Helmholtz Institute JenaGSI Helmholtzzentrum f
05 Oct 2025
High harmonic generation (HHG) is a crucial technology for compact, high-brightness extreme ultraviolet (XUV) and soft X-ray sources, which are key to advancing both fundamental and applied sciences. The availability of advanced driving lasers, with tunable wavelength, power, and pulse duration, opens new opportunities for optimizing HHG-based sources. While scaling laws for wavelength are well understood, this work focuses on how pulse duration impacts HHG efficiency and introduces a unified framework that links microscopic dynamics to macroscopic performance. We establish a practical scaling law for the single-atom dipole moment under phase-matching conditions, demonstrating a 1/t dependence at 515 nm wavelength. By connecting this microscopic scaling to macroscopic conversion efficiency, we provide clear guidelines for optimizing HHG output across different gases and driving wavelengths. Furthermore, we identify fundamental constraints, including the carrier-envelope-phase (CEP) walk-off, which limits efficiency at longer driver wavelengths and becomes especially significant for very short pulses. All predictions are based on simple, accessible formulas, eliminating the need for complex numerical simulations. Experiments confirm these predictions and highlight when short pulses are advantageous, particularly in scenarios where CEP walk-off and absorption effects are minimized. These findings offer practical principles for designing next-generation HHG sources, capable of Watt-level average power and extended spectral reach, enabling more versatile and powerful HHG-based XUV and soft X-ray sources.
Long-living, hot and dense plasmas generated by ultra-intense laser beams are of critical importance for laser-driven nuclear physics, bright hard X-ray sources, and laboratory astrophysics. We report the experimental observation of plasmas with nanosecond-scale lifetimes, near-solid density, and keV-level temperatures, produced by irradiating periodic arrays of composite nanowires with ultra-high contrast, relativistically intense femtosecond laser pulses. Jet-like plasma structures extending up to 1~mm from the nanowire surface were observed, emitting K-shell radiation from He-like Ti20+^{20+} ions. High-resolution X-ray spectra were analyzed using 3D Particle-in-Cell (PIC) simulations of the laser-plasma interaction combined with collisional--radiative modeling (FLYCHK). The results indicate that the jets consist of plasma with densities of 102010^{20}-102210^{22} cm3^{-3} and keV-scale temperatures, persisting for several nanoseconds. We attribute the formation of these jets to the generation of kiloTesla-scale global magnetic fields during the laser interaction, as predicted by PIC simulations. These fields may drive long-timescale current instabilities that sustain magnetic fields of several hundred tesla, sufficient to confine hot, dense plasma over nanosecond durations.
We present a source of coherent extreme ultraviolet (XUV) radiation with a flux of 1013^{13} photons per second at 26.5 eV. The source is based on high-harmonic generation (HHG) in argon and pumped by a frequency-doubled 100 kHz repetition rate fiber laser providing 30 fs pulses centered at 515 nm. We report on the characterization of the source and the generated XUV radiation using optical imaging and photoelectron spectroscopy. The generated radiation is quasi-monochromatized using a suitably coated XUV mirror and used for coincidence spectroscopy of ions and electrons generated from a cold gas target. The high intensity of the focused XUV pulses is confirmed by the observation of two-photon double ionization in argon. Moreover, we measure the XUV pulse duration by cross-correlation with visible laser pulses in argon.
Ghost imaging (GI) achieves 2D image reconstruction through high-order correlation of 1D bucket signals and 2D light field information, particularly demonstrating enhanced detection sensitivity and high-quality image reconstruction via efficient photon collection in scattering media. Recent investigations have established that deep learning (DL) can substantially enhance the ghost imaging reconstruction quality. Furthermore, with the emergence of large models like SDXL, GPT-4, etc., the constraints of conventional DL in parameters and architecture have been transcended, enabling models to comprehensively explore relationships among all distinct positions within feature sequences. This paradigm shift has significantly advanced the capability of DL in restoring severely degraded and low-resolution imagery, making it particularly advantageous for noise-robust image reconstruction in GI applications. In this paper, we propose the first large imaging model with 1.4 billion parameters that incorporates the physical principles of GI (GILM). The proposed GILM implements a skip connection mechanism to mitigate gradient explosion challenges inherent in deep architectures, ensuring sufficient parametric capacity to capture intricate correlations among object single-pixel measurements. Moreover, GILM leverages multi-head attention mechanism to learn spatial dependencies across pixel points during image reconstruction, facilitating the extraction of comprehensive object information for subsequent reconstruction. We validated the effectiveness of GILM through a series of experiments, including simulated object imaging, imaging objects in free space, and imaging object located 52 meters away in underwater environment. The experimental results show that GILM effectively analyzes the fluctuation trends of the collected signals, thereby optimizing the recovery of the object's image from the acquired data.
Coherent synchrotron radiation (CSR) is vital for developing powerful ultrashort light sources. We introduce a CSR generation mechanism using surface plasmon polaritons (SPPs) resonantly excited on a solid, near-critical-density microtube. A high-intensity, circularly polarised laser pulse, propagating along the microtube axis, efficiently couples the cylindrical SPP modes. This process creates azimuthally structured, rotating electromagnetic fields. These rotating fields subsequently confine, modulate, and directly accelerate surface electrons, causing them to emit CSR in the Valilov-Cherenkov angle. We further demonstrate that by improving the azimuthal symmetry, the helical modulation enables CSR emission across all azimuthal directions, significantly enhancing radiation intensity even when full coherence is imperfect. The harmonics can be well isolated for a high charge beam. Our full 3D Particle-in-Cell simulations indicate this scheme can generate X-rays with coherence enhanced by up to two orders of magnitude compared to incoherent emission.
The Facility for Antiproton and Ion Research (FAIR) will be the accelerator-based flagship research facility in many basic sciences and their applications in Europe for the coming decades. FAIR will open up unprecedented research opportunities in hadron and nuclear physics, in atomic physics and nuclear astrophysics as well as in applied sciences like materials research, plasma physics and radiation biophysics with applications towards novel medical treatments and space science. FAIR is currently under construction as an international facility at the campus of the GSI Helmholtzzentrum for Heavy-Ion Research in Darmstadt, Germany. While the full science potential of FAIR can only be harvested once the new suite of accelerators and storage rings is completed and operational, some of the experimental detectors and instrumentation are already available and will be used starting in summer 2018 in a dedicated research program at GSI, exploiting also the significantly upgraded GSI accelerator chain. The current manuscript summarizes how FAIR will advance our knowledge in various research fields ranging from a deeper understanding of the fundamental interactions and symmetries in Nature to a better understanding of the evolution of the Universe and the objects within.
In the dynamically assisted Schwinger mechanism, the pair production probability is significantly enhanced by including a weak, rapidly varying field in addition to a strong, slowly varying field. In a previous paper we showed that several features of dynamical assistance can be understood by a perturbative treatment of the weak field. Here we show how to calculate the prefactors of the higher-orders terms, which is important because the dominant contribution can come from higher orders. We give a new and independent derivation of the momentum spectrum using the worldline formalism, and extend our WKB approach to calculate the amplitude to higher orders. We show that these methods are also applicable to doubly assisted pair production.
In this article we investigate novel signatures of radiation reaction via the angular deflection of an electron beam colliding at 90 degrees with an intense laser pulse. Due to the radiation reaction effect, the electrons can be deflected towards the beam axis for plane wave backgrounds, which is not possible in the absence of radiation reaction effects. The magnitude and size of the deflection angle can be controlled by tailoring the laser pulse shapes. The effect is first derived analytically using the Landau-Lifshitz equation, which allows to determine the important scaling behavior with laser intensity and particle energy. We then move on to full scale 3D Monte Carlo simulations to verify the effect is observable with present day laser technology. We investigate the opportunities for an indirect observation of laser depletion in such side scattering scenarios.
Quantum reflection is a fascinating signature of the quantum vacuum that emerges from inhomogeneities in the electromagnetic fields. In pursuit of the prospective real-world implementation of quantum reflection in the back-reflection channel, we provide the first numerical estimates for the light-by-light scattering with dipole pulses, which are known to provide the tightest focusing of light possible. For an all-optical setup with a dipole pump and Gaussian probe of the same frequency, we find that the dominant signal signature is related mainly to the back-reflection channel from 4-wave mixing. Focusing on this, we study the particular case of a multiple focusing pulses configuration (belt configuration) as an approximation to the idealized dipole pulse. Using Bayesian optimization methods, we determine optimal parameters that maximize the detectability of a discernible back-reflection signal. Our study indicates that the optimization favors a three-beam collision setup, which we further investigate both numerically and analytically.
Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the physics of quantum amplification is not fully explored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic quantum phenomena such as time crystals. Here we investigate the magnetic-field signal amplification by periodically driven 129^{129}Xe spins and observe signal amplification at frequencies of transitions between Floquet spin states. This "Floquet amplification" allows to simultaneously enhance and measure multiple magnetic fields with at least one order of magnitude improvement, offering the capability of femtotesla-level measurements. Our findings extend the physics of quantum amplification to Floquet systems and can be generalized to a wide variety of existing amplifiers, enabling a previously unexplored class of "Floquet amplifiers".
We study the resonant sequential two-photon ionization of neutral atoms by a combination of twisted- and plane-wave light within a fully relativistic framework. In particular, the ionization of an isotropic ensemble of neutral sodium atoms (Z=11Z = 11) from their ground 32S1/23^{2}S_{1/2} state via the 32P3/23^{2}P_{3/2} level is considered. We investigate in details the influence of the kinematic parameters of incoming twisted radiation on the photoelectron angular distribution and the circular dichroism. Moreover we study the influence of the geometry of the process on these quantities. This is performed by changing the propagation directions of the incoming twisted and plane-wave light. It is found that the dependence on the kinematic parameters of the twisted photon is the strongest if the plane-wave and twisted light beams are perpendicular to each other.
This document sets out the intention of the strong-field QED community to carry out, both experimentally and numerically, high-statistics parametric studies of quantum electrodynamics in the non-perturbative regime, at fields approaching and exceeding the critical or `Schwinger' field of QED. In this regime, several exotic and fascinating phenomena are predicted to occur that have never been directly observed in the laboratory. These include Breit-Wheeler pair production, vacuum birefringence, and quantum radiation reaction. This experimental program will also serve as a stepping stone towards studies of elusive phenomena such as elastic scattering of real photons and the conjectured perturbative breakdown of QED at extreme fields. State-of-the-art high-power laser facilities in Europe and beyond are starting to offer unique opportunities to study this uncharted regime at the intensity frontier, which is highly relevant also for the design of future multi-TeV lepton colliders. However, a transition from qualitative observational experiments to quantitative and high-statistics measurements can only be performed with large-scale collaborations and with systematic experimental programs devoted to the optimisation of several aspects of these complex experiments, including detector developments, stability and tolerances studies, and laser technology.
We introduce the pCI software package for high-precision atomic structure calculations. The standard method of calculation is based on the configuration interaction (CI) method to describe valence correlations, but can be extended to attain better accuracy by including core correlations via many-body perturbation theory (CI+MBPT) or the all-order (CI+all-order) method, as well as QED corrections via QEDMOD. The software package enables calculations of atomic properties, including energy levels, g-factors, hyperfine structure constants, multipole transition matrix elements, polarizabilities, and isotope shifts. It also features modern high-performance computing paradigms, including dynamic memory allocations and large-scale parallelization via the message-passing interface, to optimize and accelerate computations.
We study electron-positron pair production by the combination of a strong, constant electric field and a thermal background. We show that this process is similar to dynamically assisted Schwinger pair production, where the strong field is instead assisted by another coherent field, which is weaker but faster. We treat the interaction with the photons from the thermal background perturbatively, while the interaction with the electric field is nonperturbative (i.e. a Furry picture expansion in α\alpha). At O(α2)\mathcal{O}(\alpha^2) we have ordinary perturbative Breit-Wheeler pair production assisted nonperturbatively by the electric field. Already at this order we recover the same exponential part of the probability as previous studies, which did not expand in α\alpha. This means that we do not have to consider higher orders, so our approach allows us to calculate the pre-exponential part of the probability, which has not been obtained before in this regime. Although the prefactor is in general subdominant compared to the exponential part, in this case it can be important because it scales as α21\alpha^2\ll1 and is therefore much smaller than the prefactor at O(α0)\mathcal{O}(\alpha^0) (pure Schwinger pair production). We show that, because of the exponential enhancement, O(α2)\mathcal{O}(\alpha^2) still gives the dominant contribution for temperatures above a certain threshold, but, because of the small prefactor, the threshold is higher than what the exponential alone would suggest.
Phase retrieval is at the heart of adaptive optics and modern high-resolution imaging. Without phase information, optical systems are limited to intensity-only measurements, hindering full reconstruction of object structures and wavefront dynamics essential for advanced applications. Here, we address a one-dimensional phase problem linking energy and time, which arises in X-ray scattering from ultrasharp nuclear resonances. We leverage the Mössbauer effect, where nuclei scatter radiation without energy loss to the lattice, and are sensitive to their magneto-chemical environments. Rather than using traditional spectroscopy with radioactive gamma-ray sources, we measure nuclear forward scattering of synchrotron X-ray pulses in the time domain, providing superior sensitivity and faster data acquisition. Extracting spectral information from a single measurement is challenging due to the missing phase information, typically requiring extensive modeling. Instead, we use multiple energetically overlapping measurements to retrieve both the transmission spectrum and the phase of the scattering response, similar to ptychographic phase retrieval in imaging. Our robust approach can overcome the bandwidth limitations of gamma-ray sources, opening new research directions with modern X-ray sources and Mössbauer isotopes.
We report the enhancement of individual harmonics generated at a relativistic ultra-steep plasma vacuum interface. Simulations show the harmonic emission to be due to the coupled action of two high velocity oscillations -- at the fundamental ωL\omega_L and at the plasma frequency ωP\omega_P of the bulk plasma. The synthesis of the enhanced harmonics can be described by the reflection of the incident laser pulse at a relativistic mirror oscillating at ωL\omega_L and ωP\omega_P.
Heavy-ion storage rings have relatively large momentum acceptance which allows for multiple ion species to circulate at the same time. This needs to be considered in radioactive decay measurements of highly charged ions, where atomic charge exchange reactions can significantly alter the intensities of parent and daughter ions. In this study, we investigate this effect using the decay curves of ion numbers in the recent 205^{205}Tl81+^{81+} bound-state beta decay experiment conducted using the Experimental Storage Ring at GSI Darmstadt. To understand the intricate dynamics of ion numbers, we present a set of differential equations that account for various atomic and nuclear reaction processes-bound-state beta decay, atomic electron recombination and capture, and electron ionization. By incorporating appropriate boundary conditions, we develop a set of differential equations that accurately simulate the decay curves of various simultaneously stored ions in the storage ring: 205^{205}Tl81+^{81+}, 205^{205}Pb81+^{81+}, 205^{205}Pb82+^{82+}, 200^{200}Hg79+^{79+}, and 200^{200}Hg80+^{80+}. Through a quantitative comparison between simulations and experimental data, we provide insights into the detailed reaction mechanisms governing stored heavy ions within the storage ring. Our approach effectively models charge-changing processes, reduces the complexity of the experimental setup, and provides a simpler method for measuring the decay half-lives of highly charged ions in storage rings.
Strong-field QED (SFQED) probability rates in the locally monochromatic approximation (LMA) have become an indispensable tool for simulations of processes like gamma-ray emission or electron-positron pair production in laser-particle collisions. We revisit the LMA derivation and explicitly demonstrate that it is based on the separation of time scales, neglection of the long-range interference effects and subsequent averaging over the cycle scale. Doing so, we obtain unambiguously LMA rates for arbitrary polarizations of the plane wave background. Additionally, we partially restore the finite bandwidth effects that are lost in the LMA derivation. The bandwidth-restored result we refer to as the LMA+^+ and show that it agrees with the full SFQED predictions better than the standard LMA. We use LMA+^+ to address previously inaccessible observables and formulate a new limitation on the applicability of locally monochromatic approximations in general. We provide analytical results for the angular-integrated LMA+^+ probability rate and the fully differential probability that account for the finite bandwidth effects.
Ghost imaging (GI) forms images from intensity-correlation data collected by a single-pixel detector, decoupling illumination and sensing. Since its quantum-photon origins, the technique has evolved through classical pseudothermal, computational and deep-learning variants to span an unprecedented spectral range--from extreme-ultraviolet (XUV) to terahertz (THz) waves and even matter waves. This review traces that evolution, highlighting how wavelength dictates modulators, detectors and propagation physics and, in turn, the attainable penetration depth, resolution and dose. We survey X-ray/XUV implementations that deliver low-damage microscopy, visible/near-IR systems that achieve video-rate lidar through fog and water, mid-IR platforms that extract molecular fingerprints in photon-starved conditions, and THz schemes that provide non-destructive inspection of concealed structures. These advances collectively position multi-wavelength GI as a versatile, low-dose alternative wherever conventional focal-plane arrays falter.
Creating a plasma dominated by strong-field QED (SFQED) effects is a major goal of new multi-PW laser facilities. This is motivated by the fact that the fundamental dynamics of such plasmas is poorly understood and plays an important role in the electrodynamics of extreme astrophysical environments such as pulsar magnetospheres. The most obvious observable for which such a regime has been reached is the production of a bright flash of x-rays, but distinguishing this from other sources of hard x-rays (e.g., bremsstrahlung) is a major challenge. Here we show that the photons from the X-ray flash are highly polarised, as compared to the unpolarised background, i.e., polarisation is an indicator that the SFQED plasma has really produced. For a laser of intensity 102110^{21} Wcm2^{-2} impinging on a solid Al target, the photons of the flash with energy >10>10\thinspace keV are >65%>65\% polarised.
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