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Within a joint experimental and theoretical research project, single photoionization of He-like B$^{3+}$ ions was investigated in the energy range from approximately 250 to 1200~eV. With the parent-ion beam in the experiment containing both $1s^2~^1S$ ground-state and $1s2s~^3S$ metastable B$^{3+}$ ions, double-core-hole resonances could be studied. Two series of hollow resonant states were observed, one populated by $K$-shell double excitation $1s^2~^1S \to 2\ell n\ell'~^1P$ ($\ell=s,p$; $\ell'=p,s$; $n=2,3,..,6$) at photon energies up to about 510~eV, the other by $K$-shell single excitation $1s2s~^3S \to 2\ell n\ell'~^3P$ ($\ell=s,p$; $\ell'=p,s$; $n=2,3,..,6$) at energies up to about 310~eV. High resolving powers up to approximately 29000 were achieved. The relativistic many-body perturbation theory was employed to determine level-to-level cross sections for $K$-shell excitation with subsequent autoionization. The resonance energies were calculated with inclusion of electron correlation and radiative contributions. The energy uncertainties of the most prominent resonances are estimated to be below $\pm 1$ meV. Convergent close coupling (CCC) calculations provided single-photoionization cross sections $\sigma_{34}$ for B$^{3+}$ including the resonant and non-resonant channels. Apart from the resonances, $\sigma_{34}$ is dominated by direct ionization in the investigated energy range. The contribution $\sigma_{34}^{\mathrm{dir}}$ of the latter process to $\sigma_{34}$ was separately determined by using the random-phase approximation with exchange and relativistic Hartree-Fock calculations which agree very well with previous calculations. Direct ionization of one electron accompanied by excitation of the remaining electron was treated by the CCC theory and found to be a minor contribution to $\sigma_{34}$., Comment: 27 pages, 19 figures

Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final states of the target. Resonant spectral features are typically associated with sharp variations in the photoionization phase, providing an opportunity for laser-assisted interferometric techniques to measure this phase and convert it into a photoemission time delay. This time delay offers a precise characterization of the timing of the photoemission process. In this review, a unified approach to resonant photoionization is presented by examining the analytic properties of ionization amplitude in the complex photoelectron energy plane. This approach establishes a connection between the resonant photoemission time delay and the corresponding photoionization cross-section. Numerical illustrations of this method include: (i) giant or shape resonances, where the photoelectron is spatially confined within a potential barrier, (ii) Fano resonances, where bound states are embedded in the continuum, (iii) Cooper minima (anti-resonances) arising from kinematic nodes in the dipole transition matrix elements, and (iv) confinement resonances in atoms encapsulated within a fullerene cage. The second part of this review focuses on two-photon resonant ionization processes, where the photon energies can be tuned to a resonance in either the intermediate or final state of the atomic target. Our examples include one- or two-electron discrete excitations both below and above the ionization threshold. These resonant states are probed using laser-assisted interferometric techniques. Additionally, we employ laser-assisted photoemission to measure the lifetimes of several atomic autoionizing states., Comment: 33 pages, 18 figures

Two-photon atomic ionization driven by time-locked XUV and IR pulses allows to study dynamics of Fano resonances in time and energy domains. Different time evolution of the two interfering pathways leading to a Fano resonance can be exploited to turn the Fano profile of the two-photon XUV/IR ionization into a symmetric Gaussian once the directly ejected photoelectron leaves the parent ion and cannot any longer absorb an IR photon. This line shape transformation allows for the direct determination of the resonant lifetime from the spectroscopic measurements without need for an extremely fine energy resolution. Ubiquitous nature of Fano resonances makes this determination a universal tool in diverse quantum systems ranging from nuclei to nano-fabricated solids., Comment: 5 pages, 3 figures

High-order harmonics generation (HHG) is the only process that enables table-top-size sources of extreme-ultraviolet (XUV) light. The HHG process typically involves light interactions with gases or plasma-material phases that hinder wider adoption of such sources. This motivates the research in HHG from nanostructured solids. Here we investigate theoretically material platforms for HHG at the nanoscale using first-principle supercomputer simulations. We reveal that wide bandgap semiconductors, aluminium nitride AlN and silicon nitride SiN, are highly promising for XUV light generation when compared to one of the most common nonlinear nanophotonic material -- silicon. In our calculations we assume excitation with 100 fs pulse duration, 10^13 W/cm^2 peak power and 800 nm central wavelength. We demonstrate that in AlN material the interplay between the crystal symmetry and the incident light direction and polarization can enable the generation of both even and odd harmonics. Our results should advance the developments of high-harmonics generation of XUV light from nanostructured solids.

Let $w(\zeta)$ be a function analytic on $\mathbb D$, $|w(\zeta)|\le 1$. Let $|t_0|=1$. Assume that $w$ and $w'$ have nontangential boundary values $w_0$ and $w'_0$, respectively, at $t_0$, $|w_0|=1$. Then (Carath\'eodory - Julia) $t_0\dfrac{w'_0}{w_0}\ge 0$. The goal of this paper is to obtain a lower bound on this ratio if $w$ is character-automorphic with respect to a Fuchsian group (Theorem 6.1)

We study formation and evolution of the electron wave-packets in the process of strong field ionization of various atomic targets. Our study is based on reformulating the problem in terms of conditional amplitudes, i.e., the amplitudes describing outcomes of measurements of different observables provided that the electron is found in the ionized state after the end of the pulse. By choosing the electron coordinate as such an observable, we were able to define unambiguously the notion of the ionized wave-packets and to study their formation and spread. We show that the evolution of the ionized wave packets obtained in this way follows closely the classical trajectories at the initial stages of evolution providing an {\it ab initio} quantum-mechanical confirmation of the basic premises of the Classical Monte Carlo Calculations approach. At the later stages of evolution the picture becomes more complicated due to the wave packets' spread and due to interference of wave packets originating from different field maxima. Our approach also allowed us to obtain information about the coordinate and velocity electron distributions at the tunnel exit.

A strong helicity dependence of reconstruction of attosecond bursts by beating of two-photon transitions (RABBITT) with circularly polarized XUV and IR pulses was reported by Han et al. [Nature Physics 19, 230 and arXiv 2302.04137 (2023)]. They attributed a circular dichroic phase in RABBITT to the helical structure of the photoelectron wave packets in the final state. We exploit this effect to determine the magnitude and phase of two-photon XUV+IR ionization amplitudes. In s-electron targets (H, He, Li), such a determination is fully ab initio and free from any instrumental limitations. In heavier noble gases like Ar, characterization of two-photon ionization amplitudes can be made from the circular dichroic phase with minimal and very realistic assumptions., Comment: 6 pages, 4 figures

The mutual angle formed by the non-collinear polarization axes of two laser pulses is used to control two-photon XUV+IR ionization of noble gas atoms in the process of reconstruction of attosecond bursts by beating of two-photon transitions (RABBITT). The magnitude and the phase of this beating can be controlled very efficiently by the mutual polarization angle. The mechanism of this control can be understood within the lowest order perturbation theory and the soft photon approximation. We offer a very sensitive test on the polarization control of the angular dependent RABBITT process which validates our numerical simulations. We apply this test to the recent theoretical and experimental results of polarization controlled RABBITT on hydrogen and helium by Boll et al., Phys. Rev. A 107, 043113 (2023) and heavier noble gases by Jiang et~al., Nature Comms. 13, 5072 (2022)., Comment: 15 pages, 7 figures

Determination and interpretation of Wigner-like photoionisation delays is one of the most active fields of attosecond science. Previous results have suggested that large photoionisation delays are associated with structured continua, but a quantitative relation between photoionisation cross sections and time delays has been missing. Here, we derive a Kramers-Kronig-like relation between these quantities and demonstrate its validity for (anti)resonances. This new concept defines a topological analysis, which rationalises the sign of photoionisation delays and thereby sheds new light on a long-standing controversy regarding the sign of the photoionisation delay near the Ar 3s Cooper minimum. Our work bridges traditional photoionisation spectroscopy with attosecond chronoscopy and offers new methods for analysing and interpreting photoionisation delays.

Shape resonances in photoionization of atoms and molecules arise from a particular geometry of the ionic potential which traps the receding photoelectron in a quasi-bound state in a particular partial wave. This mechanism allows us to connect the photoionization cross section in the resonant region with the photoelectron scattering phase in this partial wave by a simple formula $\sigma \propto \sin^2\delta_\ell$. Due to this relation, the phase $\delta_\ell$ can be extracted from an experimentally known cross section and then converted to the photoelectron group delay (Wigner time delay) $\tau_{\rm W} = \partial \delta_\ell/\partial E$ which is measurable by recently developed laser interferometric techniques. Such a direct connection of the photoionization cross section and the time delay is a fundamental property of shape resonances which provides a comprehensive test of novel measurements against a large body of older synchrotron data., Comment: 6 pages, 4 figures

Theoretical investigation is conducted of high-order harmonic generation (HHG) in silicon thin films to elucidate the effect of light propagation in reflected and transmitted waves. The first-principles simulations are performed of the process in which an intense pulsed light irradiates silicon thin films up to 3 $\mu$m thickness. Our simulations are carried within the time-dependent density functional theory (TDDFT) with the account of coupled dynamics of the electromagnetic fields and the electronic motion. It was found that the intensity of transmission HHG gradually decreases with the thickness, while the reflection HHG becomes constant from a certain thickness. Detailed analyses show that transmission HHG have two origins: the HHG generated near the front edge and propagating to the back surface, and that generated near the back edge and emitted directly. The dominating mechanism of the transmission HHG is found to depend on the thickness of the thin film and the frequency of the HHG. At the film thickness of 1 $\mu$m, the transmission HHG with the frequency below 20 eV is generated near the back edge, while that with the frequency above 20 eV is generated near the front edge and propagates from there to the back surface., Comment: 11 pages, 8 figures

We study orientation and two-center interference effects in attosecond time-resolved photoionization of the H$_2$ molecule. Time resolution of XUV ionization of H$_2$ is gained through the phase retrieval capability of attosecond angular streaking demonstrated earlier by Kheifets {\em et al} [arXiv:2202.06147 (2022)]. Once applied to H$_2$, this technique delivers an anisotropic phase and time delay which both depend sensitively on the molecular axis orientation. In addition, the photoelectron momentum distribution displays a very clear two-center interference pattern. When the interference formula due to Walter and Briggs [J. Phys. B {\bf 32} 2487 (1999)] is applied, an effective photoelectron momentum appears to be greater than the asymptotic momentum at the detector. This effect is explained by a molecular potential well surrounding the photoemission center., Comment: 8 pages, 7 figures. arXiv admin note: text overlap with arXiv:2202.06147

We demonstrate an accurate phase retrieval of XUV atomic ionization by streaking the photoelectron in a circularly polarized IR laser field. The streaking phase can then be converted to the atomic time delay containing the Wigner and continuum-continuum components. Our demonstration is based on a numerical solution of the time-dependent Schr\"odinger equation. We test this technique using the hydrogen atom ionized by an isolated attosecond XUV pulse across a wide range of photon energies. In parallel, we run a series of RABBITT simulations and demonstrate equivalence of the phase and timing information provided by the two methods. This validates the proposed technique and makes it a useful tool that can be applied to a broad range of atomic and molecular targets exposed to XUV radiation from novel free-electron laser sources., Comment: 7 pages, 5 figures

We study high order harmonics generation (HHG) in crystalline silicon and diamond subjected to near and mid-infrared laser pulses. We employ time-dependent density functional theory and solve the time-dependent Kohn-Sham equation in the single-cell geometry. We demonstrate that clear and clean HHG spectra can be generated with careful selection of the pulse duration. In addition, we simulate dephasing effects in a large silicon super-cell through displacement of atomic positions prepared by a molecular dynamics simulation. We compare our results with the previous calculations by Floss et al. [arXiv:1705.10707] [Phys. Rev. A 97, 011401(R) (2018)] on Diamond at 800 nm and by Tancogne-Dejean et al. [arXiv:1609.09298] [Phys. Rev. Lett. 118, 087403 (2017)] on Si at 3000 nm., Comment: Accepted to Phys. Rev. B

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in finite samples. The findings are illustrated empirically in an analysis of fiscal sustainability of the US government over the post-war period.

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps faithfully the discrete energy levels and the corresponding oscillator strengths. We demonstrate this sensitivity by considering the Ne atom driven by the combination of the XUV and IR pulses at the fundmanetal laser frequency in the 800 and 1000~nm ranges., Comment: 8 pages, 5 figures

Photon exchange due to nuclear bremsstrahlung during nuclear collisions can cause Coulomb excitation in the projectile and the target nuclei. The corresponding process originated in nuclear timescales can also be observed in atomic phenomenon experimentally if it delayed by at least with an attosecond or longer timescales. We have found that this happens due to a mechanism involving the Eisenbud-Wigner-Smith time delay process. We have estimated photoionization time delays in atomic collisions utilizing the nonrelativistic version of random phase approximation with exchange and Hartree-Fock methods. We present three representative processes in which we can observe the phenomena in attosecond timescales even though they originate from excitations in the zeptosecond timescales. Thus the work represents an investigation of parallels between two neighboring areas of physics. Furthermore the present work suggests new possibilities for atomic physics research near the Coulomb barrier energy, where the laser is replaced by nuclear bremsstrahlung., Comment: 6 pages, 4 figures

We study propagation effects due to the finite speed of light in ionization of extended systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shr\"odinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the \Hp molecular ion and the \Ne dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily affordable than an earlier synchrotron measurement by Grundmann {\em et al} [Science 370, 339 (2020)]

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) can become resonant with a discrete atomic level either in the intermediate or the final continuous states. Experimental observations of the former [Phys. Rev. Lett. 104, 103003 (2010)] or latter [Nat. Commun. 7, 10566 (2016)] cases revealed modification of only those parts of the photoelectron spectrum that overlapped directly with the resonance. In the lithium atom and other members of the alkali metal family, the valence shell $ns\to np$ transition to the intermediate RABBITT state affects the whole photoelectron spectrum in the final state. The strong additional resonant channel modifies entirely the ionization dynamics and opens direct access to the resonant phase of the two-photon transitions which is common for various single and multiple electron ionization processes. Elucidation of this phase has wider implications for strongly resonant laser-matter interaction., Comment: 5 pages, 5 figures

We report on kinematically complete measurements and ab initio non-perturbative calculations of double ionization of He and H2 by a single 800 eV circularly polarized photon. We confirm the quasifree mechanism of photoionization for H2 and show how it originates from the two-electron cusp in the ground state of a two-electron target. Our approach establishes a new method for mapping electrons relative to each other and provides valuable insight into photoionization beyond the electric-dipole approximation., Comment: 7 pages, 4 figures

Attosecond angular streaking, also known as the "attoclock", employs a short elliptically polarized laser pulse to tunnel ionize an electron from an atom or a molecule and to put a time stamp on this process by deflecting the photoelectron in the angular spatial direction. This deflection can be used to evaluate the time the tunneling electron spends under the classically inaccessible barrier and to determine whether this time is finite. In this review, we examine the latest experimental and theoretical findings and present a comprehensive set of evidence supporting the zero tunneling time scenario., Comment: 24 pages, 11 figures

Attosecond photoionization delays have mostly been interpreted within the single-particle approximation of multi-electron systems. The strong electron correlation between the photoionization channels associated with the 3p and 3s orbitals of argon presents an interesting arena where this single-particle approximation breaks down. Around photon energies of 42~eV, the 3s photoionization channel of argon experiences a ``Cooper-like" minimum, which is exclusively the result of inter-electronic correlations with the 3p shell. Photoionization delays around this ``Cooper-like" minimum have been predicted theoretically, but experimental verification has remained a challenge since the associated photoionization cross section is inherently very low. Here, we report the measurement of photoionization delays around the Cooper-like minimum that were acquired with the 100~kHz High-Repetition 1 laser system at the ELI-ALPS facility. We report relative photoionization delays reaching up to unprecedented values of 430 +/- 20~as, as a result of electron correlation. Our experimental results are in partial agreement with state-of-the-art theoretical results, but also demonstrate the need for additional theoretical developments.

We consider the process of high-order harmonics generation (HHG) in the xenon atom enhanced by the inter-shell correlation between the valence 5p and inner 4d shells. We derive the HHG spectrum from a numerical solution of the one-electron time-dependent Schr\"odinger equation multiplied by the enhancement factor taken as the photoionization cross-sections ratio calculated with and without the inter-shell correlation. Such a simplified approach is adequate to describe the experimental HHG spectrum reported by Shiner et al [Nat. Phys. 7, 464 (2011)] generated by a single color IR laser. Similarly, we find good agreement when applied to the two-color driven HHG spectra reported by Facciala et al [Phys. Rev. Lett. 117, 093902 (2016)].

Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schr\"odinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, we highlight a strong dependence of the width of the attoclock angular peak on the molecular orientation and attribute it to the two-center electron interference. This effect is further exemplified in the weakly bound neon dimer., Comment: 8 pages, 7 figures

We establish exact conditions for non triviality of all subspaces of the standard Hardy space in the upper half plane, that consist of character automorphic functions with respect to the action of a discrete subgroup of $SL_2(\mathbb R)$. Such spaces are natural objects in the context of the spectral theory of almost periodic differential operators and in asymptotics of approximations by entire functions. A naive idea: it should be completely parallel to the celebrated Widom characterization for Hardy spaces on Riemann surfaces with a minor modification, namely, one has to substitute the Green function of the domain with the Martin function. Basically, this is correct, but...

Smooth transition autoregressive models are widely used to capture nonlinearities in univariate and multivariate time series. Existence of stationary solution is typically assumed, implicitly or explicitly. In this paper we describe conditions for stationarity and ergodicity of vector STAR models. The key condition is that the joint spectral radius of certain matrices is below 1, which is not guaranteed if only separate spectral radii are below 1. Our result allows to use recently introduced toolboxes from computational mathematics to verify the stationarity and ergodicity of vector STAR models., Comment: Accepted to Econometric Reviews

The main content of this paper is Lectures 5 and 6 that continue lecture notes [20]. Content of Lectures 1-4 of [20] is reviewed for the reader's convenience in sections 1-4, respectively. It is shown in Lecture 5 how residual parts of the minimal unitary extensions, that correspond to solutions of the problem, yield some boundary properties of the coefficient matrix-function. These results generalize the classical Nevanlinna - Adamjan - Arov~- Krein theorem. Lecture 6 discusses how further properties of the coefficient matrices follow from denseness of certain sets in the associated function model spaces. The structure of the dense set reflects the structure of the problem data.

We demonstrate a clear similarity between attoclock offset angles and Rutherford scattering angles taking the Keldysh tunnelling width as the impact parameter and the vector potential of the driving pulse as the asymptotic velocity. This simple model is tested against the solution of the time-dependent Schr\"odinger equation using hydrogenic and screened (Yukawa) potentials of equal binding energy. We observe a smooth transition from a hydrogenic to 'hard-zero' intensity dependence of the offset angle with variation of the Yukawa screening parameter. Additionally we make comparison with the attoclock offset angles for various noble gases obtained with the classical-trajectory Monte Carlo method. In all cases we find a close correspondence between the model predictions and numerical calculations. This suggests a largely Coulombic origin of the attoclock offset angle and casts further doubt on its interpretation in terms of a finite tunnelling time.

We report on a kinematically complete measurement of double ionization of helium by a single 1100 eV circularly polarized photon. By exploiting dipole selection rules in the two-electron continuum state, we observed the angular emission pattern of electrons originating from a pure quadrupole transition. Our fully differential experimental data and companion ab initio nonperturbative theory show the separation of dipole and quadrupole contributions to photo-double-ionization and provide new insight into the nature of the quasifree mechanism., Comment: 5 Pages, 3 Figures

We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schr\"odinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy {\beta} parameter and Wigner time delay ${\tau}_W$ for the single XUV photon absorption which initiates the RABBITT process. Said {\beta} and ${\tau}_W$ parameters are compared with calculations in the random phase approximation with exchange (RPAE) which includes inter-shell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulation of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d-shell restricts the validity of the single active electron approximation to several tens of eV above the valence shell threshold.