently combined fiber CPA laser system**

**46**, 5529 (2021)

**Abstract:** An ultrafast fiber chirped-pulse amplification laser system based on a coherent combination of 16 ytterbium-doped rod-type amplifiers is presented. It generates 10 mJ pulse energy at 1 kW average power and 120 fs pulse duration. A partially helium-protected, two-staged chirped-pulse amplification grating compressor is implemented to maintain the close to diffraction-limited beam quality by avoiding nonlinear absorption in air. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

**High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau**

**126**, 113201 (2021)

**Abstract:** Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1 μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

**Atomic Cascade Computations**

**13**, 520 (2021)

**Abstract:** Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these cascades often failed because of their inherent complexity. Apart from utilizing the rotational symmetry of atoms and a proper distinction of different physical schemes, a hierarchy of useful approaches is therefore needed in order to keep cascade computations feasible. We here suggest a classification of atomic cascades and demonstrate how they can be modeled within the framework of the Jena Atomic Calculator. As an example, we shall compute within a configuration-average approach the stepwise decay cascade of atomic magnesium, following a 1s inner-shell ionization, and simulate the corresponding (final) ion distribution. Our classification of physical scenarios (schemes) and the hierarchy of computational approaches are both flexible to further refinements as well as to complex shell structures of the atoms and ions, for which the excitation and decay dynamics need to be modeled in good detail.

**Bulk, cascaded pulse compression scheme and it s application to spin emitter characterization**

**60**, 912 (2021)

**Abstract:** The 35-fs-long pulses of a commercial Ti:sapphire amplifier are compressed to similar to 20 fs via self-phase modulation in bulk glass substrates. The cascading of both nonlinear broadening and dispersion compensation stages makes use of the increasing peak power in the successive nonlinear stages. As an application example, the compressed pulses are used for electro-optical sampling of terahertz waves created by optically pumped thin-film spin emitters. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

**Application Driven Optimization of Cryogenic Current Comparators (CCC) for Beam Storage Rings**

**31**, 1600504 (2021)

**Abstract:** Non-destructive measurements of nA beam currents in particle beam storage rings by detecting the azimuthal magnetic field generated by moving charged particles with a Cryogenic Current Comparator (CCC) are well established. The detection of beam currents with small amplitudes with a CCC in a storage ring demands a high slew rate which is caused by the rapid change of the beam current exceeding the operational limit of the SQUID in flux-locked loop mode. Previous solutions to increase the slew rate used a LCR first-order low-pass filter were a small resistor, unfortunately, dominated the current noise of the CCC. In this work we present a novel take by adding a second resonator into the CCC which in turn allows for higher resistances of the LCR low-pass filter and therefore lower thermal current noise. A second challenge connected with this CCC approach is the residual magnetization of the highly permeable magnetic core and the resulting shielding currents in the superconducting circuits of the CCC. The timing of a storage ring in the range of minutes opens a way to reduce these DC currents using a LR high-pass filter. Using serial sub-micro ohm resistors, time constants in the hour range can be achieved to improve the stability and performance of the CCC system.

**Bright, high-repetition-rate water window soft X-ray source enabled by nonlinear pulse self-compression in an antiresonant hollow-core fibre**

**10**, 2021 (2021)

**Abstract:** Bright, coherent soft X-ray radiation is essential to a variety of applications in fundamental research and life sciences. To date, a high photon flux in this spectral region can only be delivered by synchrotrons, free-electron lasers or high-order harmonic generation sources, which are driven by kHz-class repetition rate lasers with very high peak powers. Here, we establish a novel route toward powerful and easy-to-use SXR sources by presenting a compact experiment in which nonlinear pulse self-compression to the few-cycle regime is combined with phase-matched high-order harmonic generation in a single, helium-filled antiresonant hollow-core fibre. This enables the first 100 kHz-class repetition rate, table-top soft X-ray source that delivers an application-relevant flux of 2.8 x 10(6) photon s(-1) eV(-1) around 300 eV. The fibre integration of temporal pulse self-compression (leading to the formation of the necessary strong-field waveforms) and pressure-controlled phase matching will allow compact, high-repetition-rate laser technology, including commercially available systems, to drive simple and cost-effective, coherent high-flux soft X-ray sources.

**Coherent X-ray-optical control of nuclear excitons**

**590**, 401 (2021)

**Abstract:** Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications1. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics2. Recently, coherent control in the extreme-ultraviolet range was demonstrated3, with a few-attosecond temporal resolution of the phase control. At hard-X-ray energies (above 5--10 kiloelectronvolts), Mössbauer nuclei feature narrow nuclear resonances due to their recoilless absorption and emission of light, and spectroscopy of these resonances is widely used to study the magnetic, structural and dynamical properties of matter4,5. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques6--16. However, coherent control of atomic nuclei using suitably shaped near-resonant X-ray fields remains an open challenge. Here we demonstrate such control, and use the tunable phase between two X-ray pulses to switch the nuclear exciton dynamics between coherent enhanced excitation and coherent enhanced emission. We present a method of shaping single pulses delivered by state-of-the-art X-ray facilities into tunable double pulses, and demonstrate a temporal stability of the phase control on the few-zeptosecond timescale. Our results unlock coherent optical control for nuclei, and pave the way for nuclear Ramsey spectroscopy17 and spin-echo-like techniques, which should not only advance nuclear quantum optics18, but also help to realize X-ray clocks and frequency standards19. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science20.