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High-harmonic generation (HHG) is used as a source for various imaging applications in the extreme ultraviolet spectral range. It offers spatially coherent radiation and unique elemental contrast with the potential for attosecond time resolution. The unfavorable efficiency scaling to higher photon energies prevented the imaging application in the soft X-ray range so far. In this work we demonstrate the feasibility of using harmonics for imaging in the water window spectral region (284$\,$eV to 532$\,$eV). We achieve nondestructive depth profile imaging in a heterostructure by utilizing a broadband and noise-resistant technique called soft X-ray Coherence Tomography (SXCT) at a high-flux lab-scale HHG source. SXCT is derived from Optical Coherence Tomography, a Fourier based technique, that can use the full bandwidth of the source to reach an axial resolution of 12$\,$nm in this demonstration. The employed source covers the entire water window, with a photon flux exceeding 10$^\text{6}\,$photons/eV/s at a photon energy of 500$\,$eV. We show local cross sections of a sample consisting of Aluminium oxide and Platinum layers of varying thickness on a Zinc oxide substrate. We validate the findings with scanning and transmission electron microscopy after preparation with focused ion beam milling., Comment: 9 pages, 4 figures, preprint

Strong-field ionization can induce electron motion in both the continuum and the valence shell of the parent ion. Here, we explore their interplay by studying laser-induced electron diffraction (LIED) patterns arising from interaction with the potentials of two-hole states of the xenon cation. The quantitative rescattering theory is used to calculate the corresponding photoelectron momentum distributions, providing evidence that the spin-orbit dynamics could be detected by LIED. We identify the contribution of these time-evolving hole states to the angular distribution of the rescattered electrons, particularly noting a distinct change along the backward scattering angles. We benchmark numerical results with experiments using ultrabroad and femtosecond laser pulses centered at \SI{3100}{nm}.

Non-destructive cross-sectional characterization of materials systems with a resolution in the nanometer range and the ability to allow for time-resolved in-situ studies is of great importance in material science. Here, we present such a measurements method, extreme ultraviolet coherence tomography (XCT). The method is non-destructive during sample preparation as well as during the measurement, which is distinguished by a negligible thermal load as compared to electron microscopy methods. Laser-generated radiation in the extreme ultraviolet (XUV) and soft x-ray range is used for characterization. The measurement principle is interferometric and the signal evaluation is performed via an iterative Fourier analysis. The method is demonstrated on the metallic material system Al-Al$_2$Cu and compared to electron and atomic force microscopy measurements. We also present advanced reconstruction methods for XCT which even allow for the determination of the roughness of outer and inner interfaces., Comment: First two authors contributed equally to this work and are ordered alphabetically. 14 pages

Above-treshold ionization (ATI) by femtosecond laser pulses centered at 515\,nm is studied for a gas mixture containing the Van-der-Waals complex Ar-H$_2$O. By detecting photoions and -electrons in coincidence, the ATI spectra for Ar, Ar$_2$, \HHO, and Ar-\HHO are discerned and measured simultaneously. Using an intensity-scanning technique, we observe the red-shift of the ATI spectra as a function of the laser intensity. The intensity-dependent shift of the ATI peak positions observed for Ar-H$_2$O and H$_2$O match but significantly differ from the ones measured for Ar and Ar$_2$. This indicates that the photoelectron is emitted from the \HHO site of the complex and the vertical ionization potential of Ar-H$_2$O is determined as $(12.4 \pm 0.1)$\,eV. For resacttered electrons, however, an enhancement of high-order ATI is observed for Ar-H$_2$O, as compared to H$_2$O, suggesting that the relatively large Ar atom acts as a scattering center, which influences the ionization dynamics., Comment: 8 pages, 7 figures

Correlative microscopy is a powerful technique that combines the advantages of multiple imaging modalities to achieve a comprehensive understanding of investigated samples. For example, fluorescence microscopy provides unique functional contrast by imaging only specifically labeled components, especially in biological samples. However, the achievable structural information on the sample in its full complexity is limited. Here, the intrinsic label-free carbon contrast of water window soft X-ray microscopy can complement fluorescence images in a correlative approach ultimately combining nanoscale structural resolution with functional contrast. However, soft X-ray microscopes are complex and elaborate, and typically require a large-scale synchrotron radiation source due to the demanding photon flux requirements. Yet, with modern high-power lasers it has become possible to generate sufficient photon flux from laser-produced plasmas, thus enabling laboratory-based setups. Here, we present a compact table-top soft X-ray microscope with an integrated epifluorescence modality for 'in-situ' correlative imaging. Samples remain in place when switching between modalities, ensuring identical measurement conditions and avoiding sample alteration or destruction. We demonstrate our new method by multimodal images of several exemplary samples ranging from nanoparticles to various multicolor labeled cell types. A structural resolution of down to 50 nm was reached., Comment: 15 pages, 8 figures, preprint

We study the perspectives of measuring the phenomenon of vacuum birefringence predicted by quantum electrodynamics using an x-ray free-electron laser (XFEL) alone. We devise an experimental scheme allowing the XFEL beam to collide with itself under a finite angle, and thus act as both pump and probe field for the effect. The signature of vacuum birefringence is encoded in polarization-flipped signal photons to be detected with high-purity x-ray polarimetry. Our findings for idealized scenarios underline that the discovery potential of solely XFEL-based setups can be comparable to those involving optical high-intensity lasers. For currently achievable scenarios, we identify several key details of the x-ray optical ingredients that exert a strong influence on the magnitude of the desired signatures., Comment: 26 pages, 2 figures; matches journal version

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

Linear polarization analysis of hard x-rays is employed to probe electronic anisotropies in metal-containing complexes with very high selectivity. We use the pronounced linear dichroism of nuclear resonant x-ray scattering to determine electric field gradients in an iron(II) containing compound as they evolve during a temperature-dependent high-spin/low-spin phase transition. This method constitutes a novel approach to analyze changes in the electronic structure of metal-containing molecules as function of external parameters or stimuli. The polarization selectivity of the technique allows us to monitor defect concentrations of electronic valence states across phase transitions. This opens new avenues to trace electronic changes and their precursors that are connected to structural and electronic dynamics in the class of metal compounds ranging from simple molecular solids to biological molecules., Comment: 6 pages, 4 figures

We report on an experimental and theoretical study of the ionization-fragmentation dynamics of argon dimers in intense few-cycle laser pulses with a tagged carrier-envelope phase. We find that a field-driven electron transfer process from one argon atom across the system boundary to the other argon atom triggers sub-cycle electron-electron interaction dynamics in the neighboring atom. This attosecond electron-transfer process between distant entities and its implications manifest themselves as a distinct phase-shift between the measured asymmetry of electron emission curves of the $\text{Ar}^{+}+\text{Ar}^{2+}$ and $\text{Ar}^{2+}+\text{Ar}^{2+}$ fragmentation channels. Our work discloses a strong-field route to controlling the dynamics in molecular compounds through the excitation of electronic dynamics on a distant molecule by driving inter-molecular electron-transfer processes.

We establish a generalized picture of the phase-sensitivity of laser-induced directional bond-breaking using the H$_2$ molecule as the example. We show that the well-known proton ejection anisotropy measured with few-cycle pulses arises as an amplitude-modulation of an intrinsic anisotropy that is sensitive to the laser phase at the ionization time and determined by the molecule's electronic structure. Our work furthermore reveals a strong electron-proton correlation that may open up a new approach to experimentally accessing the laser-sub-cycle intramolecular electron dynamics also in large molecules.

High-brilliance synchrotron radiation sources have opened new avenues for X-ray polarization analysis that go far beyond conventional polarimetry in the optical domain. With linear X-ray polarizers in a crossed setting polarization extinction ratios down to 10$^{-10}$ can be achieved. This renders the method sensitive to probe tiniest optical anisotropies that would occur, for example, in strong-field QED due to vacuum birefringence and dichroism. Here we show that high-purity polarimetry can be employed to reveal electronic anisotropies in condensed matter systems with utmost sensitivity and spectral resolution. Taking CuO and La$_2$CuO$_4$ as benchmark systems, we present a full characterization of the polarization changes across the Cu K-absorption edge and their separation into dichroic and birefringent contributions. At diffraction-limited synchrotron radiation sources and X-ray lasers, where polarization extinction ratios of 10$^{-12}$ can be achieved, our method has the potential to assess birefringence and dichroism of the quantum vacuum in extreme electromagnetic fields., Comment: 10 pages, 4 figures, 13 pages supplemental material (4 figures)

Using a three-dimensional semiclassical method, we theoretically investigate frustrated double ionization (FDI) of Ar atoms subjected to strong laser fields. The double-hump photoelectron momentum distribution generated from FDI observed in a recent experiment [S. Larimian et al., Phys. Rev. Research 2, 013021 (2020)] is reproduced by our simulation. We confirm that the observed spectrum is due to recollision. The laser intensity dependence of FDI is investigated. We reveal that the doubly excited states of Ar atoms and excited states of Ar+ are the dominant pathways for producing FDI at relatively low and high intensities, respectively. Our work demonstrates that at modest intensities, FDI is a general strong-field physical process accompanied with nonsequential double ionization and it is an important consequence of recollision.

We report on the unambiguous observation of the sub-cycle ionization bursts in sequential strong-field double ionization of H$_2$ and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase in combination with multi-particle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state specific Coulomb-distortions on emitted electrons in polyatomic molecules., Comment: 5 pages + Supplemental material

We introduce and experimentally demonstrate a method, where the two intrinsic time scales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photo-electron photo-ion coincidence experiment. In our experiment, elliptically polarized, 750~nm, 4.5~fs laser pulses were focused to an intensity of $9\times10^{14}\mathrm{W/cm}^2$ onto H$_2$. Using coincidence imaging, we directly observe the nuclear wavepacket evolving on the \ssg{} state of H$_2^+$ during its first roundtrip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

We investigate dissociative single and double ionization of HeH+ induced by intense femtosecond laser pulses. By employing a semi-classical model with nuclear trajectories moving on field-dressed surfaces and ionization events treated as stochastical jumps, we identify a strong-field mechanism wherein the molecules dynamically align along the laser polarization axis and stretch towards a critical internuclear distance before getting dissociative ionized. As the tunnel-ionization rate is greater for larger internuclear distance and for aligned samples, ionization is enhanced. The strong dynamical rotation is traced back to a maximum in the parallel component of the internuclear-distance-dependent polarizability tensor. Qualitative agreement with our experimental observations is found. Finally the criteria for observing the isotope effect for the ion angular distribution is discussed., Comment: 7 pages

With the emergence of high-repetition-rate few-cycle laser pulse amplifiers, aimed at investigating ultrafast dynamics in atomic, molecular and solid state science, the need for ever faster carrier-envelope phase (CEP) detection and control has arisen. Here we demonstrate a high speed, continuous, every-single-shot measurement and fast feedback scheme based on a stereo above-threshold ionization time-of-flight spectrometer capable of detecting the CEP and pulse duration at a repetition rate of up to 400 kHz. This scheme is applied to a 100 kHz optical parametric chirped pulse amplification (OPCPA) few-cycle laser system, demonstrating improved CEP stabilization and allowing for CEP tagging.

Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today. Based on electron back-scattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical cycle time resolution. Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared laser pulse. The observed optical phase deviates substantially from the monochromatic Gouy phase - exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser-matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry, ophthalmological optical coherence tomography and light-wave electronics., Comment: See journal reference for supplementary material

Ionization of an atom or molecule by a strong laser field produces sub-optical cycle wave packets whose control has given rise to attosecond science. The final states of the wave packets depend on ionization and deflection by the laser field, which are convoluted in conventional experiments. Here, we demonstrate a technique enabling efficient electron deflection, separate from the field driving strong-field ionization. Using a mid-infrared deflection field permits one to distinguish electron wave packets generated at different field maxima of an intense few-cycle visible laser pulse. We utilize this capability to trace the scattering of low-energy electrons driven by the mid-infrared field. Our approach represents a general technique for studying and controlling strong-field ionization dynamics on the attosecond time scale., Comment: 5 Pages, 4 figures

We experimentally demonstrate robust selective excitation and attenuation of atomic Rydberg level populations in sodium vapor (Na I) using intense laser pulses in the strong field limit ($> 10^{12} W/cm^{2}$). The coherent control of the atomic population and related ionization channels is realized for intensities above the over-the-barrier ionization intensity. A qualitative model predicts that this strong field coherent control arises through the manifestation of a Freeman resonance., Comment: 7 pages, 6 figures

Spin effects in above-threshold ionization of hydrogenlike highly charged ions in super-strong laser fields are investigated. Spin-resolved ionization rates in the tunneling regime are calculated by employing two versions of a relativistic Coulomb-corrected strong-field approximation (SFA). An intuitive simple-man model is developed which explains the derived scaling laws for spin-flip and spin-asymmetry effects. The intuitive model as well as our ab initio numerical simulations support the analytical results for the spin effects obtained in the dressed SFA where the impact of the laser field on the electron spin evolution in the bound state is taken into account. In contrast, the standard SFA is shown to fail in reproducing spin effects at ionization even at a qualitative level. The anticipated spin-effects are expected to be measurable with modern laser techniques combined with an ion storage facility., Comment: 5 pages, 2 figures

The control of light-matter interaction at the quantum level usually requires coherent laser fields. But already an exchange of virtual photons with the electromagnetic vacuum field alone can lead to quantum coherences, which subsequently suppress spontaneous emission. We demonstrate such spontaneously generated coherences (SGC) in a large ensemble of nuclei operating in the x-ray regime, resonantly coupled to a common cavity environment. The observed SGC originates from two fundamentally different mechanisms related to cooperative emission and magnetically controlled anisotropy of the cavity vacuum. This approach opens new perspectives for quantum control, quantum state engineering and simulation of quantum many-body physics in an essentially decoherence-free setting., Comment: 5 pages, 3 figures

Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wavepackets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of pre-determining fragmentation and isomerization reactions in polyatomic molecules on sub-femtosecond time-scales.

We show experimentally that XUV radiation is produced when a laser pulse is Thomson backscattered from sheets of relativistic electrons which are formed at the rear-surface of a foil irradiated on its front side by a high-intensity laser. An all-optical setup is realized using the Jena Titanium:Sapphire TW laser system (JETI). The main pulse is split into two pulses: one to accelerate electrons from thin aluminum foil targets to energies of the order of some MeV and the other, counterpropagating probe pulse is Thomson-backscattered off these electrons when they exit the target rear side. The process produced photons within a wide spectral range of some tens of eV as a result of the broad electron energy distribution. The highest scattering intensity is observed when the probe pulse arrives at the target rear surface 100 fs after the irradiation of the target front side by the pump pulse, corresponding to the maximum flux of hot electrons at the interaction region. These results can provide time-resolved information about the evolution of the rear-surface electron sheath and hence about the dynamics of the electric fields responsible for the acceleration of ions from the rear surface of thin, laser-irradiated foils., Comment: resubmitted to New Journal of Physics

Harmonic generation in the limit of ultra-steep density gradients is studied experimentally. Observations demonstrate that while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale-lengths ($L_p/\lambda < 1$) the absolute efficiency of the harmonics declines for the steepest plasma density scale-length $L_p \to 0$, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of harmonics reflected from the laser driven plasma surface via the Relativistic Oscillating Mirror (ROM) was estimated to be in the range of 10^{-4} - 10^{-6} of the laser pulse energy for photon energies ranging from 20-40 eV, with the best results being obtained for an intermediate density scale-length.

We report on a reflective wave-plate system utilizing phase-shifting mirrors (PSM) for a continuous variation of elliptical polarization without changing the beam position and direction. The scalability of multilayer optics to large apertures and the suitability for high-intensity broad-bandwidth laser beams make reflective wave-plates an ideal tool for experiments on relativistic laser-plasma interaction. Our measurements confirm the preservation of the pulse duration and spectrum when a 30-fs Ti:Sapphire laser beam passes the system.

We consider a two-photon transition in a specific ladder system driven by a chirped laser pulse. In the weak field limit, we find that the excited state probability amplitude arises due to interference of multiple quantum paths which are weighted by quadratic phase factors. The excited state population has the form of a Gauss sum which plays a prominent role in number theory.

We demonstrate experimentally the generation of square and hexagonal lattices of optical vortices and reveal their propagation in a saturable nonlinear medium. If the topological charges of the vortices are of the same sign the lattice exhibit rotation, while if alternative, we observe stable propagation of the structures. In the nonlinear medium the lattices induce periodic modulation of the refractive index. Diffraction of a probe beam by this nonlinearity-induced periodic structure is observed., Comment: 8 pages, 6 figures, accepted JOSA B