# Publications by

Dr. Daniel Seipt

## 2018

**Higher-Dimensional Caustics in Nonlinear Compton Scattering**

**120**, 044802 (2018)

**Abstract:** A description of the spectral and angular distributions of Compton scattered light in collisions of intense laser pulses with high-energy electrons is unwieldy and usually requires numerical simulations. However, due to the large number of parameters affecting the spectra such numerical investigations can become computationally expensive. Using methods of catastrophe theory we predict higher-dimensional caustics in the spectra of the Compton scattered light, which are associated with bright narrow-band spectral lines, and in the simplest case can be controlled by the value of the linear chirp of the pulse. These findings require no full-scale calculations and have direct consequences for the photon yield enhancement of future nonlinear Compton scattering x-ray or gamma-ray sources.

## 2017

**Velocity map imaging of scattering dynamics in orthogonal two-color fields**

**51**, 015001 (2017)

**Abstract:** In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

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

**96**, 023407 (2017)

**Abstract:** In a recent experiment, Schmiegelow et al. [Nat. Commun. 7, 12998 (2016)] investigated the magnetic sublevel population of Ca^+ ions in a Laguerre-Gaussian light beam if the target atoms were just centered along the beam axis. They demonstrated in this experiment that the sublevel population of the excited atoms is uniquely defined by the projection of the orbital angular momentum of the incident light. However, little attention has been paid so far to the question of how the magnetic sublevels are populated when atoms are displaced from the beam axis by some impact parameter b. Here, we analyze this sublevel population for different atomic impact parameters in first-order perturbation theory and by making use of the density-matrix formalism. Detailed calculations are performed especially for the 4s ^2S_1/2 -> 3d ^2D_5/2 transition in Ca^+ ions and for the vector potential of a Laguerre-Gaussian beam in Coulomb gauge. It is shown that the magnetic sublevel population of the excited ^2D_5/2 level varies significantly with the impact parameter and is sensitive to the polarization, the radial index, as well as the orbital angular momentum of the incident light beam.

**Spin-dependent quantum theory of high-order above-threshold ionization**

**95**, 063408 (2017)

**Abstract:** The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as Li^+ and Be^2+ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.

**Depletion of Intense Fields**

**118**, 154803 (2017)

**Abstract:** The interaction of charged particles and photons with intense electromagnetic fields gives rise to multiphoton Compton and Breit-Wheeler processes. These are usually described in the framework of the external field approximation, where the electromagnetic field is assumed to have infinite energy. However, the multiphoton nature of these processes implies the absorption of a significant number of photons, which scales as the external field amplitude cubed. As a result, the interaction of a highly charged electron bunch with an intense laser pulse can lead to significant depletion of the laser pulse energy, thus rendering the external field approximation invalid. We provide relevant estimates for this depletion and find it to become important in the interaction between fields of amplitude a0∼103 and electron bunches with charges of the order of 10 nC.

**Depletion of intense fields**

**1812**, 100006 (2017)

**Abstract:** The problem of backreaction of quantum processes on the properties of the background field still remains on the list of outstanding questions of high intensity particle physics. Usually, photon emission by an electron or positron, photon decay into electron-positron pairs in strong electromagnetic fields, or electron-positron pair production by such fields are described in the framework of the external field approximation. It is assumed that the external field has infinite energy and is not affected by these processes. However, the above-mentioned processes have a multi-photon nature, i.e., they occur with the absorption of a significant number of field photons. As a result, the interaction of an intense electromagnetic field with either a highly charged electron bunch or a fast growing population of electrons, positrons, and gamma photons (as in the case of an electromagnetic cascade) may lead to a depletion of the field energy, thus making the external field approximation invalid. Taking the multi-photon Compton process as an example, we estimate the threshold of depletion and find it to become significant at field strengths (a0∼10^3) and electron bunch charge of about tens of nC.

**Spin-dependent rescattering in strong-field ionization of helium**

**50**, 065001 (2017)

**Abstract:** We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1s2s¹S and ³S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.

## 2016

**Polarization transfer in Rayleigh scattering of hard x-rays**

**18**, 103034 (2016)

**Abstract:** We report on the first elastic hard x-ray scattering experiment where the linear polarization characteristics of both the incident and the scattered radiation were observed. Rayleigh scattering was investigated in a relativistic regime by using a high- Z target material, namely gold, and a photon energy of 175 keV. Although the incident synchrotron radiation was nearly 100% linearly polarized, at a scattering angle of θ=90° we observed a strong depolarization for the scattered photons with a degree of linear polarization of +27% ± 12% only. This finding agrees with second-order quantum electrodynamics calculations of Rayleigh scattering, when taking into account a small polarization impurity of the incident photon beam which was determined to be close to 98%. The latter value was obtained independently from the elastic scattering by analyzing photons that were Compton-scattered in the target. Moreover, our results indicate that when relying on state-of-the-art theory, Rayleigh scattering could provide a very accurate method to diagnose polarization impurities in a broad region of hard x-ray energies.

**Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light**

**94**, 053420 (2016)

**Abstract:** The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4s valence-shell photoionization of Ca+ ions.

**Photoionization of neutral atoms by X waves carrying orbital angular momentum**

**94**, 041402 (2016)

**Abstract:** In contrast to plane waves, twisted or vortex beams have a complex spatial structure. Both their intensity and energy flow vary within the wave front. Beyond that, polychromatic vortex beams, such as X waves, have a spatially dependent energy distribution. We propose a method to measure this (local) energy spectrum. The method is based on the measurement of the energy distribution of photoelectrons from alkali-metal atoms. On the basis of our fully relativistic calculations, we argue that even ensembles of atoms can be used to probe the local energy spectrum of short twisted pulses.

**Elastic scattering of vortex electrons provides direct access to the Coulomb phase**

**94**, 076001 (2016)

**Abstract:** Vortex electron beams are freely propagating electron waves carrying adjustable orbital angular momentum with respect to the propagation direction. Such beams were experimentally realized just a few years ago and are now used to probe various electromagnetic processes. So far, these experiments used the single vortex electron beams, either propagating in external fields or impacting a target. Here, we investigate the elastic scattering of two such aligned vortex electron beams and demonstrate that this process allows one to experimentally measure features which are impossible to detect in the usual plane-wave scattering. The scattering amplitude of this process is well approximated by two plane-wave scattering amplitudes with different momentum transfers, which interfere and give direct experimental access to the Coulomb phase. This phase (shift) affects the scattering of all charged particles and has thus received significant theoretical attention but was never probed experimentally. We show that a properly defined azimuthal asymmetry, which has no counterpart in plane-wave scattering, allows one to directly measure the Coulomb phase as function of the scattering angle.

**Double-slit experiment in momentum space**

**115**, 41001 (2016)

**Abstract:** Young's classic double-slit experiment demonstrates the reality of interference when waves and particles travel simultaneously along two different spatial paths. Here, we propose a double-slit experiment in momentum space, realized in the free-space elastic scattering of vortex electrons. We show that this process proceeds along two paths in momentum space, which are well localized and well separated from each other. For such vortex beams, the (plane-wave) amplitudes along the two paths acquire adjustable phase shifts and produce interference fringes in the final angular distribution. We argue that this experiment can be realized with the present-day technology. We show that it gives experimental access to the Coulomb phase, a quantity which plays an important role in all charged particle scattering but which usual scattering experiments are insensitive to.

**Probing the energy flow in Bessel light beams using atomic photoionization**

**94**, 033420 (2016)

**Abstract:** The growing interest in twisted light beams also requires a better understanding of their complex internal structure. Particular attention is currently being given to the energy circulation in these beams as usually described by the Poynting vector field. In the present study we propose to use the photoionization of alkali-metal atoms as a probe process to measure (and visualize) the energy flow in twisted light fields. Such measurements are possible since the angular distribution of photoelectrons, emitted from a small atomic target, appears sensitive to and is determined by the local direction of the Poynting vector. To illustrate the feasibility of the proposed method, detailed calculations were performed for the ionization of sodium atoms by nondiffractive Bessel beams.

**Temporal laser-pulse-shape effects in nonlinear Thomson scattering**

**93**, 063801 (2016)

**Abstract:** The influence of the laser-pulse temporal shape on the nonlinear Thomson scattering on-axis photon spectrum is analyzed in detail. Using the classical description, analytical expressions for the temporal and spectral structure of the scattered radiation are obtained for the case of symmetric laser-pulse shapes. The possibility of reconstructing the incident laser pulse from the scattered spectrum averaged over interference fringes in the case of high peak intensity and symmetric laser-pulse shape is discussed.

**Pair production by Schwinger and Breit–Wheeler processes in bi-frequent fields**

**82**, 65582030 (2016)

**Abstract:** Counter-propagating and suitably polarized light (laser) beams can provide conditions for pair production. Here, we consider in more detail the following two situations: (i) in the homogeneity regions of anti-nodes of linearly polarized ultra-high intensity laser beams, the Schwinger process is dynamically assisted by a second high-frequency field, e.g. by an XFEL beam; and (ii) a high-energy probe photon beam colliding with a superposition of co-propagating intense laser and XFEL beams gives rise to the laser-assisted Breit–Wheeler process. The prospects of such bi-frequent field constellations with respect to the feasibility of conversion of light into matter are discussed.

**Analytical results for nonlinear Compton scattering in short intense laser pulses**

**82**, 655820203 (2016)

**Abstract:** We study in detail the strong-field QED process of nonlinear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the backscattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly nonlinear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the nonlinear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines.

**Caustic structures in x-ray Compton scattering off electrons driven by a short intense laser pulse**

**18**, 023044 (2016)

**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.

**Determination of the carrier envelope phase for short, circularly polarized laser pulses**

**93**, 045010 (2016)

**Abstract:** We analyze the impact of the carrier envelope phase on the differential cross sections of the Breit- Wheeler and the generalized Compton scattering in the interaction of a charged electron (positron) with an intensive ultrashort electromagnetic (laser) pulse. The differential cross sections as a function of the azimuthal angle of the outgoing electron have a clear bump structure, where the bump position coincides with the value of the carrier phase. This effect can be used for the carrier envelope phase determination.

**Spectral caustics in laser assisted Breit–Wheeler process**

**755**, 162 (2016)

**Abstract:** Electron–positron pair production by the Breit–Wheeler process embedded in a strong laser pulse is analyzed. The transverse momentum spectrum displays prominent peaks which are interpreted as caustics, the positions of which are accessible by the stationary phases. Examples are given for the superposition of an XFEL beam with an optical high-intensity laser beam. Such a configuration is available, e.g., at LCLS at present and at European XFEL in near future. It requires a counter propagating probe photon beam with high energy which can be generated by synchronized inverse Compton backscattering.

**Laser Assisted Breit-Wheeler and Schwinger Processes**

**Abstract:** The assistance of an intense optical laser pulse on electron-positron pair production by the Breit-Wheeler and Schwinger processes in XFEL fields is analyzed. The impact of a laser beam on high-energy photon collisions with XFEL photons consists in a phase space redistribution of the pairs emerging in the Breit-Wheeler sub-process. We provide numerical examples of the differential cross section for parameters related to the European XFEL. Analogously, the Schwinger type pair production in pulsed fields with oscillating components referring to a superposition of optical laser and XFEL frequencies is evaluated. The residual phase space distribution of created pairs is sensitive to the pulse shape and may differ significantly from transiently achieved mode occupations.

## 2015

**Effect of bound-state dressing in laser-assisted radiative recombination**

**92**, 053426 (2015)

**Abstract:** We present a theoretical study on the recombination of a free electron into the ground state of a hydrogenlike ion in the presence of an external laser field. Emphasis is placed on the effects caused by the laser dressing of the residual ionic bound state. To investigate how this dressing affects the total and angle-differential cross section of laser-assisted radiative recombination (LARR) we apply first-order perturbation theory and the separable Coulomb-Volkov continuum ansatz. Using this approach, detailed calculations are performed for low-Z hydrogenlike ions and laser intensities in the range from I_L=10^12 to 10^13W/cm2. It is seen that the total cross section as a function of the laser intensity is remarkably affected by the bound-state dressing. Moreover, the laser dressing becomes manifest as asymmetries in the angular distribution and the (energy) spectrum of the emitted recombination photons.

**Compton scattering of twisted light: Angular distribution and polarization of scattered photons**

**92**, 013401 (2015)

**Abstract:** Compton scattering of twisted photons is investigated within a nonrelativistic framework using first-order perturbation theory. We formulate the problem in the density-matrix theory, which enables one to gain new insights into scattering processes of twisted particles by exploiting the symmetries of the system. In particular, we analyze how the angular distribution and polarization of the scattered photons are affected by the parameters of the initial beam such as the opening angle and the projection of orbital angular momentum. We present analytical and numerical results for the angular distribution and the polarization of Compton scattered photons for initially twisted light and compare them with the standard case of plane-wave light.

**Scattering of twisted relativistic electrons by atoms**

**92**, 012705 (2015)

**Abstract:** The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal polarization of the scattered electrons. In order to evaluate these angular and polarization properties we consider two experimental setups in which the twisted electron beam collides with either a single well-localized atom or macroscopic atomic target. Detailed relativistic calculations have been performed for both setups and for the electrons with kinetic energy from 10 to 1000 keV. The results of these calculations indicate that the emission pattern and polarization of outgoing electrons differ significantly from the scattering of plane-wave electrons and can be very sensitive to the parameters of the incident twisted beam. In particular, it is shown that the angular- and polarization-sensitive Mott measurements may reveal valuable information about both the transverse and longitudinal components of the linear momentum and the projection of the total angular momentum of twisted electron states. Thus, the Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.

**Dynamical Schwinger process in a bifrequent electric field of finite duration: Survey on amplification**

**91**, 105018 (2015)

**Abstract:** The electron-positron pair production due to the dynamical Schwinger process in a slowly oscillating strong electric field is enhanced by the superposition of a rapidly oscillating weaker electric field. A systematic account of the enhancement by the resulting bifrequent field is provided for the residual phase space distribution. The enhancement is explained by a severe reduction of the suppression in both the tunneling and multiphoton regimes.

**Narrowband inverse Compton scattering x-ray sources at high laser intensities**

**91**, 033402 (2015)

**Abstract:** Narrowband x- and γ-ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow one to operate narrowband Compton sources in the high-intensity regime. In this paper we therefore present the theory of nonlinear Compton scattering in a frequency-modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitively this compensation depends on the electron-beam energy spread and emittance, as well as the laser focusing.

**Interaction of twisted light with many-electron atoms and ions**

**91**, 013403 (2015)

**Abstract:** The excitation of many-electron atoms and ions by twisted light has been studied within the framework of the density-matrix theory and Dirac's relativistic equation. Special attention is paid to the magnetic sublevel population of excited atomic states as described by means of the alignment parameters. General expressions for the alignment of the excited states are obtained under the assumption that the photon beam, prepared as a coherent superposition of two twisted Bessel states, irradiates a macroscopic target. We demonstrate that for this case the population of excited atoms can be sensitive to both the transverse momentum and the (projection of the) total angular momentum of the incident radiation. While the expressions are general and can be employed to describe the photoexcitation of any atom, independent on its shell structure and number of electrons, we performed calculations for the 3s→3p transition in sodium. These calculations indicate that the “twistedness” of incoming radiation can lead to a measurable change in the alignment of the excited P3/22 state as well as the angular distribution of the subsequent fluorescence emission.

**Lifting shell structures in the dynamically assisted Schwinger effect in periodic fields**

**740**, 335 (2015)

**Abstract:** Abstract The dynamically assisted pair creation (Schwinger effect) is considered for the superposition of two periodic electric fields acting in a finite time interval. We find a strong enhancement by orders of magnitude caused by a weak field with a frequency being a multitude of the strong-field frequency. The strong low-frequency field leads to shell structures which are lifted by the weaker high-frequency field. The resonance type amplification refers to a new, monotonously increasing mode, often hidden in some strong oscillatory transient background, which disappears during the smoothly switching off the background fields, thus leaving a pronounced residual shell structure in phase space.

## 2014

**Structured x-ray beams from twisted electrons by inverse Compton scattering of laser light**

**90**, 012118 (2014)

**Abstract:** The inverse Compton scattering of laser light on high-energetic twisted electrons is investigated with the aim to construct spatially structured x-ray beams. In particular, we analyze how the properties of the twisted electrons, such as the topological charge and aperture angle of the electron Bessel beam, affect the energy and angular distribution of scattered x rays. We show that with suitably chosen initial twisted electron states one can synthesize tailor-made x-ray beam profiles with a well-defined spatial structure, in a way not possible with ordinary plane-wave electron beams.

**Laser-assisted Compton scattering of x-ray photons**

**89**, 023433 (2014)

**Abstract:** The Compton scattering of x-ray photons, assisted by a short intense optical laser pulse, is discussed. The differential scattering cross section reveals the interesting feature that the main Klein-Nishina line is accompanied by a series of side lines forming a broad plateau where up to O(10^(3)) laser photons participate simultaneously in a single scattering event. An analytic formula for the width of the plateau is given. Due to the nonlinear mixing of x-ray and laser photons a frequency-dependent rotation of the polarization of the final-state x-ray photons relative to the scattering plane emerges. A consistent description of the scattering process with short laser pulses requires to work with x-ray pulses. An experimental investigation can be accomplished, e.g., at LCLS or the European XFEL, in the near future.

## 2013

**High Resolution Energy-Angle Correlation Measurement of Hard X Rays from Laser-Thomson Backscattering**

**111**, 114803 (2013)

**Abstract:** Thomson backscattering of intense laser pulses from relativistic electrons not only allows for the generation of bright x-ray pulses but also for the investigation of the complex particle dynamics at the interaction point. For this purpose a complete spectral characterization of a Thomson source powered by a compact linear electron accelerator is performed with unprecedented angular and energy resolution. A rigorous statistical analysis comparing experimental data to 3D simulations enables, e.g., the extraction of the angular distribution of electrons with 1.5% accuracy and, in total, provides predictive capability for the future high brightness hard x-ray source PHOENIX (photon electron collider for narrow bandwidth intense x rays) and potential gamma-ray sources.

**Asymmetries of azimuthal photon distributions in nonlinear Compton scattering in ultrashort intense laser pulses**

**88**, 012127 (2013)

**Abstract:** Nonlinear Compton scattering in ultrashort intense laser pulses is discussed with the focus on angular distributions of the emitted photon energy. This is an observable which is easily accessible experimentally. Asymmetries of the azimuthal distributions are predicted for both linear and circular polarization. We present a systematic survey of the influence of the laser intensity, the carrier envelope phase, and the laser polarization on the emission spectra for single-cycle and few-cycle laser pulses. For linear polarization, the dominant direction of the emission changes from a perpendicular pattern with respect to the laser polarization at low-intensity to a dominantly parallel emission for high-intensity laser pulses.