Research topics
The theoretical investigation of the interaction of matter with laser or other intense photon pulses by now has reached a level at which fundamental aspects such as the quantum nature of both light and matter, relativity and correlations among the involved particles have become key issues and substantial challenges alike. In this overview, our efforts are summarized towards a detailed understanding of the quantum mechanical interplay of all constituents of atomic, ionic and nuclear systems as well as quantum vacuum and quantum plasma with strong laser fields. Emphasis is placed on various applications with strong connection to experiments at the Institute (see Fig. 1): High-precision calculations involving quantum electrodynamical and nuclear effects are employed for accurate determinations, e.g., of ionic spectra, binding energies and g-factors. Coherent control of atomic and nuclear ensembles is investigated in the light of advanced synchrotron and x-ray free-electron laser sources. And finally our research on extreme field laser physics is directed towards carrying out quantum electrodynamics, nuclear, high-energy and astrophysics with the strongest laser pulses presently available or under construction.
Correspondingly please find below links to our three key areas which you please click for more details on the topics, a second click will close the topic:
Precision Studies with Ions and Nuclei
High-precision experiments with ions and nuclei enable a direct access to fundamental physics. In a highly charged ion, inner-shell electrons experience the strongest electromagnetic fields accessible nowadays, providing an ideal testing ground to prove weather quantum electrodynamics, the field theory of the electromagnetic interaction, is valid in intense external fields. Precision measurements with these systems, when combined with sufficiently accurate theoretical calculations, also yield the values of fundamental constants such as the electron mass, the Rydberg constant and the fine-structure constant, or can test whether these vary in space and time. Such studies are also anticipated to provide access to tests of physical phenomena beyond the Standard Model of particle physics. Furthermore, nuclei become also attractive in this direction being both increasingly accessible with advanced light sources and stable against external perturbations. Due to their typical MeV energy scale, they appear attractive for applications such as compact nuclear batteries or quantum information devices.
An external static magnetic field gives rise to the Zeeman splitting of atomic energy levels, with a strength characterized by the dimensionless g-factor of the atomic state. The theory of the g-factor of an electron bound in the attractive potential of an atomic nucleus is investigated in the group around Zoltán Harman. These studies are paralleled with a quantum leap in the experimental accuracy in the investigation of the g-factor, especially in Penning trap measurements performed by the division headed by Klaus Blaum. Measuring the electron's g-factor in highly charged ions provide an exciting possibility for testing fundamental theories. Effects of strong-field quantum electrodynamics (QED) are increasingly relevant at higher and higher ionic charges (see Fig. 2). Bound-state QED effects are scrutinized to the highest precision in recent trapped-ion experiments, which have reached the 10-11 level in terms of relative precision. From a combined analysis of experimental and theoretical data for carbon ions, an improved value of the mass of the electron has been determined to world-leading accuracy. The ALPHATRAP Penning-trap setup also enables the experimental investigation of highly charged ions in virtually arbitrary charge states, which, in collaboration with theoretical calculations, largely enriches the field of applications. Penning-trap measurements have very recently also enabled a novel determination of electronic binding energies. The achieved experimental accuracy on the 1-eV precision level is matched by our large-scale atomic structure calculations. Applications of this collaboration include the discovery of ultranarrow ionic transitions suitable for constructing future atomic clocks, the measurement of nuclear and atomic masses, and the determination of the Q value of the β decay of various atomic isotopes, relevant for constraining the neutrino mass.
The g-factor experiments are currently being extended to a range of ions along the periodic table, including the heaviest stable elements. In a recent study, single-electron tin ions have been experimentally investigated. Due to the high charge of its nucleus, extremely high electrostatic fields of around 1015 volts per centimetre are present at the location of the bound electron. Our theoretical calculations reach excellent agreement with the measured value after the highly demanding computations of two-loop self-energy corrections, which were evaluated taking into account the nonperturbative nuclear background field. A similar accuracy has been reached for the three-electron tin ion, in which, in addition to the quantum fluctuations of virtual particles created and annihilated from the vacuum, also photons exchanged between the electrons need to be accounted for. In recent studies, we put forward the use of high-precision measurements of the g-factor of such few-electron ions and its isotope shifts as a probe for physics beyond the standard model. The contribution of a hypothetical fifth fundamental force is calculated, and we found that, combining measurements from different ions at accuracy levels projected to be accessible in the near future, one may constrain the new physics coupling constant competitively. This idea was implemented in a recent experiment performed with ALPHATRAP, in which the difference between the g factors of two Ne isotopes was measured with a remarkable precision (see Fig. 3). The combination of theory and experiment provided a novel way of proving the existence of a hypothetical exotic interaction. Another essential motivation of such studies is that g-factor measurements with highly charged ions are anticipated to yield a new value of the fine-structure constant, i.e. the fundamental constant defining the strength of any kind of electromagnetic interactions in the Universe. Furthermore, our theory also enables to extract the magnetic properties of He-3 and Be-9 from high-precision experimental data obtained with the μTEx trap, relevant for the calibration of new nuclear magnetic resonance probes.
Optical and x-ray spectroscopy of highly charged ions for testing fundamental theories
Highly charged ions do not only allow for the precision determination of the values of physical constants, but they have also been proposed as improved optical clocks, and ideal systems for testing a potential variation in time of fundamental constants. Open-shell ions near level crossings have been predicted to be particularly sensitive to a variation of the fine-structure constant, and their optical and extreme ultraviolet spectra are being investigated by ion trap experiments by the group of José Crespo López-Urrutia. We perform large-scale calculations of the atomic structural properties of these ions to accompany the experiments, and put forward further ions and transition schemes for an efficient testing of the potential variation of the fine-structure constant and the electron-proton mass ratio. To extend the studies with highly charged ions, recently we also theoretically describe nuclear effects such as the hyperfine splitting of optical transitions in neutral atoms or singly charged ions, in collaboration with collinear laser spectroscopic measurements of the division of Klaus Blaum at the ISOLDE radioactive ion beam facility at CERN.
As these trapped-ion experiments are reaching extreme precision in the microwave and optical range, it would be desirable to also achieve high accuracy in a broader regime of the electromagnetic spectrum up to x-ray frequencies. While research with new x-ray free electron lasers has already produced remarkable results, the spectral qualities of these light sources are still far from those of optical lasers. In collaboration with the experimental group of Thomas Pfeifer at the Institute, we have developed x-ray pulse shaping schemes which are anticipated to decrease the bandwidth and improve the temporal coherence of the x-ray light. In recent studies, we have put forward a scheme to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using x-ray free-electron-laser pulses in a laser-produced plasma. Our numerical simulations show that one can obtain high-intensity, femtosecond x-ray pulses with bandwidths orders of magnitude narrower than in x-ray free-electron-laser pulses, at wavelengths down to the sub-ångström regime. Furthermore, Investigations have been started into the excitation dynamics of highly charged ions interacting with extreme ultraviolet (EUV) frequency combs, as such experiments are currently under construction in the Institute. We have put forward a scheme to infer the temporal coherence of EUV combs generated from intracavity high-order harmonic generation. Such short-wavelength lasers and frequency combs may be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopic studies in laboratory astrophysics.
The group led by Natalia Oreshkina has developed an accurate theoretical description of the structure of heavy muonic atoms and their corresponding X-ray emission spectra. Due to their larger mass, muons have a probability density that significantly overlaps with the atomic nucleus, enabling precise determination of nuclear parameters. For example, in a recent study, her group presented a new value for the nuclear charge radius of the doubly magic lead nucleus, based on rigorous quantum electrodynamics calculations, state-of-the-art numerical methods, and a systematic reanalysis of uncertainties. In collaboration with new muonic X-ray spectroscopic measurements at the Paul Scherrer Institute in Switzerland, this study paves the way for a systematic reevaluation of all nuclear radii based on muonic spectroscopy. Additionally, the methods developed for muonic atoms can be further applied to electronic systems, where nuclear effects play a crucial role in high-precision studies. One such example involves the search for physics beyond the Standard Model through nonlinearities in King’s plot.
Access to nuclear structure with muonic atoms spectroscopy
Muonic atoms are highly sensitive to nuclear parameters and therefore serve as valuable probes of atomic nuclei. At the same time, being essentially hydrogen-like highly charged ions, they can be treated using well-established quantum electrodynamics (QED) methods — though with a significantly stronger influence from nuclear physics. By combining detailed knowledge of level structures with high-precision experimental measurements of transition energies, muonic atoms have enabled determinations of key nuclear parameters such as charge radii, electric quadrupole moments, and magnetic dipole moments.
Starting from well-known effects - such as finite nuclear size, Uehling corrections, and hyperfine structure - we have significantly improved the theoretical treatment of heavy muonic atoms. Nuclear shape effects are incorporated to all orders using a deformed Fermi model, with QED and screening contributions now calculated to the 1 keV level, as required by current experimental precision. Furthermore, dynamical splitting - a distinctive feature caused by strong mixing of nuclear and muonic states - can now be predicted with high accuracy. For the first time, three of the four largest QED contributions to muonic spectra - nuclear polarization, self-energy, and nuclear recoil - have been rigorously calculated.
Recently, as part of a broader campaign to reevaluate nuclear radii, we presented a new value for the double-magic nucleus ²⁰⁸Pb, derived from muonic atom spectroscopy (see Fig. 4). By integrating rigorous QED calculations, state-of-the-art numerical methods, and a systematic reanalysis of uncertainties, we reduced the long-standing fine-structure anomaly and improved the fit quality by a factor of twenty. More broadly, our results strongly support a systematic, theory-driven reevaluation of rms charge radii across the periodic table - as demonstrated here using muonic spectroscopy combined with modern QED theory.
X-ray Quantum Dynamics with Atoms, Ions and Nuclei
High-precision research is increasingly enriched by advanced light sources, pushing the boundaries of physical research to shorter and shorter wavelengths. However, also in its own right x-ray free electron lasers and synchrotron sources allow for novel fundamental research on correlated relativistic quantum dynamics in ions as well as on x-ray quantum optics with nuclei, and on control of nuclear forward scattering.
Highly charged ions in x-ray fields
In highly charged atomic ions, inner-shell electrons experience extremely high nuclear binding fields. The dynamics of electrons becomes relativistic. Also, the electronic probability density has a considerate overlap with the nuclear matter. These properties render highly charged ions an ideal tool for basic research in relativistic atomic structure theory, quantum electrodynamics at extreme fields, and in the study of nuclear effects. In many-electron ions, relativistic and nuclear contributions are intertwined with electron correlation. Because of this complex interplay, accurate large-scale theoretical calculations, performed by the groups around Zoltán Harman and Natalia Oreshkina, are necessary to decipher the physical phenomena from the increasingly accurate experimental spectra. In recent studies, in collaboration with local experimentators, we theoretically investigate the ionization dynamics of highly charged krypton ions exposed to ultraintense x-ray free electron laser pulses. The subsequent resonant absorption of two quasi-monochromatic x-ray photons greatly increases the efficiency of two-photon ionization, dominating nonlinear light-matter interactions in the x-ray regime, with possible applications in future precision metrology.
The knowledge of the structural and dynamical properties of highly charged ions is also necessary for the modeling and diagnostics of astrophysical and fusion plasmas. The spectra of inner-shell transitions are of great relevance for astrophysical line diagnostics of x-ray binaries and stars, aiming at determining physical parameters of the emitter medium such as element decomposition, density, temperature, and velocity. These transitions are predominantly in the x-ray range, therefore, their efficient radiative excitation has been rather challenging until the advent of modern x-ray sources such as free electron lasers and synchrotrons, providing high intensities in the appropriate wavelength range. Our calculations have contributed to the resolution of a conondrum that has puzzled astrophysicists for decades: The intensity of two important, strong x-ray lines of a certain highly charged iron ion in astrophysical data and in laboratory experiments did not agree with predictions, obscuring the interpretation of astronomical observations (see Fig. 5). A recent electron beam ion trap measurement at the high-brilliance PETRA III synchrotron facility finally agrees with our large-scale calculations and with other modern theoretical results.
X-ray nuclear quantum dynamics
Recent advances in existing and upcoming light sources provide access to laser-like light in the x-ray and gamma-ray frequency domain, with a multitude of novel applications across all the natural sciences. Nevertheless, the implementation of advanced laser-coupled quantum systems in the x-ray domain remains a challenge due to basic experimental limitations. We develop methods to overcome these limitations, and to establish x-ray quantum optics. This on the one hand will be required to unleash the full potential of the new x-ray light sources, and on the other hand provides a new platform for quantum optics as a whole.
In the group of Jörg Evers, currently the emphasis is on atomic Mössbauer nuclei, which have proven successful in ground-breaking experiments on x-ray quantum optics. A central goal is to establish large interacting ensembles of Mössbauer nuclei in solid-state targets as a new platform for quantum dynamics, and to develop novel control schemes for the interaction of the x-rays with the nuclei based on coherence-, interference, nonlinear and quantum effects. Such control schemes open up novel applications for Mössbauer science and powerful tools for x-ray science alike. Over the last years, we developed sophisticated quantum optical frameworks for the description of the nuclear quantum dynamics driven by intense x-ray fields. They allow us to identify and separate all physical processes contributing to the recorded signal, and encompass nonlinear and quantum effects. Based on these models, we engineer advanced quantum optical setups, and we verified a number of predictions of this model experimentally in collaboration with experimental teams around Ralf Röhlsberger (Helmholtz Institute Jena and DESY, Hamburg), Thomas Pfeifer at the Institute, and G. G. Paulus (University and Helmholtz Institute Jena).
Mössbauer nuclei feature resonances with exceptionally narrow spectral line widths, which form the basis for a broad range of applications across the natural sciences. For x-ray quantum optics, the narrow resonance is favorable, because it translates into long nuclear coherence lifetimes. However, the narrow line width also implies weak driving, since only a tiny fraction of the x-ray pulses is resonant with the nuclei. To address this challenge, a group around Jörg Evers explores the possibility to simulate the effect of strong control fields using mechanical motion of a nuclear target (see Fig. 6). A short x-ray pulse impinging on a nuclear target may either pass without interaction, or interact with the nuclei. By applying a suitable motion to the target immediately after the non-interacting part passed the target, an arbitrary time-dependent phase can be imprinted on the delayed interacting part. In our initial experiments, we used this control to shape the x-ray pulses such that the number of resonant photons is increased – thereby allowing for a stronger driving of nuclei. Further, we demonstrated that the shaped pulses can be used to coherently control nuclear dynamics, by switching between stimulated emission and coherent excitation of the nuclei. Recently, we developed a dynamically tuneable x-ray interferometer for Mössbauer science based on this control (see Fig. 6). Interferometric methods are central to advancing precision measurements, but difficult to realize due to the extreme stability requirements imposed by the short x-ray wavelength. In our setup, two Mössbauer targets act as beam splitters to implement an inline interferometer with spatially overlapping interfering pathways to improve the stability. We engineer the interference such that the transmission vanishes for the empty interferometer (dark-fringe mode) to improve the sensitivity. The relative phase of the two pathways can dynamically be tuned by displacing one of the targets. In the experiment with teams around Ralf Röhlsberger (Helmholtz Institute Jena and DESY) and Thomas Pfeifer (MPIK) at the High Resolution Dynamics Beamline P01 of the synchrotron source PETRA III (DESY), we showcased the new measurement capabilities by interferometrically observing minuscule deformations of a host material due to propagating sound waves. We further demonstrated the control capabilities by switching the interferometer transmission in order to gate the intensity of an x-ray pulse on nanosecond time scales. Our interferometer concept opens avenues towards polarization-sensitive phase measurements, the generation of coherent multi-pulse sequences for controlling nuclear dynamics, and the implementation of feedback loops to adaptively optimize the interferometer, thereby fueling the further development of nuclear quantum optics.
In a collaboration with a team around Ralf Röhlsberger (HI Jena and DESY), we have recently established nuclear resonance scattering on the archetype Mössbauer isotope 57Fe at the MID instrument of the European X-ray free electron laser. The high-repetition rate pulse structure together with self-seeding enable a qualitative change in experimental capabilities for Mössbauer science. Most notably, in our experiments, we routinely observed higher excitations of the nuclear ensemble, with up to about 1000 signal photons in the coherent scattering after a single x-ray excitation (see Fig. 7). By contrast, the corresponding average number of signal photons at synchrotron sources is far below one. This progress enables a multitude of new science cases and observables, such as photon correlations or the excitation-dependent study of collective effects. As a first application, we explored Mössbauer spectroscopy on the level of individual x-ray excitations. This addresses the longstanding challenge that in traditional setups, Mössbauer spectroscopy inevitably requires an averaging over extended measurement times. The averaging impedes the study of non-repetitive non-equilibrium phenomena in the nuclear dynamics or in the surrounding host material, e.g., after impulsive stimuli. Previously it had been suggested that an increase in the number of resonant photons delivered by the source could allow for spectroscopy using single x-ray pulses. However, we found that this approach is limited by a finite detector dynamical range, which typically does not suffice to capture the full decay dynamics. It further excludes the vast majority of experimental repetitions with lower signal photon number due to the XFEL photon statistics. To overcome these challenges, we developed a sorting approach, which utilizes the presence of different dynamics classes, i.e. different nuclear evolutions after each excitation. We employ machine learning to identify models for the dynamics classes by a suitable clustering of the data. Interestingly, this approach does not require any theory input and can be used to search for unknown phenomena. Afterwards, also the low-count repetitions can be sorted according to the identified classes, and thereby crucially contribute to the result. The successful demonstration based on data measured at EuXFEL opens up a path towards the future exploration of out-of-equilibrium transient dynamics of the nuclei or their environment. Next to the high number of resonant photons per pulse, EuXFEL also offers an increase in the number of resonant photons per second. In a collaboration with Yuri Shvyd’ko (Argonne National Labs, USA), Olga Kocharovskaya (Texas A&M University, USA; external scientific member at MPIK) and Ralf Röhlsberger (HI Jena and DESY), this allowed us to resonantly excite the ultra-narrow nuclear transition in 45Sc at 12.4 keV resonance energy for the first time. The nuclear resonance has a natural lifetime of about half a second (line width 1.4 femto-electronvolt), and its coherent spectroscopy would enable new fundamental tests and potentially a nuclear clock operation at energies of hard x-rays. In the experiment, the nuclear resonance energy was determined 250 times more accurate than before, which sets the stage for the further exploration of the resonance.
Towards nuclear quantum dynamics beyond the linear low-excitation limit
The recent progress in establishing Mössbauer science at free electron lasers prompts the development of corresponding theoretical modeling in order to harness the new capabilities. A particularly promising experimental platform is x-ray cavity quantum electrodynamics with Mössbauer nuclei embedded in thin-film cavities probed by near-resonant x-ray light. In the low-excitation limit, the response of the joint nuclei-cavity system is equivalent to that of a tunable x-ray quantum optical few-level scheme. By optimizing the cavity structure, a wide range of level schemes can be implemented, which enabled the demonstration of a number of important quantum optical phenomena with nuclei. We have recently started to generalize this platform to stronger excitations. In particular, the enhancement of the interaction between x-rays and nuclei enabled by the cavity prompted us to revisit the long-standing goal of non-linear excitation of nuclei, possibly up to full inversion. To this end, we developed a comprehensive theory of nonlinear nuclear excitation in thin-film x-ray cavities by focused x-ray pulses. Interestingly, we found that the rigorous modeling of the focusing leads to optimum cavity structures that qualitatively differ from well-established design paradigms for collimated x-ray beams (see Fig. 8). The reason for this is that the x-ray beam divergence increases with stronger focusing, imposing a requirement of a larger angular acceptance of the optimized cavity modes. We then calculated the necessary source parameters to enter the regime of nuclear excitation beyond the linear low-excication limit. Depending on the considered isotope, focusing may bring this regime within reach at self-seeded XFEL sources or upcoming x-ray free electron laser oscillators.
In parallel, we have also explored the de-excitation dynamics of an ensemble of strongly excited Mössbauer nuclei. In contrast to the ultrafast x-ray excitation, this dynamics proceeds on the slow nuclear lifetime scale and therefore is a challenging many-body problem since the coherent- and the incoherent nuclear processes compete on comparable time scales. Unlike previous approaches to this problem, we apply a perturbative expansion in the coupling between the nuclei, which is valid for moderate couplings as they appear in typical nuclear forward scattering settings. Under homogeneous excitation conditions, we derived an effective single-particle nonlinear equation which captures the full many-body dynamics in leading order in the nuclear correlations. We show that the dynamics at higher excitation features a non-linear phase evolution, and propose an interferometric setup to experimentally explore it. Furthermore, we identify interesting finite-size effects in smaller ensembles of nuclei. which are not only interesting in their own right, but are also expected to become relevant in Mössbauer spectroscopy with highest spatial resolution.
Extremely Intense Laser and High-energy Lepton Beam Interactions
Recent sustained technological progress such as the construction of the Extreme Light Infrastructure (ELI) is opening up the possibility of employing intense laser radiation to trigger or substantially influence physical processes beyond atomic physics energy scales. Various topics in our division are devoted to laser-driven relativistic quantum dynamics and investigations of high-energy processes within the realm of quantum electrodynamics, nuclear and particle physics in extremely intense laser fields and high-energy lepton beams.
Quantum dynamics in moderately intense laser fields
Quantum effects such as wave packet interference, entanglement, spin oscillations, and tunneling may be relevant when extremely intense laser pulses are impinging on atomic systems. In particular, a quantum tunneling barrier may be built up in an atom or a highly charged ion by the attractive Coulomb forces that attach the electron to the atomic core and the electric field of a strong laser that pulls the electron away from the core. Moreover, ultra-strong lasers can no longer be treated as pure electric fields; the laser's magnetic field component has to be taken into account, too (nondipole effects). The recent results of the group around Karen Hatsagortsyan contributed to an understanding of the role of sub-barrier as well as nondipole dynamics for shaping subtle features of the photoelectron momentum distribution in tunneling ionization.
One typical topic of interest is the time-resolved understanding of quantum processes during ionization of an atom in a very strong field. A simple model of this process claims that the electron tunnels instantaneously through the laser-generated quantum barrier. However, the accurate description of the sub-barrier dynamics can significantly modify this simple picture. Previously, we have identified a new pathway of strong-laser-field-induced ionization of an atom via recollisions under the tunneling barrier, showing that the interference of the direct and the under-the-barrier recolliding quantum orbits induces tunneling time delay. Recently, we have found that the under-the-barrier-recollision dynamics can induce transient population of the Rydberg states which, counterintuitively, can be much more efficient than the direct multiphoton transitions (see Fig. 9). Accordingly, we have developed the under-the-barrier-recollision theory for Freeman resonances, which predicts distinct features of phenomena in the strong field regime that cannot be explained by the existing direct multiphoton transition scenario. Specifically, it predicts the dominance of high-order Freeman resonances over above-threshold ionization in the photoelectron energy spectra and the flat dependence of the signal of Freeman resonances on the laser intensity, both in the nonadiabatic tunneling regime. We collaborated on this topic with the Korean experimental group around Professor Dong-Eon Kim from POSTECH institute. They were able to experimentally demonstrate these features of Freeman resonances in strong field regime, substantiating the under-the-barrier-recollision dynamics. Thus, the under-the-barrier-recollision is not only responsible for inducing tunneling time delays on the order of attoseconds, but also, with this experimental demonstration, are likely to induce similar substantial amendments in comparable scenarios, modifying, e.g., strong-field molecular, solid-state, and even high-energy tunneling quantum dynamics.
Recently, ion-photoelectron entanglement effects during strong field ionization have experienced special attention of the strong field community. In our recent study, we have shown how nondipole effects can facilitate observation of the ion-photoelectron entanglement. We investigated the three-body dynamics of the photoelectron and nuclei in the dissociative photoionization of diatomic molecules initiated by x-ray photoabsorption. The ion-photoelectron entanglement transfers information of the electronic interference to the ion dynamics. As a consequence, the ion momentum distributions of dissociative molecular photoionization present Young’s double-slit interference when the photoelectron emission angle is fixed. In the ionization of heteronuclear molecules, a nondipole recoil momentum arises due to the different ion masses. Quantifying the nondipole effect via the average of the relative nuclear momentum along the photon propagation direction, we demonstrate that double-slit interference signatures persist in the average longitudinal momentum shift. The interference due to the photoelectron-ion entanglement could serve as an additional leverage for coherent control of molecular dynamics in dissociative photoionization.
Furthermore, the role of the spin may become essential in intense laser-matter interaction, where we have previously investigated its dynamics and back action as well as compared deviating semiclassical models. More recently, we have revealed a counter-intuitive effect of the spin polarization of photoelectrons in tunneling ionization induced by a linearly polarized laser pulse. It was known that ionization can serve as a source of spin-polarized electrons, because spin-orbit coupling in an atomic bound state creates a strong correlation between the electron’s spin and orbital angular momentum. This correlation, combined with the significant angular momentum-dependent ionization probability, results in photoelectron polarization in nonadiabatic tunneling ionization in circularly polarized laser fields. While the conservation law of angular momentum implies that net electron polarization is impossible when ionizing the spinless ground state of rare gas atoms with a linearly polarized laser field, angle-resolved spin polarization can still occur. We demonstrate a nontrivial spin texture of photoelectrons in momentum space, exhibiting a vortex structure relative to the laser polarization axis. In contrast to a circularly polarized pulse, the total polarization of the ionized electron vanishes here; nevertheless, we demonstrate the emergence of significant momentum-resolved spin polarization. We trace the origin of this spin texture to the correlation between spin and the initial transverse velocity of the photoelectron at the tunnel exit, giving rise to spin-dependent quantum orbits. Two distinct mechanisms of photoelectron polarization can exist: one for direct electrons, visible in few-cycle laser pulses, and the other for recolliding electrons, prominent in long pulses. In the latter case, we show that forward rescattering of the spin-dependent quantum orbits is responsible for generating nontrivial momentum-resolved spin texture. Furthermore, the interference between direct and rescattering ionization allows for spin-polarized electron holography (see Fig.10), offering an alternative method to extract atomic fine structural information.
QED and high-energy processes in very strong laser fields
The success of QED in vacuum calls for testing this theory under more extreme conditions such as those provided by strong electromagnetic background fields. The typical fields scale of QED is provided by the so-called Schwinger or critical fields of QED: Ecr=1.3×1016 V/cm and Bcr=4.4×1013 G. Antonino Di Piazza still keeps a small team in Heidelberg investigating theoretically the possibility of testing QED by means of ultra-strong electromagnetic fields with a focus on ultra-intense laser beams in these areas, where processes effectively occur in the presence of strong background fields of the order of the critical ones (strong-field QED). A linearly polarized laser field with an amplitude of the order of Ecr, would have a peak intensity Icr of about 4.6×1029W/cm2. Present laser systems are able to produce electromagnetic fields of intensities of the order of 1022 W/cm2 and future facilities like the Extreme Light Insfrastructure (ELI) and the Exawatt Center for Extreme Light Studies (XCELS) aim at laser intensities of the order of or exceeding 1024 W/cm2. Although the intensity Icr seems to be out of reach in the near future, the experimental investigation of strong-field QED is still possible. In fact, if an ultra-relativistic electron with energy ε collides head-on with a strong laser beam with electric field amplitude E, the strong-field QED effects depend on the Lorentz-invariant parameter χ≈2(ε/mc2) (E/Ecr), where mc2 is the electron rest energy. Therefore, by employing ultra-relativistic electron beams and intense laser fields, it is possible to render the parameter χ of the order of unity or larger, enter the strong-field QED regime, and test the predictions of QED under such extreme conditions. Systematic analytical methods to investigate theoretically strong-field QED processes in intense laser fields have relied on approximating the background field as a plane wave, which allows to solve exactly the corresponding Dirac equation.
The understanding of the structure of QED in the presence of strong background fields cannot be fully accomplished without a thorough investigation of radiative corrections. Among these we have studied the self-interaction of the electron with its own electromagnetic field (mass operator) and the temporary transformation of a photon into a virtual electron-positron pair (polarization operator). Both analyses have shown qualitatively new effects with respect to the vacuum case. On the one hand, the structure of the mass operator has indicated that, unlike in vacuum, the electron spin dynamics can be substantially altered by the electron self-field. On the other hand, the investigation of the polarization operator has even shown that in the presence of a strong laser beam, virtual electron-positron pairs can propagate along distances which exceed by orders of magnitude the typical microscopic QED lengths of the order of the Compton wavelength λC=3.9×10-11 cm and are comparable with the laser wavelength (of the order of micrometers for optical lasers). As a consequence, the electron and the positron can absorb a very large number of laser photons (of the order of a million for an optical laser of intensity 1022 W/cm2) and the corresponding energy can be potentially exploited to prime high-energy reactions once the virtual pair again annihilates (see Fig. 11). A thorough analysis shows that this process is the analogous in the high-energy domain of the well-known recollision processes in atomic and molecular physics responsible, for example, of high-harmonic generation. Thus, such high-energy recollision processes may represent a basic, key ingredient for a miniaturized version of a high-energy "vacuum" collider.
The relation between the electromagnetic and the gravitational interactions has always fascinated theoretical physicists especially in view of the unification of the four fundamental forces. We have recently exploited our experience in strong-field QED to investigate the gravitational radiation emitted by electrons driven by ultra-intense laser beams. By generalizing results obtained in classical electrodynamics and in QED in vacuum, we have demonstrated that the probability amplitude of emitting a graviton by an electron in an arbitrary plane wave is proportional to the corresponding amplitude of NCS. We have also demonstrated that the proportionality constant is the same in classical electrodynamics and in vacuum QED unifying in this way the previous findings in the more general treatment of strong-field QED coupled with linear gravity. Furthermore Antonino Di Piazza's team discovered intriguing effects in Compton scattering in nonlinear gravitational fields.
Coherent extreme ultraviolet (XUV) light sources capable of generating attosecond pulses have become essential tools for probing ultrafast dynamics in atoms, molecules, and solids. Traditionally, such pulses have been produced via high-harmonic generation (HHG), a nonlinear optical process that enables access to attosecond timescales but suffers from low conversion efficiency, particularly at higher photon energies. To overcome these limitations, free-electron lasers (FELs) have emerged as alternative sources offering substantially higher intensities and broader spectral coverage, albeit at the cost of size and complexity. FELs achieve coherence through the formation of microbunches in an electron beam, which emit collectively as they traverse an undulator. Although recent work has demonstrated FEL-based attosecond pulse generation, these facilities remain large and costly. A promising route toward miniaturization is the optical FEL (OFEL), in which an intense laser pulse replaces the undulator. The shorter wavelength of the optical driver offers significant potential for compactness, but the requirement for dense, low-energy electron beams introduces challenges due to emittance growth and Coulomb repulsion. Recent advances in producing collimated and relativistic particle beams, including those composed of both electrons and positrons, open new possibilities for realizing compact coherent light sources in the XUV regime.
The group around Matteo Tamburini has introduced a novel approach to generating coherent broadband XUV radiation through the use of relativistic electron-positron (e-/e+) beams interacting with an intense laser pulse (see Fig. 12). Using analytic modeling, first principles N-Body simulations, and state-of-the-art three dimensional particle-in-cell simulations, the authors demonstrate that such a system can produce trains of attosecond pulses—each 8 attoseconds in duration—spaced by 92 attoseconds, over interaction lengths of less than a millimeter. This process arises from the laser-induced microbunching of the (e-/e+) beam, enabled by the inherent quasi-neutrality and equal-mass composition of the system. The mutual attraction between the oppositely charged species suppresses Coulomb expansion, a limiting factor in conventional OFEL schemes using only electrons. As a result, the system maintains the beam quality necessary for coherent emission over compact spatial scales. This key insight paves the way for the realization of compact, high-brightness XUV sources with significantly reduced physical footprints relative to conventional FELs. By exploiting the unique stability of electron-positron beams, the work establishes a fundamentally new regime of coherent light generation with potential applications across disciplines ranging from fundamental physics to ultrafast spectroscopy and structural biology.
Quantum plasmas in very strong external fields and astrophysics
QED processes like pair production, cascades and gamma ray emission with radiation reaction are also relevant in quantum plasmas and in astrophysical environments. The formation and dynamics of QED cascades in the magnetospheres of pulsars, particularly above their polar caps, represent a cornerstone of modern pulsar astrophysics. Pulsars are highly magnetized, rapidly rotating neutron stars whose magnetospheres are thought to be filled with dense e± plasmas generated through QED cascades occurring in vacuum gaps. These cascades are initiated by primary particles accelerated along strong magnetic field lines, which emit high-energy photons via curvature radiation. The curvature radiation photons, in turn, decay into e± pairs that subsequently emit synchrotron radiation, driving a self-sustained cascade process. Traditional models and numerical approaches—ranging from magnetohydrodynamic to heuristic particle-in-cell simulations—have provided essential insights into global magnetospheric structure and cascade dynamics, yet often neglect spin and polarization effects intrinsic to QED processes. Recent developments in strong-field QED, propelled by the advent of petawatt-class laser facilities, have revived interest in polarization-resolved dynamics, although most studies focus on terrestrial or laboratory conditions where field configurations differ significantly from those in pulsars. In the pulsar context, where the motion of particles is aligned with the magnetic field rather than perpendicular, polarization and spin effects are expected to play a distinct and potentially nontrivial role. Prior QED-PIC simulations typically adopted unpolarized radiation and pair production rates, thereby omitting the subtle influence of photon polarization on cascade efficiency and structure. This gap underscores the necessity of incorporating polarization-resolved QED processes to accurately capture the microphysics governing cascade initiation and evolution in pulsar polar cap regions.
An international team led by Matteo Tamburini has systematically investigated the role of photon polarization in QED cascades over pulsar polar caps, achieved through the implementation of a Monte Carlo-based QED algorithm that accounts for both e± spin and γ-photon polarization. By employing both 3D single-particle and 1D QED-PIC simulations, the authors demonstrate that curvature radiation photons exhibit strong linear polarization aligned with the plane of the magnetic field, while synchrotron radiation photons are weakly polarized due to the randomized orientation of e± acceleration during their gyration (see Fig. 13). As the cascade develops, synchrotron radiation photons become increasingly dominant, leading to a net reduction in average photon polarization. Crucially, the study quantifies the effect of polarization on pair production rates, revealing that the high polarization of curvature radiation photons enhances e± pair creation by approximately 5% compared to unpolarized models—a finding that contrasts with the suppression typically observed in analogous laser-plasma settings. The simulations further distinguish between “shower-type” cascades, driven by injected electrons without sustained electric fields, and "avalanche-type" cascades that are self-sustained by persistent parallel electric fields. In both cases, polarization-dependent phenomena remain robust, as confirmed by consistency between single-particle and QED-PIC approaches. This work thus constitutes a significant advancement in our understanding of magnetospheric pair creation, providing the first fully self-consistent, polarization-resolved simulation framework for QED cascades in the unique geometrical and dynamical context of pulsar polar caps.
Fast Radio Bursts (FRBs), as another example, are extremely short, intense flashes of radio waves typically lasting only a few milliseconds. Since their discovery in 2007, they have become one of the most intriguing open problems in contemporary astrophysics. Traditionally, the short observed duration of FRBs has been interpreted as a direct constraint on the size of their central engine. Recent observations of FRBs on the microsecond time-scale challenge this interpretation. In a recent work, we have has put forward a new explanation of the short duration of FRBs: high-energy photons from a FRB’s X-ray/soft gamma-ray counterpart can trigger an electron–positron pair cascade via Compton scattering and the Breit–Wheeler process in the plasma surrounding the source. This cascade rapidly increases the local plasma density, rendering it opaque to the FRB’s radio emission after a light-travel time of up to a few milliseconds, thus truncating the observable burst regardless of the intrinsic emission duration (see Fig. 14). This mechanism, motivated by observations of FRB 200428 from the Galactic magnetar SGR J1935+2154, implies that FRB sources are not necessarily constrained to produce intrinsically millisecond-long radio pulses, and that similar propagation-induced truncation could be common among FRBs, potentially impacting how their duration is interpreted in relation to their origins.
In ultrastrong fields in plasma which can be generated during plasma interaction with petawatt-class lasers, or during different astrophysical instabilities, spin polarized electrons and polarized gamma photons are produced due to radiative polarization. Previously, Karen Hatsagortsyan and co-workers have investigated new methods for the plasma imaging via polarization properties of ejected particles, which will enable in situ probing the plasma dynamical characteristics. In our further study, we established the potential of electron polarization as a source of new information on laboratory and astrophysical plasma instabilities. One of the studies was devoted to the investigation of the polarization properties of electrons during plasma current filamentation of an ultrarelativistic electron beam impinging on an overdense plasma. We showed that electron radiative polarization emerges during the instability along the azimuthal direction in the momentum space. The correlation between the emerging spin polarization and the collective behaviors enables decoding current filamentation instability scenarios via polarization detection.
In another study we address relativistic preturbulent shocks, and examined the mechanisms of electron acceleration. We have revealed a new mechanism of acceleration, dubbed as “Slingshot Acceleration in Relativistic Preturbulent Shocks”, which has been found analyzing the emitted photon polarization. We investigated the transient electron dynamics in the transition to turbulence near the counter-streaming interface of an unmagnetized pair-loaded relativistic collisionless shocks (RCS) precursor, which is potentially associated with the outflow of Gamma-ray bursts (GRBs). We found that the integrated radiation from the RCS exhibits a counterintuitive nonmonotonic dependence of the photon linear polarization degree along the transverse acceleration on the photon energy. The analysis showed that this uncommon polarization behavior of gamma-photons originated from the accelerated electron in the transition region from the preturbulent laminar motion to a chaotic turbulence. This slingshotlike acceleration mechanism is distinct from the well-known stochastic acceleration and is induced by the drifting electric field sustained by the flowing focus of backward-moving electrons (see Fig. 15). Our results demonstrate the potential of photon polarization as an essential information source in exploring intricate transient dynamics in RCSs with relevance for Earth-based plasma and astrophysical scenarios.
Further, we applied a fully polarization resolved study via particle-in-cell simulations, both for the electron spin and gamma-photon polarization, to radiation reaction dominated magnetic reconnection. We identify a condensation transient plasma evolution of plasmoids accumulated into multiple tiny islands within the reconnection layer, where electrons are strongly polarized while emitting energetic γ-ray photons to undergo radiative spin flips (see Fig. 16). Nonlinear analyses elucidate that the condensation is caused by a spiral attractor appearing in the electron’s phase space due to radiation reaction. The spiral rotation and contraction of the attractor lead to the electrons’ polarization aligned with the magnetic field. In its turn, the spin-flip during a γ-ray emission is responsible for the anomalous linear polarization along the magnetic field. Thus, from our fully polarization resolved study we conclude that spin-polarized condensed plasmoids may be realized with around 1010 G magnetic fields in extreme power laser facilities and intrinsically can exist in extreme astrophysical reconnection scenarios, potentially explaining atypical polarization features in observed high-energy cosmic radiation.
















