Abschlussarbeiten

Spectroscopy of highly charged ions and nuclei is a field with great potential to open new frontiers for precision metrology, act as a scientific test bed for quantum electrodynamics, and contribute to the advancement of technology in applied physics. However, precision spectroscopy of these species typically requires laser sources with high photon energies and narrow line widths in the vacuum ultraviolet (VUV) part of the electromagnetic spectrum. The aim of this dissertation is to develop key methods which will enable to create a VUV laser source tailored to the demands set by this spectroscopy application. Laser pulses with a duration of few optical cycles have a key potential for VUV generation, and therefore for spectroscopy of highly charged ions or nuclei. Furthermore, high average power lasers play a key role in addressing narrow transitions. However, laser sources supporting high average power such as Ytterbium-based laser systems, have a pulse duration of a few hundred femtoseconds. It is therefore essential to compress the pulses to a short duration. In this dissertation, we address temporal pulse compression of such high average power laser sources to few cycles. A well-known demanding objective for VUV spectroscopy is the low energy transition of the Thorium 229 (229Th) nucleus. When this dissertation work started, the energy of this transition was known within a range of 149.7 +/- 3.1 nm. However, a laser with a narrow linewidth, high-power and wavelength tunability covering this range is not yet available. This dissertation addresses the development of a high-power frequency comb laser to support tunable VUV generation to drive the low energy nuclear transition of 229Th. Finally, we discuss a preliminary experiment to investigate the low energy VUV nuclear transition of highly charged 229Th89+ ions. This experiment has the potential to locate the low energy nuclear transition of 229Th at a precision two orders of magnitude higher than the currently known uncertainty range.

Engineered photons from spontaneous parametric down-conversion (SPDC) are a valuable tool for studying and applying photonic entanglement, as well as serving as an effective source of single photons. In SPDC, a nonlinear crystal converts a high-energy photon from a laser field into a photon pair, commonly known as signal and idler. Both the theoretical and experimental research conducted by SPDC has primarily focused on the paraxial regime, where the transverse momentum of photons is referred to as the spatial degree of freedom (DOF), and frequency is considered as the spectral DOF. Hence, this dissertation also considers the paraxial regime. Photon pairs generated through SPDC inherently exhibit spatio-spectral coupling, which implies that photons with different spatial DOFs possess varying spectra. While quantum optics applications often focus on either spatial or spectral DOFs independently, the correlation between them poses a fundamental challenge in protocols involving entangled photon sources or single-mode photon states. Theoretical studies on SPDC, that address both space and spectrum together, are mostly limited to approximate wave functions of photon pairs or involve numerical computations. Such theoretical studies usually consider either monochromatic signal and idler photons (the narrowband approximation), loosely focused pump and collection beams (the plane wave approximation), or infinitesimally thin crystals (the thin crystal approximation). This dissertation aims to bridge the gap between the fundamental theory of SPDC and its practical applications. In particular, we have developed a comprehensive theory that does not rely on a specific pump beam or nonlinear crystal and goes beyond the common narrowband, plane wave, and thin crystal approximations. The developed approach accurately describes the inseparability of spatial and spectral DOF and applies to a wide range of experimental setups. Furthermore, we show that the origin of the spatio-spectral coupling is closely related to the Gouy phase of the interacting beams. We utilize the developed theory, taking into account the spatio-spectral coupling insights, to control the entanglement of photon pairs from SPDC. As an application, we shape the spatial distribution of the pump beam to design an efficient source of high-dimensional entangled states in the spatial DOF. In our second application, we tailor simultaneously the effective nonlinearity of the crystal and spatial distribution of the pump, to engineer single-mode photons.

The dynamics of quantum information lies at the heart of future technologies that aim to utilize the laws of quantum mechanics for practical purposes. Beyond that, it provides a unifying language that shines new light on longstanding problems home to historically separate fields of theoretical physics. Considering how quantum information propagates and spreads over the degrees of freedom of a quantum many-body system far from equilibrium has proven particularly helpful for various subjects, ranging from the emergence of statistical mechanics in isolated quantum systems to the black hole information paradox. Crucial for these developments are impressive experimental advances that nowadays allow us to explore the nonequilibrium physics of paradigmatic, simple, and (almost) isolated quantum many-body systems in the laboratory. In this thesis, we investigate the dynamics of quantum information in one-dimensional systems of interacting qubits, i.e., spin-chains, where we particularly consider systems that embody nonlocal interactions. The latter are ubiquitous in many experimental platforms for quantum simulation. Our results reveal an interesting connection between two complementary probes of quantum information dynamics, i.e., entanglement growth and operator spreading. This connection allows us to characterize different dynamical classes and underlines that nonlocal interactions induce rich behavior, such as slow thermalization accompanied by superballistic information propagation. In particular, we show that the famous slowdown of entanglement growth in systems with powerlaw interactions implies a slowdown of operator dynamics. The latter clearly distinguishes a system with powerlaw interactions from a system possessing fast scrambling, a characteristic property of black holes and holographic duals to theories of quantum gravity.

One of the many astonishing predictions of quantum field theory is the nonlinear nature of the quantum vacuum. In the context of quantum electrodynamics this enables classically forbidden, nonlinear interactions between electromagnetic fields in the vacuum. One much pursued idea to test this prediction is to excite the quantum vacuum with high-intensity laser pulses to emit signal photons that can be distinguished from the driving laser photons, for example, by their polarization or photon energy. A major experimental challenge is the small number of signal photons compared to the background photons. With the aim of identifying a potential discovery experiment of quantum vacuum nonlinearity, we provide theoretically firm predictions for two different quantum vacuum signatures with an emphasize on experimentally feasible setups. This covers on the one side the much studied effect of vacuum birefringence, for which we analyze an innovative setup using a single X-ray free-electron laser. Special attention is paid to the influence of the optical components in the setup on the laser pulse properties. On the other side, we perform an in-depth study of a signature of quantum vacuum nonlinearity that has received less attention so far, namely laser photon merging. The signal photons here have the outstanding property that they differ in photon energy from the background photons and can thus be isolated efficiently. We show that, using state-of-the-art technology, the merging signal can compete with the vacuum birefringence signal in terms of its suitability for a potential discovery experiment of quantum vacuum nonlinearity.

In this dissertation, the experiments are conducted at the Jenaer Titanium: Sapphire 200 Terawatt Laser System (JETi200) located in Jena, Germany. With its excellent temporal contrast, the few-nanometer freestanding target can remain in a solid state for a few picoseconds before the main pulse arrives, greatly reducing the pre-expansion of the target. The resulting proton beams exhibit distinctive features in terms of cut-off energy and energy spectrum distribution. The proton beams in the presented experiment show a more than 30 MeV monoenergetic peak under the circularly polarized laser, and the highest peak particle kinetic energy per Joule of laser energy is around 20MeV/J. As opposed to the circularly polarized driving light, the cut-off energy shows weak dependence on the target thickness when irradiated with linearly polarized light. Moreover, the implementation of a transmission light diagnostic in the experiment indicates that the transmission light of the main pulse is significantly weaker than that in other similar experiments. The energy and energy spectrum of the protons provide the potential to conduct in vivo research and proton skin therapy using the Terawatt-level laser system. Laser contrast significantly impacts laser-driven ion acceleration, as low contrast can lead to premature expansion of thin targets. The evolution of premature expansion, caused by pre-pulses, is primarily based on numerical calculations research. However, in this paper, I conduct a comprehensive experimental study of pre-pulse-induced pre-plasma evolution, including the measurement of pre-plasma evolution time and comparison with a previous numerical model. This investigation is especially beneficial for the latest generation of laser ion accelerators, as it enables the precise quantification of temporal contrast requirements in the Petawatt laser driver era.

Starke Laserfelder sind für die Erforschung der Laser-Atom-Dynamik in der modernen Physik unerlässlich. Die Erzeugung von Harmonischen höherer Ordnung (HHG) ist ein bedeutender Starkfeldprozess, bei welchem ein ionisiertes Elektron durch das elektrische Feld des einfallenden Lasers beschleunigt wird und anschließend mit seinem Mutterion rekombiniert. Das beschleunigte Elektron emittiert bei der Rekombination schlussendlich ein Photon, welches auf makroskopischer Ebene höherer harmonische Strahlung entspricht. Jüngste Fortschritte in der Lasertechnologie ermöglichen die Erzeugung intensiver Laserfelder im mittleren Infrarotbereich. Diese neuen Laserquellen erweitern den Parameterbereich der HHG erheblich bezüglich des schwach relativistischen Bereichs, in welchem das Magnetfeld des einfallenden Laserfeldes zu diesem Prozess beiträgt. In dieser Dissertation wird ein theoretisches Modell der HHG vorgestellt, welches eine formale Erweiterung der bekannten Starkfeld-Näherung auf den schwach relativistischen Bereich darstellt. Generell kann das Modell im Gegensatz zu aktuellen Ansätzen beliebig räumlich strukturierte Lichtfelder berücksichtigen und bietet somit die Möglichkeit, verdrillte Lichtstrahlen im schwach relativistischen Regime zu untersuchen. Das hier entwickelte Modell betrachtet explizit einen elliptisch polarisierten ebenen Laserstrahl als Beispiel. Darüber hinaus werden auch komplexere Laserfelder betrachtet und anschließend kurz diskutiert. Darüber hinaus wird in dieser Dissertation die Phasenanpassung im Kontext der HHG untersucht, die mit einer geringen Konversionseffizienz von weniger als 0, 1 % behaftet ist. Die Suche nach geeigneten externen Parametern, unter denen die Konversionseffizienz entsprechend hoch ist, ist daher von großem In- teresse für die Starkfeldgemeinde. Es wird ein analytischer Ausdruck für die kritische Intensität abgeleitet, der die Bedingung der Phasenanpassung für einen beliebigen Satz von Anfangsparametern erfüllt. Der Ansatz ist auf wasserstoffähnliche Edelgase und linear polarisierte Gauß-Laserpulse mit beliebigen Laserfeldparametern beschränkt, die die üblicherweise verwendeten Konfigurationen umfassen. Der analytische Fehler im Vergleich zu numerischen Berechnungen ist kleiner als 1 %, während die Berechnungszeit um vier bis sechs Größenordnungen verbessert wird.

Every interesting quantity to be investigated in the realm of bound-state quantum electrodynamics (BSQED), such as, for example, the Lamb shift, the (hyper)fine-splitting or the g-factor, is closely or remotely connected to the energy levels of the considered system. Therefore, as a prerequisite, it is mandatory to have the ability to accurately assess energy levels of increasingly sophisticated electronic configurations of atoms or ions. BSQED predictive powers are nowadays limited to either simple light systems, where an αZ expansion is justified, or heavy few-electron highly-charged ions, where specialized all-order methods in αZ are required, to reliably capture interelectronic interactions. The redefined vacuum state approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool allowing analytical insights. This thesis elaborates on this approach within BSQED perturbation theory, based on the two-time Green’s function method. In addition to a rather formal formulation, the particular example of a single-particle (electron or hole) excitation with respect to the redefined vacuum state is considered. Starting with simple one-particle Feynman diagrams, characterized by radiative corrections to identical single incoming and single outgoing state, first- and second-order many-electron contributions are derived, namely screened self-energy, screened vacuum-polarization, one-photon-exchange, and two-photon-exchange. The redefined vacuum state approach provides a straightforward and streamlined derivation facilitating its application to any electronic configuration. Moreover, based on the gauge invariance of the one-particle diagrams, various gauge-invariant subsets within analysed many-electron QED contributions are identified. The identification of gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, where the decomposition into simpler subsets is crucial.

Intense laser-matter interactions are generally determined by the instantaneous electric field of the laser pulse. For light-matter interactions with few-cycle pulses, the carrier-envelope phase (CEP) plays a critical role as the temporal variation of the electric field depends on the phase. This has a profound impact on many scientific applications. More importantly, controlling the CEP provides an additional degree of freedom to control field-driven processes in atomic, molecular and solid-state systems. In this thesis, we will demonstrate the development and implementation of a single-shot CEP measurement technique, i.e., the so-called carrier-envelope phasemeter based on stereo-above-threshold ionization in Xe and operating at short-wave infrared (SWIR) wavelengths, which allows for simultaneous pulse duration measurement. The experimental results are compared to simulations with two different theoretical models. Next, we will demonstrate the significance of the phase-volume effect, i.e. the reduction of the CEP-dependence due to the spatial distribution of the CEP in focused few-cycle pulsed beams. We formulate a general description of the impact of the focal phase for laser-matter interactions of different nonlinear orders to answer the general question: if, when, and how much should one be concerned about the phase-volume effect? At last, CEP-dependent strong-field ionization of Xe using 3.2um few-cycle pulses as a benchmark will be studied. In order to find an alternative target for a single-shot CEPM at mid-infrared (MIR) wavelengths, Cs will be investigated. We observed an anomalous CEP-dependence in Cs, particularly at high intensities, which can be interpreted as the interference of two backscattered quantum orbits from adjacent optical cycles. Viewed from a higher perspective, this thesis demonstrates a precise characterization of the CEP and an accurate analysis of CEP-dependent light-matter interaction from the NIR, via the SWIR to the MIR range.

In this work, we report on the first x-ray spectroscopy study associated with the RR processes for bare lead ions at the electron cooler of the CRYRING@ESR, as storage rings are currently the only facilities routinely delivering hydrogen-like ions at high-Z in large quantities. With ultra-cold electron beam temperatures and near zero electron-ion collision energies, the effective production of characteristic projectile x-rays was well demonstrated at 0 deg and 180 deg observation geometries in our experiment by decelerated 10 MeV/u hydrogen-like lead ions. To reveal the role of radiative feeding transitions in the formation of observed intense Lyman and Balmer lines, an elaborate theoretical model describing the radiative decay dynamics and each (n, l, j)-state population varying over time is put to a test. As a result, the presented rigorous treatment reproduces observed x-ray spectroscopy really well in terms of the RR transitions and characteristic x-ray lines. In addition, we found a strong enhancement for l = n − 1 states in inner shells due to radiative Yrast-cascades from high Rydberg states, that finally contribute strikingly to the observed intensities of characteristic x-ray lines. Further on the current thesis lays the basis for a successful effort to push the experimental resolution of x-ray spectroscopy for L → K ground-state transitions at high-Z of below 80 eV at about 100 keV. This was done in an RR experiment of free electrons into the bound states of initially hydrogen-like uranium ions by adopting low temperature x-ray detectors, namely metallic magnetic calorimeters. Such an experiment allowed us for the first time to resolve the substructure of the Kα2 line and partially the Kα1 line in helium-like uranium ions. The preliminary data again prove the unique potential of the experimental method based on x-ray spectroscopy at the electron cooler of the CRYRING@ESR.

One of the most intriguing physics processes that remain untested is the pure photon electron-positron pair production via quantum-vacuum fluctuations described by the nonlinear Breit-Wheeler theory. These fluctuations generate virtual pairs that can be turned into observable particles by applying strong electric fields above the Schwinger critical limit of \num{1.3d18}~V/m~\cite{Schwinger.1951, Ritus.1985}. Despite the advent of high-intense lasers, the critical limit is still far beyond achievable. However, such fields can be achieved on the rest frame of the real particles after the collision of a high-energy $\gamma$-ray photons with the laser beam. To diagnose the created pairs, this thesis describes the design of a particle detection system capable of successfully probing the single leptons created from strong-field quantum electrodynamics (SF-QED) interactions at the upcoming SF-QED experiments E-320 at FACET-II and FOR2783 at CALA. The designed detection system is composed of tracking layers made of LYSO:Ce scintillating screens and a Cherenkov calorimeter that, having their signals combined, can identify a positive event with a confidence level above 99%. At the E-320 experiment, electron beams generated by the FACET-II linear accelerator with an energy of 13~GeV collide with an intense laser beam of $\anot \approx 10$, and nonlinear Breit-Wheeler pairs are produced in the nonperturbative full quantum regime of SF-QED interaction ($\chie > 1$ and $\anot > 1$). About 100 electron-positron pairs per shot are expected to be created. According to Monte-Carlo simulations of the experimental layout, the detection system will be placed on a region permeated by a shower of x-rays and few-MeV $\gamma$-photons, however, a signal-to-noise ratio of $\SNRsig \approx 18$ on the detectors is achieved.

In this work, we demonstrate how new theoretical concepts enable measurements of the signature of the QED vacuum nonlinearity beyond the background in collision experiments of all-optical high-intensity laser pulses. Using the vacuum emission picture, we develop the method of channel analysis of the signal. Based on these findings, we study two different experimental scenarios and identify discernible signals. In the first case, we consider the collision of two high-intensity laser pulses that differ only in their focus waist sizes. We present a numerical method to identify the regions where the signal dominates the background. Furthermore, we use this to investigate the behavior of the discernible signal, particularly with respect to the effects of the waist size of the probe beam. Of particular note, maximization of the measurable signal photons is not achieved by minimal focusing. This can be explained by the interplay of intensity in the interaction volume and decay behavior of the background in the far field. With the help of an elliptical cross section of the probe pulse, the signal can be further enhanced. Moreover, we show that a discernible signature of vacuum birefringence is achievable in the all-optical regime. In a second setup, elastic and inelastic photon-photon scattering mediated by the nonlinearity of the quantum vacuum is investigated. Based on a collision of four laser pulses of different oscillation frequencies, we observe signals in regions beyond the forward direction of the driving lasers as well as with frequencies beyond the laser frequencies. These features allow us to measure the signal beyond the background. The preceding channel analysis not only helps in the interpretation of the results, but it also allows effective amplification of the signal while maintaining experimental constraints.

Quantum electrodynamics (QED) is the first quantum field theory that describes all phenomena associated with electrically charged particles. Despite its mathematical complexity, it is quite effective in describing and predicting experimental results. With the introduction of lasers, atomic spectroscopy is constantly evolving, contributing to QED testing and continuous improvements in the precision of physical constants determination. Atomic systems offer many opportunities for high-precision QED tests. In the present dissertation, we focus on the magnetic sector of QED: the hyperfine structure and the Zeeman effect in few-electron ions. We present the systematic QED treatment of the electron correlation effects in the ground-state hyperfine structure in lithiumlike ions for the wide range of nuclear charge numbers Z = 7 - 82. The one- and two-photon exchange corrections are evaluated rigorously within the QED formalism. The electron-correlation contributions due to the exchange by three and more photons are accounted for within the Breit approximation employing the recursive perturbation theory. The calculations are performed in the framework of the extended Furry picture, i.e., with the inclusion of the effective local screening potential in the zeroth-order approximation. In comparison to previous theoretical computations, we improve the accuracy of the interelectronic-interaction correction to ground-state hyperfine structure in lithiumlike ions. The g factor of a bound electron is a rigorous tool for verifying the Standard Model and searching for new physics. Recently, a measurement of the g factor for lithiumlike silicon was reported and it disagrees by 1.7! with theoretical prediction [D. A. Glazov et al., Phys. Rev. Lett. 123, 173001 (2019)]. Attempting to resolve this deviation another theoretical value for silicon has been delivered. It results in a disagreement with experimental value [V. A. Yerokhin et al., Phys. Rev. A 102, 022815 (2020)]. We perform large-scale high-precision computations of the interelectronic-interaction and many-electron QED corrections to determine the cause of this disagreement. Similar to the case of hyperfine splitting, we carry out the calculations within the extended Furry picture of QED. And we carefully analyze the final values’ dependence on the binding potential. As a result, the agreement between theory and experiment for the g factor of lithiumlike silicon improves significantly. We also present the most accurate theoretical prediction for lithiumlike calcium too, which perfectly agrees with the experimental value.

Laser plasma accelerators (LPAs) have the potential to revolutionize research fields that rely on relativistic particle beams and secondary radiation sources thanks to their 10-100 GV/m accelerating fields. In the Laser Wakefield Acceleration (LWFA) scheme, a relativistically intense pump or driver laser is focused into a low-Z gas target, ionizing the gas and driving a relativistic, electron plasma wave. Under the proper conditions, such a plasma wave can be used to accelerate electrons to GeV kinetic energies in only centimeters of plasma propagation. As LPAs continue to be tested and refined, nondestructive measurement techniques must be developed to further investigate and understand the dynamic laser-plasma interaction as well as to help ensure reliable operation and measurement of future accelerator facilities based on plasma technology. In this thesis, experiment, theory and simulation are combined to investigate the magnetized, relativistic plasma coinciding with the pump laser at the front of the plasma wave. Experimentally, the Jeti 40 TW laser system was used at the Institute of Optics and Quantum Electronics in Jena, Germany to drive a LWFA in tenuous plasma. The plasma wave was then shadowgraphically imaged using a transverse, few-cycle probe pulse in the visible to near-infrared spectrum and an achromatic microscope using various polarizers and spectral interference filters. The resulting shadowgrams were sorted depending on the properties of the LWFA’s accelerated electron bunches, and subsequently stitched together based on the timing delay between the pump and probe beams. This allowed for the detailed investigation of the laser-plasma interaction’s propagation and evolution as imaged in different polarizations and spectral bands. The resulting data showed two primary signatures unique to the relativistic, magnetized plasma near the pump pulse. Firstly, a significant change in the brightness modulation of the shadowgrams, coinciding with the location of the pump pulse, is seen to have a strong dependence on the pump’s propagation length and the probe’s spectrum. Secondly, after ~1.5 mm of propagation through the plasma, diffraction rings, whose appearance is polarization dependent, appear in front of the plasma wave. A mathematical model using relativistic corrections to the Appleton-Hartree equation was developed to explain these signals. By combining the model with data from 2D PIC simulations using the VSim code, the plasma’s birefringent refractive index distribution was investigated. Furthermore, simulated shadowgrams of a 3D PIC simulation using the EPOCH code were analyzed with respect to the aforementioned signals from magnetized, relativistic plasma near the pump pulse. The results of the study present a compelling description of the pump-plasma interaction. The previously unknown signals arise from relativistic, electron-cyclotron motion originating in the 10s of kilotesla strong magnetic fields of the pump pulse. Advantageously, a VIS-NIR probe is resonant with the cyclotron frequencies at the peak of the pump. With further refinement, the measurement of this phenomenon could allow for the non-invasive experimental visualization of the pump laser’s spatiotemporal energy distribution and evolution during propagation through the plasma.

A good way to test the common theories in atomic physics and astronomy is to determine the degree of polarization of the emitted radiation. The short wavelengths in the X-ray range make a direct determination of the polarization impossible and the use of known interaction mechanisms necessary. A simple mechanism with significant anisotropy with respect to the polarization of the incident photons and a high effective cross section in the low to medium keV energy range is Compton scattering. Taking advantage of position- and energy-sensitive semiconductor detectors, this anisotropy provides the basis for Compton polarimetry. Double sided segmented semiconductor strip detectors have therefore been used for polarization determination for several years. Within the SPARC collaboration of FAIR, the design of a Si(Li) polarimeter has now been further developed. This novel Compton polarimeter with a cooled first preamplifier stage is characterized in detail in this work. Compared to the previous models, it allows for a better energy resolution and a more precise polarization determination, as well as for the first time a precise determination of the degree of polarization and the orientation of the polarization vector at photon energies well below 100 keV. This makes the emission properties of radiative transitions of heavy atoms accessible for polarization spectroscopy for the first time. Until now, the precision of the determination of the degree of polarization was largely limited by the statistics of the investigated data set. Studies based on simulations, which are presented in this thesis, show that for the sizes of experimental data sets available here, statistical uncertainty continues to dominate systematic sources of error. In particular, the improved detector setup allowed for the first time the determination of the degree of polarization for radiative electron capture into the K-shell (KREC) of ions for the previously inaccessible range of photon energies below 70 keV. Close to complete polarization has been demonstrated for this important electron capture process, which is very prominent in collisions of heavy ions and light targets. This demonstration was achieved for the interaction of a Xe54+ ion beam with an H2 gas target and a K-REC photon energy of 56 keV. In the present work, it has thus been shown that radiative electron capture (REC), in particular into the K-shell, is one of the most significant mechanisms of the production of strongly linearly polarized X-rays. In particular, with variation of projectile ion and energy and observation angle, it provides a well-defined source of polarized X-rays with tunable energy and, at the same time, variable polarization properties.