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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 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.

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.

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.

The angular momentum of light is present in two different forms: spin angular momentum (SAM), related to the field's polarization, and orbital angular momentum (OAM), associated with the spatial profile of the phase of the electromagnetic wave. While these properties have been long studied and exploited in the visible/infrared regions, recent developments have extended SAM [1,2] and OAM [3,4] control into the EUV/soft x-ray regions. However, to date it has not been possible to generate coherent EUV beams with fully controlled SAM and OAM.

During the last five years, there has been an increasing interest in generating high-frequency —short wavelength— beams with controllable polarization, due to their potential applications to perform ultrafast studies of chiral and/or dichroic systems at the nanometer scales. Rather sophisticated configurations have already demonstrated polarization control at the sub-femtosecond scale through high-order harmonic generation (HHG) in atomic gases [1,2]. In parallel, different works have recently shown the suitability of solid systems to emit high-order harmonics in a non-perturbative regime [3,4]. Among them, gapless graphene is a relevant system due to its unique optical and conductivity properties. Very recently, in opposite to what happens in atomic systems, it has been shown experimentally that high-order harmonics are emitted in graphene when driven by elliptically polarized laser pulses [5].

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).

Extreme-ultraviolet, attosecond beams with custom spin and orbital angular momentum are produced via high-harmonic generation, for the first time. Entwined angular momentum conservation rules yield exquisite control over their polarization, divergence, and vortex charge.

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

Phase space tomography is a technique of light characterization. Its fundamentals are considered in detail for the case of analysis of spatial structure of partially coherent beams. Similar approaches used for the characterization of optical pulses and quantum states are briefly discussed.

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

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.

New capabilities at accelerator-based and laser-based sources are continuously being developed, being possible to nowadays generate two-color XUV/x-ray pulses with controlled time delay. In the optical regime, in which lasers have achieved a high-degree of spatio-temporal coherence several decades ago, we find many control techniques for atoms and molecules based on coherence. The novel two-color XUV/x-ray sources will allow exploring novel quantum control schemes by using the intrinsic site-specificity excitation of high-energy photons.

Optical vortices are structures of the electromagnetic field with a spiral phase ramp about a point-phase singularity, carrying orbital angular momentum (OAM). These beams are commonly generated in the optical and infrared (IR) regimes, being used in a wide range of applications: classical and quantum communications, micromanipulation, microscopy, etc. [1]. The production of OAM beams in the extreme ultraviolet (EUV)/x-ray regimes is of great interest, as it allows to extend the applications of optical vortices down to the nanometric and attosecond scales. The nonperturbative process of high harmonic generation (HHG) conveys a unique possibility of mapping properties of the driving IR field into shorter-wavelength radiation. For instance, EUV vortices have been obtained through OAM-driven HHG [2], being emitted in the form of helical attosecond beams [3, 4]. It has been theoretically [3, 5] and experimentally [6] shown that OAM is conserved in HHG driven by single-mode vortices through the simple conservation law l q = ql, i.e., each harmonic is generated with OAM of ql, being q the harmonic order and l the OAM of the driver. This simple rule follows the energy conservation of the harmonic conversion process, also found in perturbative harmonic generation.

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).

Extreme-ultraviolet (EUV) attosecond vortices carrying orbital angular momentum (OAM) are produced through high-order harmonic generation (HHG) from the nonlinear conversion of infrared twisted beams. While previous works demonstrated a linear scaling law of the vortex OAM content with the harmonic order, an unexpectedly rich scenario for the OAM buildup appears when HHG is driven by a vortex combination. The non-perturbative nature of HHG increases the OAM content of the attosecond vortices when the driving field presents an azimuthally varying intensity profile. We theoretically explore the underlying mechanisms for this diversity and disentangle the perturbative and non-perturbative nature in the generation of EUV attosecond twisted through numerical simulations.

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.

We experimentally produce extreme-ultraviolet vector beams — from radially to azimuthally polarized — through high-order harmonic generation. Our simulations predict the generation of unique spatio-temporal structures in the form of attosecond vector beams.

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.

Many quantum information and quantum computation protocols exploit high-dimensional Hilbert spaces. Photons, which constitute the main carrier of information between nodes of quantum networks, can store high-dimensional quantum bits in their spatial degrees of freedom. These degrees of freedom can be tailored by resorting to the symplectic invariant approach based on lossless linear canonical transformations. These transformations enable one to manipulate the transverse structure of a single photon prepared in superpositions of paraxial modes. We present a basic introduction of these transformations acting on photons and discuss some of their applications for elementary quantum information processing.

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

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.

The technological development of ultrashort laser pulses makes it possible to monitor and control the dynamics of the electrons in atoms and molecules. In this Chapter we first review recent experimental and theoretical progress towards tracking and understanding of electron motion in nature’s simplest molecule, the hydrogen molecular ion, on its natural time scale. A complex and counterintuitive dynamics appears due to a strong coupling between different electronic states and of the electron with the external field. Different approaches for the observation of these single-active electron effects in the hydrogen molecular ion as well as of electron rearrangement in the valence shell of more complex molecules are presented. Based on these new insights we then turn to a discussion of recently proposed strategies to control electron localization in molecules with carrier-envelope phase locked pulses, attosecond pump-probe set-ups as well as circularly polarized laser pulses. In particular, results of experiments, in which the asymmetry of localization probabilities at the protons in the hydrogen molecular ion is observed, are complemented with theoretical results and analysis from ab-initio numerical simulations.

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.

Light beams carrying orbital angular momentum, such as Laguerre-Gaussian beams, give rise to the violation of the standard dipolar selection rules during the interaction with matter yielding, in general, an exchange of angular momentum larger than hbar per absorbed photon. By means of ab initio 3D numerical simulations, we investigate in detail the interaction of a hydrogen atom with intense Gaussian and Laguerre-Gaussian light pulses. We analyze the dependence of the angular momentum exchange with the polarization, the orbital angular momentum, and the carrier-envelope phase of light, as well as with the relative position between the atom and the light vortex. In addition, a quantum-trajectory approach based on the de Broglie-Bohm formulation of quantum mechanics is used to gain physical insight into the absorption of angular momentum by the hydrogen atom.

Intense laser ionization expands Einstein's photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of an intense ultraviolet beam bearing OAM, envisaging new scenarios for quantum optics.

We present a theoretical study of high-order harmonic generation and propagation driven by an infrared field carrying orbital angular momentum (OAM). We show that extreme-ultraviolet high-OAM vortices with helical attosecond pulse structure are generated.

In the past few years a great interest has been raising in helical beams that are able to transport spin and orbital angular momentum (OAM) in its propagation direction [1,2], such as Laguerre-Gaussian beams. OAM is related to the transverse profile of the beam, exhibiting also an angular-momentum-like behavior. These characteristic transverse profiles have been exploited in a wide range of applications; spanning from optical tweezers to quantum information protocols [3]. For most of them, a suitable model to describe the light-matter interaction is required. Here, we address the problem of photoionization by means of the interaction of a pulse beam carrying orbital angular momentum with the simplest atom that one can consider; Hydrogen. This academic problem clarifies a fundamental question: the OAM transfer from light to the electron quantum state.

The study of light beams carrying integer orbital angular momentum (OAM) has become ubiquitous during the last two decades because of their unique capability to harness light matter-interaction with applications in different fields such as optical communications, super-resolution imaging, and quantum optics [1]. Alternatively, light beams carrying non-integer OAM have also recently been demonstrated. In particular, it has been demonstrated that half-integer OAM beams can be easily generated by means of conical refraction (CR) produced with optically biaxial crystals, with applications in optical trapping, free-space optical communications, material processing, and super-resolution imaging [2]. However, these applications are limited to the VIS-NIR domain due to the spectral bandwidth at which biaxial crystals are transparent (typically 400 nm–3000 nm). Therefore, new generation mechanisms of fractional-OAM beams at shorter wavelengths — such as the EUV and soft x-rays-are needed to extend the applicability of these techniques to the nanometer scale. High-order harmonic generation (HHG) stands as a unique frequency up-conversion process for the generation of coherent EUV and soft x-ray radiation, emitted in the form of attosecond bursts. A remarkable aspect of HHG is its natural ability to map the characteristics of the driving field to the high-frequency harmonics, this being fundamental in the generation of highly charged OAM beams in the EUV/x-ray domain [3-5].

We present a theoretical study of high-order harmonic generation and propagation driven by an infrared field carrying orbital angular momentum (OAM). We show that extreme-ultraviolet high-OAM vortices with helical attosecond pulse structure are generated.

Attosecond transient absorption is an ultrafast technique that has opened the possibility to study electron dynamics in condensed matter systems at its natural timescale. The extension to the x-ray regime permits one to use this powerful technique in combination with the characteristic element specificity of x-ray spectroscopy. At these timescales, the coherent effects of the electron transport are essential and have a relevant signature on the absorption spectrum. Typically, the complex light-driven dynamics requires a theoretical modeling for shedding light on the time-dependent changes in the spectrum. Here we construct a semiconductor Bloch equation model for resolving the light-induced and core-electron dynamics simultaneously, which enables to easily disentangle the interband and intraband contributions. By using the Bloch model, we demonstrate a universal feature on attosecond x-ray transient absorption spectra that emerges from the light-induced coherent intraband dynamics. This feature is linked to previous studies of light-induced Fano resonances in atomic systems, This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 702565 as well as from Comunidad de Madrid through the TALENTO program with ref. 2017-T1/IND-5432. LP acknowledges support from Junta de Castilla y León (Project SA046U16) and MINECO (FIS2016-75652-P). JB acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO), through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV- 2015-0522) Fundació Cellex Barcelona and the CERCA Programme / Generalitat de Catalunya, the European Research Council for ERC Advanced Grant TRANSFORMER (788218), MINECO for Plan Nacional FIS2017-89536-P; AGAUR for 2017 SGR 1639 and Laserlab-Europe (EU-H2020 654148)