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In this manuscript, we present a theoretical framework and its numerical implementation to simulate the out-of-equilibrium electron dynamics induced by the interaction of ultrashort laser pulses in condensed-matter systems. Our approach is based on evolving in real time the density matrix of the system in reciprocal space. It considers excitonic and nonperturbative light−matter interactions. We show some relevant examples that illustrate the efficiency and flexibility of the approach to describe realistic ultrafast spectroscopy experiments. Our approach is suitable for modeling the promising and emerging ultrafast studies at the attosecond time scale that aim at capturing the electron dynamics and the dynamical electron−electron correlations via X-ray absorption spectroscopy, G.C., M.M., and A.P. acknowledge Comunidad de Madrid through TALENTO Grant Ref 2017-T1/IND-5432 and 2021- 5A/IND-20959, Grants Ref RTI2018-097355-A-I00 and ref PID2021-126560NB-I00 (MCIU/AEI/FEDER, UE), and computer resources and assistance provided by Centro de Computación Científica de la Universidad Autónoma de Madrid (FI-2021-1-0032), Instituto de Biocomputación y Física de Sistemas Complejos de la Universidad de Zaragoza (FI-2020-3-0008), and Barcelona Supercomputing Center (FI2020-1-0005, FI-2021-2-0023, FI-2021-3-0019). J.J.P., J.J.E.-P., and A.J.U.-Á . acknowledge funding from Grant No. PID2019- 109539GB-C43 (MCIU/AEI/FEDER, UE), the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321), and the Generalitat Valenciana through Programa Prometeo/2021/01. F.M. acknowledges the MICIN project PID2019-105458RB-I00, the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2016-0686), and the “María de Maeztu” Programme for Units of Excellence in R&D (CEX2018-000805-M). R.E.F.S. acknowledges support from the fellowship LCF/BQ/PR21/11840008 from “La Caixa” Foundation (ID 100010434)

Recent developments in attosecond technology led to table-top x-ray spectroscopy in the soft x-ray range, thus uniting the element- and state-specificity of core-level x-ray absorption spectroscopy with the time resolution to follow electronic dynamics in real-time. We describe recent work in attosecond technology and investigations into materials such as Si, SiO2, GaN, Al2O3, Ti, and TiO2, enabled by the convergence of these two capabilities. We showcase the state-of-the-art on isolated attosecond soft x-ray pulses for x-ray absorption near-edge spectroscopy to observe the 3d-state dynamics of the semi-metal TiS2 with attosecond resolution at the Ti L-edge (460 eV). We describe how the element- and state-specificity at the transition metal L-edge of the quantum material allows us to unambiguously identify how and where the optical field influences charge carriers. This precision elucidates that the Ti:3d conduction band states are efficiently photo-doped to a density of 1.9 × 1021 cm−3. The light-field induces coherent motion of intra-band carriers across 38% of the first Brillouin zone. Lastly, we describe the prospects with such unambiguous real-time observation of carrier dynamics in specific bonding or anti-bonding states and speculate that such capability will bring unprecedented opportunities toward an engineered approach for designer materials with pre-defined properties and efficiency. Examples are composites of semiconductors and insulators like Si, Ge, SiO2, GaN, BN, and quantum materials like graphene, transition metal dichalcogens, or high-Tc superconductors like NbN or LaBaCuO. Exiting are prospects to scrutinize canonical questions in multi-body physics, such as whether the electrons or lattice trigger phase transitions.

The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle $\theta$ and its polarization by a multiple $\gamma\theta$ of that angle. These symmetries are generated by mixed angular momenta of the form $J_\gamma = L + \gamma S$ and they generally induce M\"obius-strip topologies, with the coordination parameter $\gamma$ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary $\gamma$, by exploiting the higher internal symmetry of 'bicircular' superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum $J_\gamma$, and we characterize the resulting optical polarization singularity using third-and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography., Comment: Submitted Manuscript, including a subset of the figures from the published Supplementary Information

[EN]Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light–matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses—from linear to circular—and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum., The authors are thankful for useful and productive conversations with E. Pisanty, C. Durfee, D. Hickstein, S. Alperin and M. Siemens. H.C.K. and M.M.M. graciously acknowledge support from the Department of Energy BES Award No. DE-FG02–99ER14982 for the experimental implementation, as well as a MURI grant from the Air Force Office of Scientific Research under Award No. FA9550–16–1–0121 for the theory. J.L.E., N.J.B. and Q.L.N. acknowledge support from National Science Foundation Graduate Research Fellowships (Grant No. DGE-1144083). C.H.-G., J.S.R. and L.P. acknowledge support from Junta de Castilla y León (SA046U16) and Ministerio de Economía y Competitividad (FIS2013–44174-P, FIS2016–75652-P). C.H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. L.R. acknowledges support from Ministerio de Educación, Cultura y Deporte (FPU16/02591). A.P. acknowledges support from the Marie Sklodowska-Curie Grant, Agreement No. 702565. We thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-AECT-2014–2–0085). This research made use of the high-performance computingresources of the Castilla y León Supercomputing Center (SCAYLE, www.scayle.es),financed by the European Regional Development Fund (ERDF). Certain commercial instruments are identified to specify the experimental study adequately. This does not imply endorsement by the National Institute of Standards and Technology (NIST) or that the instruments are the best available for the purpose.

Recent developments in attosecond technology led to tabletop X-ray spectroscopy in the soft X-ray range, thus uniting the element- and state-specificity of core-level x-ray absorption spectroscopy with the time resolution to follow electronic dynamics in real time. We describe recent work in attosecond technology and investigations into materials such as Si, SiO2, GaN, Al2O3, Ti, TiO2, enabled by the convergence of these two capabilities. We showcase the state-of-the-art on isolated attosecond soft x-ray pulses for x-ray absorption near edge spectroscopy (XANES) to observe the 3d-state dynamics of the semi-metal TiS2 with attosecond resolution at the Ti L-edge (460 eV). We describe how the element- and state-specificity at the transition metal L-edge of the quantum material allows to unambiguously identify how and where the optical field influences charge carriers. This precision elucidates that the Ti:3d conduction band states are efficiently photo-doped to a density of 1.9 x 10^21 cm^-3 and that the light-field induces coherent motion of intra-band carriers across 38% of the first Brillouin zone. Lastly, we describe the prospects with such unambiguous real-time observation of carrier dynamics in specific bonding or anti-bonding states and speculate that such capability will bring unprecedented opportunities towards an engineered approach for designer materials with pre-defined properties and efficiency. Examples are composites of semiconductors and insulators like Si, Ge, SiO2, GaN, BN, quantum materials like graphene, TMDCs, or high-Tc superconductors like NbN or LaBaCuO. Exiting are prospects to scrutinize canonical questions in multi-body physics such as whether the electrons or lattice trigger phase transitions., 5 figures

Recent techniques in x-ray free electron lasers allow the generation of highly coherent, intense x-ray pulses with time lengths on the order of femtoseconds. Here we explore the possibilities of using such x-ray pulses to control matter based on coherence. In particular we propose a theoretical scheme to perform stimulated Raman adiabatic passage in the x-ray regime by using inner-hole excited states. Numerical results in two well-known systems, the neon atom and the carbon monoxide molecule, show a robust control of population transfer. In the molecule, vibrational selectivity is achieved with femtosecond x-ray pulses. This work supports the possibility of using two-color x-ray pulses for coherent control.

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light–matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses—from linear to circular—and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Chemistry - a European journal 26(47), 10801 - 10810 (2020). doi:10.1002/chem.202001393, Time���resolved X���ray (Tr���XAS) and optical transient absorption (OTA) spectroscopy on the pico���microsecond timescale coupled with density functional theory calculations are applied to study the light���induced spin crossover processes of a Fe���based macrocyclic complex in solution. Tr���XAS analysis after light illumination shows the formation of a seven���coordinated high���spin quintet metastable state, which relaxes to a six���coordinated high���spin configuration before decaying to the ground state. Kinetic analysis of the macrocyclic complex reveals an unprecedented long���lived decay lifetime of approximately 42.6 ��s. Comparative studies with a non���macrocyclic counterpart illustrate a significantly shortened approximately 568���fold decay lifetime of about 75 ns, and highlight the importance of the ligand arrangement in stabilizing the reactivity of the excited state. Lastly, OTA analysis shows the seven���coordinated high���spin state to be formed within approximately 6.2 ps. These findings provide a complete understanding of the spin crossover reaction and relaxation pathways of the macrocyclic complex, and reveal the importance of a flexible coordination environment for their rational design., Published by Wiley-VCH, Weinheim

Free-electron lasers provide a source of x-ray pulses short enough and intense enough to drive nonlinearities in molecular systems. Impulsive interactions driven by these x-ray pulses provide a way to create and probe valence electron motions with high temporal and spatial resolution. Observing these electronic motions is crucial to understand the role of electronic coherence in chemical processes. A simple nonlinear technique for probing electronic motion, impulsive stimulated x-ray Raman scattering (ISXRS), involves a single impulsive interaction to produce a coherent superposition of electronic states. We demonstrate electronic population transfer via ISXRS using broad bandwidth (5.5eV full width at half maximum) attosecond x-ray pulses produced by the Linac Coherent Light Source. The impulsive excitation is resonantly enhanced by the oxygen 1s→2π^{*} resonance of nitric oxide (NO), and excited state neutral molecules are probed with a time-delayed UV laser pulse.

We report the use of time-resolved X-ray absorption spectroscopy in the ns-μs time scale to track the light induced two electron transfer processes in a multi-component photocatalytic system, consisting of [Ru(bpy)3](2+)/ a diiron(iii,iii) model/triethylamine. EXAFS analysis with DFT calculations confirms the structural configurations of the diiron(iii,iii) and reduced diiron(ii,ii) states.

The $1s\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}np$ Rydberg transitions below the $1s$ ionization thresholds of Kr and Xe are obscured in x-ray absorption spectra due to core-hole lifetime broadening. However, the $np$ spectator electrons associated with those resonances can affect the core-hole decay spectra. We report on ion charge-state distributions of Kr and Xe measured in coincidence with ${KL}_{2,3}$ ($K{\ensuremath{\alpha}}_{1,2}$), ${KM}_{2,3}$ ($K{\ensuremath{\beta}}_{1,3}$), and ${\mathrm{KN}}_{2,3}$ ($K{\ensuremath{\beta}}_{2}$) x-ray fluorescence as the incident x-ray energy is scanned through pre-edge resonances and ionization thresholds. The coincidence measurements select vacancy cascades that begin with a radiative transition that transfers $1s$ holes to the $2p$, $3p$, and $4p$ shells followed by emission of Auger electrons. We observe shifts of ion yields from higher to lower charge states that we attribute to $np$ spectator electrons. For the special case of ${\mathrm{Kr}}^{1+}$ that is produced in coincidence with $K{\ensuremath{\beta}}_{2}$ x rays, the ion yield decreases in the pre-edge region. This is attributed to production of neutral, metastable Kr $4{p}^{\ensuremath{-}1}np$ states that reduce the ${\mathrm{Kr}}^{1+}$ yield. Model fits to the x-ray absorption spectra are presented to show the lifetime broadened pre-edge resonances and ionization thresholds. High-level relativistic coupled-cluster calculations that treat relativistic, electron correlation, and wave function relaxation effects on the same footing obtain agreement with the experimental $1s$ ionization energies of Kr and Xe to $l2$ eV. The Xe $K$-edge x-ray absorption spectrum and ion charge-state distributions of ${\mathrm{XeF}}_{2}$ were also recorded. Excitation of the $7{\ensuremath{\sigma}}_{u}$ lowest unoccupied molecular orbital (LUMO) in ${\mathrm{XeF}}_{2}$ is observed in the pre-edge region. Our ab initio calculations find that the $6{p}_{z}$ Rydberg state is strongly perturbed by the presence of the $7{\ensuremath{\sigma}}_{u}$ LUMO. A fit to the measured LUMO, $6{p}_{x}$, $6{p}_{y}$, $6{p}_{z}$ Rydberg states, and ionization threshold is guided by the relativistic coupled-cluster calculations. The F ligands modify the valence electron charge distribution and result in a $\ensuremath{\sim}2.3$ eV chemical shift of the Xe $1s$ ionization energy relative to atomic Xe. Xe $1{s}^{\ensuremath{-}1}$ core-hole decay in ${\mathrm{XeF}}_{2}$ results in ionization of the F ligands and energetic fragmentation into atomic ions. Ion charge-state spectra of ${\mathrm{XeF}}_{2}$ were recorded in coincidence with x-ray fluorescence for excitation on the LUMO resonance and above the Xe $1s$ ionization threshold. For the ion time of flight spectra recorded on the LUMO resonance, the ${\mathrm{F}}^{q+}$ ($q=1$--4) peaks are split into two peaks along the linear polarization direction of the incident x-ray beam. This effect is attributed to spatial alignment of ${\mathrm{XeF}}_{2}$ molecules by resonant x-ray absorption, and the peak splittings are used to measure the F ion fragmentation energies following $K{\ensuremath{\alpha}}_{1,2}$, $K{\ensuremath{\beta}}_{1,3}$, and $K{\ensuremath{\beta}}_{2}$ x-ray fluorescence. We observe variations of the F ion charge state yields and fragmentation energies for the three fluorescence pathways that leave the molecule in different outer-shell hole states.

High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum Jγ, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge Jγ of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum., We thank T. Ruchon for helpful observations. E. P. acknowledges Cellex-ICFO-MPQ fellowship funding; E. P. and M. L. acknowledge the Spanish Ministry MINECO (National Plan 15 Grants: FISICATEAMO No. FIS2016-79508-P, SEVERO OCHOA No. SEV-2015-0522, FPI), European Social Fund, Fundació Cellex, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR1341 and CERCA/Program), ERC AdG OSYRIS, EU FETPRO QUIC, and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. A. P. acknowledges funding from Comunidad de Madrid through TALENTO Grant No. 2017-T1/IND-5432. J. S. R., L. P., and C. H.-G acknowledge support from Junta de Castilla y León (SA046U16) and Ministerio de Economía y Competitividad (FIS2013-44174-P, FIS2016-75652-P). C. H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation and Ministerio de Ciencia, Innovación y Universidades for a Ramón y Cajal contract (RYC-2017-22745), co-funded by the European Social Fund. L. R. acknowledges support from Ministerio de Educación, Cultura y Deporte (FPU16/02591). H. C. K. and M.M.M. acknowledge support from the Department of Energy BESAwardNo.DE-FG02–99ER14982, as well as aDARPATEE Award No. D18AC00017. We thankfully acknowledge thecomputer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-AECT-2014-2-0085). This research made use of the high-performance computing resources of the Castilla yLeón Supercomputing Center (SCAYLE), financed by the European Regional Development Fund (ERDF).

The new capacity of X-ray free-electron laser (XFEL) facilities to produce multi-color X-ray femtosecond pulses paves the way to explore ultrafast phenomena in matter induced by X-ray photons. In the present study, we exploit the site-selectivity and the high temporal resolution of a two-color X-ray femtosecond pump-probe sequence to investigate the isomerization of formamide. The pump pulse excites a particular atomic site in the molecule, while the probe pulse captures changes in the chemical environment at a remote atomic site. The response of the system is found to strongly depend on the nature of the excited site, and the core excitation provides selective control over chemical bond breaking. In particular, we show that the N1s → π* transition can induce the isomerization reaction in formamide and demonstrate the possibility to observe in real time hydrogen migration by measuring the chemical shifts with the X-ray probe pulse. This work opens a unique prospect for X-ray-induced photochemistry at XFEL facilities.

Topological materials are of interest to both fundamental science and advanced technologies, because topological states are robust with respect to perturbations and dissipation. Experimental detection of topological invariants is thus in great demand, but it remains extremely challenging. Ultrafast laser-matter interactions, and in particular high-harmonic generation (HHG), meanwhile, were proposed several years ago as tools to explore the structural and dynamical properties of various matter targets. Here we show that the high-harmonic emission signal produced by a circularly-polarized laser contains signatures of the topological phase transition in the paradigmatic Haldane model. In addition to clear shifts of the overall emissivity and harmonic cutoff, the high-harmonic emission shows a unique circular dichroism, which exhibits clear changes in behavior at the topological phase boundary. Our findings pave the way to understand fundamental questions about the ultrafast electron-hole pair dynamics in topological materials via non-linear high-harmonic generation spectroscopy., 9 pages including references, then 16 pages of Supplementary Material

A possible route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal and nanometer spatial resolution is to employ recolliding electrons as `probes'. The recollision process in molecules is, however, very challenging to treat using {\it ab initio} approaches. Even for the simplest diatomic systems, such as H$_2$, today's computational capabilities are not enough to give a complete description of the electron and nuclear dynamics initiated by a strong laser field. As a consequence, approximate qualitative descriptions are called to play an important role. In this contribution we extend the work presented in N. Su\'arez {\it et al.}, Phys.~Rev. A {\bf 95}, 033415 (2017), to three-center molecular targets. Additionally, we incorporate a more accurate description of the molecular ground state, employing information extracted from quantum chemistry software packages. This step forward allows us to include, in a detailed way, both the molecular symmetries and nodes present in the high-occupied molecular orbital. We are able to, on the one hand, keep our formulation as analytical as in the case of diatomics, and, on the other hand, to still give a complete description of the underlying physics behind the above-threshold ionization process. The application of our approach to complex multicenter - with more than 3 centers, targets appears to be straightforward., Comment: 45 pages, 14 Figures. arXiv admin note: text overlap with arXiv:1607.07560

Reports on progress in physics 82(11), 116001 - (2019). doi:10.1088/1361-6633/ab2bb1, This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum–continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60., Published by IOP Publ., Bristol

We report the light-induced electronic and geometric changes taking place within a heteroleptic CuI photosensitizer, namely [(xant)Cu(Me2 phenPh2 )]PF6 (xant=xantphos, Me2 phenPh2 =bathocuproine), by time-resolved X-ray absorption spectroscopy in the ps-μs time regime. Time-resolved X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) analysis enabled the elucidation of the electronic and structural configuration of the copper center in the excited state as well as its decay dynamics in different solvent conditions with and without triethylamine acting as a sacrificial electron donor. A three-fold decrease in the decay lifetime of the excited state is observed in the presence of triethylamine, showing the feasibility of the reductive quenching pathway in the latter case. A prominent pre-edge feature is observed in the XANES spectrum of the excited state upon metal to charge ligand transfer transition, showing an increased hybridization of the 3d states with the ligand p orbitals in the tetrahedron around the Cu center. EXAFS and density functional theory illustrate a significant shortening of the Cu-N and an elongation of the Cu-P bonds together with a decrease in the torsional angle between the xantphos and bathocuproine ligand. This study provides mechanistic time-resolved understanding for the development of improved heteroleptic CuI photosensitizers, which can be used for the light-driven production of hydrogen from water.

Novel perspectives of controlling molecular systems have recently arisen from the possibility of generating attosecond pulses in the ultraviolet regime and tailoring electron dynamics in its natural time scale. The cornerstone mechanism is the so-called charge migration, he production of a coherent charge transfer with subfemtosecond oscillations across a molecule. Typically, charge migration is induced by the ionization of valence molecular orbitals. However, recent technological developments allow the generation of attosecond pulses in the x-ray regime. In this case, the absorption of photons creates core-hole states. In light elements, core-hole states mainly decay by Auger processes that, driven by electron correlations, involve valence orbitals. We theoretically demonstrate in a fluoroacetylene molecule a double-hole charge migration triggered by attosecond core-electron photoionization, followed by Auger electron relaxations. This opens a new route for inducing with x rays charge transfer processes in the subfemtosecond time scale, This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement No. 702565, from Comunidad de Madrid through the TALENTO program with Reference No. 2017-T1/IND-5432, and from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences through Argonne National Laboratory under Contract No. DE-AC02-06CH11357. We acknowledge support from Junta de Castilla y León (Project No. SA046U16) and MINECO (Grant No. FIS2016- 75652-P). C.H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation

Vector beams are light beams with spatially variant polarization. During the last decade vector beams have become an indispensable tool in many areas of science and technology such as optical trapping, quantum memories, and quantum optics. In particular, radially and azimuthally polarized light beams are the paradigm of vector beams. Radial vector beams are especially interesting due to the non-vanishing longitudinal electric field component present in tightly focusing systems, which allows to sharply focus light below the diffraction limit. On the other hand, azimuthal vector beams can induce longitudinal magnetic fields with potential applications in spectroscopy and microscopy. However, the spectral limitations of the generation techniques of vector beams based on linear optics prevent their efficient generation in the extreme-ultraviolet (EUV) and x-ray regimes, which would further extend their applications down to the nanometric scale. High-order harmonic generation (HHG) is known as a unique non-perturbative frequency up-conversion process for the generation of coherent EUV and soft x-ray radiation. A remarkable aspect of HHG is its fully coherent nature, mapping the characteristics of the driving field to the high frequency spectral region and thus allowing to harness the angular momentum properties of the harmonic radiation through modifications of the driving field.In this work EUV vector beams are generated for the first time using HHG. To do so, an infrared fs radially polarized vector beam –generated with a s-waveplate – is focused into an argon gas target, whose atoms emit coherent EUV radiation through HHG. Our experimental and theoretical results demonstrate that HHG imprints the polarization state of the infrared beam, ranging from radial to azimuthal, into the higher frequency radiation. Our numerical simulations also demonstrate that the generated high-order harmonic beams can be synthesized into attosecond vector beams in the EUV/soft x-ray regime. Our proposal overcomes the state of the art limitations for the generation of vector beams far from the visible domain and could be applied in fields such as diffractive imaging, EUV lithography, or ultrafast control of magnetic properties.

Vortex light beams are structures of the electromagnetic field with a spiral phase ramp around a point-phase singularity. These vortices have many applications in the optical regime, ranging from optical trapping and quantum information to spectroscopy and microscopy. The extension of vortices into the extreme-ultraviolet (XUV)/X-ray regime constitutes a significant step forward to bring those applications to the nanometer or even atomic scale. The recent development of a new generation of X-ray sources, and the refinement of other techniques, such as harmonic generation, have boosted the interest of producing vortex beams at short wavelengths. In this manuscript, we review the recent studies in the subject, and we collect the major prospects of this emerging field. We also focus on the unique and promising applications of ultrashort XUV/X-ray vortex pulses, A.P. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 702565. C.H.-G. acknowledges support from the Marie Curie International Outgoing Fellowship within the EU Seventh Framework Programme for Research and Technological Development (2007-2013), under REA grant Agreement No 328334. We acknowledge support and from Junta de Castilla y León (Project SA046U16) and MINECO (FIS2013-44174-P, FIS2015-71933-REDT, FIS2016-75652-P).

X-ray spectroscopy is an important tool for the investigation of matter. X rays primarily interact with inner-shell electrons, creating core (inner-shell) holes that will decay on the time scale of attoseconds to a few femtoseconds through electron relaxations involving the emission of a photon or an electron. The advent of femtosecond x-ray pulses expands x-ray spectroscopy to the time domain and will eventually allow the control of core-hole population on time scales comparable to core-vacancy lifetimes. For both cases, a theoretical approach that accounts for the x-ray interaction while the electron relaxations occur is required. Here we describe a time-dependent framework, based on solving the time-dependent Schrödinger equation, that is suitable for describing the induced electron and nuclear dynamics., A.P. is grateful to C. Bostedt for inspiring this project, scientific discussions, and his support. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division and supported by the Argonne group under Contract No. DE-AC02-06CH11357. A.P. also acknowledges support from the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement No. 702565.

A molecular water oxidation catalyst based on the copper complex of general formula [(Lpy)CuII]2-, 22-, (Lpy is 4-pyrenyl-1,2-phenylenebis(oxamidate) ligand) has been rationally designed and prepared to support a more extended π-conjugation through its structure in contrast with its homologue, the [(L)CuII]2- water oxi-dation catalyst, 12- (L is o-phenylenebis(oxamidate)). The catalytic performance of both catalysts has been comparatively studied in homogeneous phase and in heterogeneous phase by π-stacking anchorage to graphene-based electrodes. In the homogeneous sys-tem, the electronic perturbation provided by the pyrene functionality translates into a 150 mV lower overpotential for 22- respect to 12- and an impressive increase in the kcat from 6 s-1 to 128 s-1. Upon anchorage, π-stacking interactions with the graphene sheets provide further π-delocalization that improves the catalytic performance of both catalysts. In this sense, 22- turned out to be the most active catalyst due to the double influence of both the pyrene and the graphene, displaying an overpotential of 538 mV, a kcat of 540 s-1 and producing more than 5300 TONs

High-order harmonic generation (HHG) has been recently proven to produce harmonic vortices carrying orbital angular momentum (OAM) in the extreme-ultraviolet (XUV) region from the nonlinear up-conversion of infrared vortex beams. In this work we present two methods to control and extend the OAM content of the harmonic vortices. First, we show that when a driver combination of different vortex modes is used, HHG leads to the production of harmonic vortices with a broad OAM content due to its nonperturbative nature. Second, we show that harmonic vortices with two discrete OAM contributions –so called fractional OAM modes– are generated when HHG is driven by conical refraction beams. Our work offers the possibility of generating tunable OAM beams in the XUV regime, potentially extensible to the soft x rays, overcoming the state of the art limitations for the generation of OAM beams far from the visible domain.

Optical vortices are structures of the electromagnetic field with a spiral phase ramp about a point-phase singularity, carrying orbital angular momentum (OAM). Recently, OAM has been imprinted to short-wavelength radiation through high-order harmonic generation (HHG), leading to the emission of attosecond twisted beams in the extreme-ultraviolet (XUV) regime. We explore the details of the mapping of the driving vortex to its harmonic spectrum. In particular, we show that the geometry of the harmonic vortices is convoluted, arising from the superposition of the contribution from the short and long quantum paths responsible of HHG. Finally, we show how to take advantage of transverse phase-matching to select twisted attosecond beams with different spatiotemporal properties., C.H.-G. acknowledges support from the Marie Curie International Outgoing Fellowship within the EU Seventh Framework Programme for Research and Technological Development (2007–2013), under REA grant Agreement No. 328334. The authors acknowledge support from Junta de Castilla y León (Projects SA116U13, SA046U16) and MINECO (Projects FIS2013-44174-P, FIS2016-75652-P). A.P. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under the contract no. DE-AC02-06CH11357 and support from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 702565.

High-order harmonic generation (HHG) has been recently proven to produce extreme-ultraviolet (XUV) vortices from the nonlinear conversion of infrared twisted beams. Previous works have demonstrated a linear scaling law of the vortex charge with the harmonic order. We demonstrate that this simple law hides an unexpectedly rich scenario for the buildup of orbital angular momentum (OAM) due to the nonperturbative behavior of HHG. The complexity of these twisted XUV beams appears only when HHG is driven by nonpure vortex modes, where the XUV OAM content is dramatically increased. We explore the underlying mechanisms for this diversity and derive a general conservation rule for the nonperturbative OAM buildup. The simple scaling found in previous works corresponds to the collapse of this scenario for the particular case of pure (single-mode) OAM driving fields., C.H.-G. acknowledges support by a Marie Curie International Outgoing Fellowship within the EU Seventh Framework Programme for Research and Technological Development (2007–2013), under REA Grant Agreement No. 328334. We acknowledge support from Junta de Castilla y León (Projects No. SA116U13 and No. SA046U16) and Ministerio de Economía y Competitividad (FIS2013-44174- P, FIS2016-75652-P). A. P. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Contract No. DE-AC02- 06CH11357.

Quantum optics with X-rays has long been a somewhat exotic activity, but it is now rapidly becoming relevant as precision x-ray optics and novel X-ray light sources, and high-intensity lasers are becoming available. This article gives an overview of the current state of the field and an outlook to future prospects.

Nature Communications 7, 11652 (2016). doi:10.1038/ncomms11652, New capabilities at X-ray free-electron laser facilities allow the generation of two-colour femtosecond X-ray pulses, opening the possibility of performing ultrafast studies of X-ray-induced phenomena. Particularly, the experimental realization of hetero-site-specific X-ray-pump/X-ray-probe spectroscopy is of special interest, in which an X-ray pump pulse is absorbed at one site within a molecule and an X-ray probe pulse follows the X-ray-induced dynamics at another site within the same molecule. Here we show experimental evidence of a hetero-site pump-probe signal. By using two-colour 10-fs X-ray pulses, we are able to observe the femtosecond time dependence for the formation of F ions during the fragmentation of XeF$_2$ molecules following X-ray absorption at the Xe site., Published by Nature Publishing Group, London

Physical review / A covering atomic, molecular, and optical physics and quantum information 94(1), 013426(2016). doi:10.1103/PhysRevA.94.013426, The capability of generating two intense, femtosecond x-ray pulses with a controlled time delay opens the possibility of performing time-resolved experiments for x-ray-induced phenomena. We have applied this capability to study the photoinduced dynamics in diatomic molecules. In molecules composed of low-Z elements, K-shell ionization creates a core-hole state in which the main decay mode is an Auger process involving two electrons in the valence shell. After Auger decay, the nuclear wave packets of the transient two-valence-hole states continue evolving on the femtosecond time scale, leading either to separated atomic ions or long-lived quasibound states. By using an x-ray pump and an x-ray probe pulse tuned above the K-shell ionization threshold of the nitrogen molecule, we are able to observe ion dissociation in progress by measuring the time-dependent kinetic energy releases of different breakup channels. We simulated the measurements on N$_2$ with a molecular dynamics model that accounts for K-shell ionization, Auger decay, and the time evolution of the nuclear wave packets. In addition to explaining the time-dependent feature in the measured kinetic energy release distributions from the dissociative states, the simulation also reveals the contributions of quasibound states., Published by Inst., Woodbury, NY

X-ray transient absorption spectroscopy (X-TAS) has been used to study the light-induced hydrogen evolution reaction catalyzed by a tetradentate macrocyclic cobalt complex with the formula [LCoIIICl2]+ (L = macrocyclic ligand), [Ru(bpy)3]2+ photosensitizer, and an equimolar mixture of sodium ascorbate/ascorbic acid electron donor in pure water. X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) analysis of a binary mixture of the octahedral Co(III) precatalyst and [Ru(bpy)3]2+ after illumination revealed in situ formation of a Co(II) intermediate with significantly distorted geometry and electron-transfer kinetics of 51 ns. On the other hand, X-TAS experiments of the complete photocatalytic system in the presence of the electron donor showed the formation of a square planar Co(I) intermediate species within a few nanoseconds, followed by its decay in the microsecond time scale. The Co(I) structural assignment is supported by calculations based on density functional theory (DFT). At longer reaction times, we observe the formation of the initial Co(III) species concomitant to the decay of Co(I), thus closing the catalytic cycle. The experimental X-ray absorption spectra of the molecular species formed along the catalytic cycle are modeled using a combination of molecular orbital DFT calculations (DFT-MO) and finite difference method (FDM). These findings allowed us to assign the full mechanistic pathway, followed by the catalyst as well as to determine the rate-limiting step of the process, which consists in the protonation of the Co(I) species. This study provides a complete kinetics scheme for the hydrogen evolution reaction by a cobalt catalyst, revealing unique information for the development of better catalysts for the reductive side of hydrogen fuel cells.

High-order harmonic generation (HHG) driven by beams carrying orbital angular momentum has been recently demonstrated as a unique process to generate spatio-temporal coherent extreme ultraviolet (XUV)/x-ray radiation with attosecond helical structure.Weexplore the details of the mapping of the driving vortex to its harmonic spectrum. In particular we show that the geometry of the harmonic vortices is complex, arising from the superposition of the contribution from the short and long quantum paths responsible of HHG. Transversal phase-matching and quantum path interferences provide an explanation of the dramatic changes in theXUVvortex structure generated at different relative positions of the target respect to the laser beam focus. Finally, we show how to take advantage of transversal phase-matching to select helical attosecond beams generated from short or long quantum paths, exhibiting positive or negative temporal chirp respectively., CH-G acknowledges fruitful discussions with Mette B Gaarde and support from the Marie Curie International Outgoing Fellowship within the EUSeventh Framework Programme for Research and Technological Development (2007–2013), under REA grant Agreement No 328334 CH-G, JSR and LP acknowledge support from Junta de Castilla y León (Project SA116U13) and MINECO (FIS2013-44174-P). AP acknowledges financial support of the US Department of Energy, Basic Energy Sciences, Office of Science, under contract No DE-AC02- 06CH11357.

Photoionization cross sections and partial ion yields of Xe and XeF$_2$ from Xe 3d$_{5/2}$, Xe 3d$_{3/2}$, and F 1s subshells in the 660--740 eV range are compared to explore effects of the F ligands. The Xe 3d - $\epsilon$f continuum shape resonances dominate the photoionization cross sections of both the atom and molecule, but prominent resonances appear in the XeF$_2$ cross section due to nominal excitation of Xe 3d and F 1s electrons to the lowest unoccupied molecular orbital (LUMO), a delocalized anti-bonding MO. The subshell ionization thresholds, the LUMO resonance energies and their oscillator strengths are calculated by relativistic coupled-cluster methods. Several charge states and fragment ions are produced from the atom and molecule due to alternative decay pathways from the inner-shell holes. Total and partial ion yields vary in response to the shape resonances and LUMO resonances. Previous calculations and measurements of atomic Xe 3d core-hole decay channels and our calculated results for XeF$_2$ guide interpretations of the molecular ion products. The partial ion yields of XeF$_2$ are dominated by Xe 3d core-hole decays, but distinct ion products are measured at the F 1s - LUMO resonance. Xe 3d core-hole decays from XeF$_2$ produce lower charge states in comparison with atomic Xe, and energetic F ions are produced by Coulomb explosions of the molecular ions. The measurements support a model of molecular core-hole decay that begins with a localized hole, stepwise Auger electron emission spreads charge across neighboring atoms, and the system fragments energetically.

We have unveiled coherent multiphoton interferences originating from different quantum paths taken by the Auger electron induced by a high-intensity x-ray/XUV pulse under the presence of a strong optical field. These interferences give rise to a clear signature in the angle-resolved Auger electron spectrum: an asymmetry with respect to the energy of the Auger decay channel. In order to illustrate this effect we have considered the resonant Auger decay of the transition $2p^{5} \!\leftrightarrow\! 1s^{-1}2p^{6}$ in Ne$^{+}$. The simulations show that these interferences are very sensitive to the parameters of the x-ray and optical fields.

We theoretically show that core-excited-state populations can be efficiently manipulated with strong optical fields during their decay, which takes place in a few femtoseconds. We focus on the $1{s}^{\ensuremath{-}1}3p$ resonant excitation in neon, where the $1{s}^{\ensuremath{-}1}3p$ and $1{s}^{\ensuremath{-}1}3s$ core-excited states are coupled by an optical field. By analyzing the Auger electron spectrum we observe the inner-shell population transfer induced by the optical coupling. We also show that the angular anisotropy of the Auger electron is imprinted in the multipeak structure induced by the optical-dressed continuum, namely sidebands.

We study vibrational excitations, dissociation, and ionization of H(2)(+) in few-cycle laser pulses over a broad wavelength regime. Our results of numerical simulations supported by model calculations show a many orders-of-magnitude enhancement of vibrational excitation and dissociation (over ionization) of the molecular ion at infrared wavelengths. The enhancement occurs without any chirping of the pulse, which was previously applied to take account of the anharmonicity of the molecular vibrations. The effect is related to strong-field two- and higher-order photon transitions between different vibrational states.

We analyze two-center interference effects in the yields of ionization of a dissociating hydrogen molecular ion by an ultrashort vuv laser pulse. To this end, we performed numerical simulations of the time-dependent Schr\"odinger equation for a ${\mathrm{H}}_{2}{}^{+}$ model ion interacting with two time-delayed laser pulses. The scenario considered corresponds to a pump-probe scheme, in which the first (pump) pulse excites the molecular ion to the first excited dissociative state and the second (probe) pulse ionizes the electron as the ion dissociates. The results of our numerical simulations for the ionization yield as a function of the time delay between the two pulses exhibit characteristic oscillations due to interferences between the partial electron waves emerging from the two protons in the dissociating hydrogen molecular ion. We show that the photon energy of the pump pulse should be in resonance with the ${\ensuremath{\sigma}}_{g}\ensuremath{-}{\ensuremath{\sigma}}_{u}$ transition and the pump pulse duration should not exceed 5 fs in order to generate a well-confined nuclear wave packet. The spreading of the nuclear wave packet during the dissociation is found to cause a decrease of the amplitudes of the oscillations as the time delay increases. We develop an analytical model to fit the oscillations and show how dynamic information about the nuclear wave packet, namely, velocity, mean internuclear distance, and spreading, can be retrieved from the oscillations. The predictions of the analytical model are tested well against the results of our numerical simulations.

We present results of numerical simulations indicating a complex laser driven electron dynamics inside simple molecular systems on the attosecond time scale. This attosecond electron dynamics influences the instant of ionization of the molecule and the final electron momentum distributions.