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Intense light–matter interactions have revolutionized our ability to probe and manipulate quantum systems at sub-femtosecond timescales1, opening routes to the all-optical control of electronic currents in solids at petahertz rates2–7. Such control typically requires electric-field amplitudes in the range of almost volts per angstrom, when the voltage drop across a lattice site becomes comparable to the characteristic bandgap energies. In this regime, intense light–matter interaction induces notable modifications to the electronic and optical properties8–10, dramatically modifying the crystal band structure. Yet, identifying and characterizing such modifications remain an outstanding problem. As the oscillating electric field changes within the driving field’s cycle, does the band structure follow and how can it be defined? Here we address this fundamental question, proposing all-optical spectroscopy to probe the laser-induced closing of the bandgap between adjacent conduction bands. Our work reveals the link between nonlinear light–matter interactions in strongly driven crystals and the sub-cycle modifications in their effective band structure.

Modern light generation technology offers extraordinary capabilities for sculpting light pulses, with full control over individual electric field oscillations within each laser cycle1–3. These capabilities are at the core of lightwave electronics—the dream of ultrafast lightwave control over electron dynamics in solids on a sub-cycle timescale, aiming at information processing at petahertz rates4–8. Here, bringing the frequency-domain concept of topological Floquet systems9,10 to the few-femtosecond time domain, we develop a theoretical method that can be implemented with existing technology, to control the topological properties of two-dimensional materials on few-femtosecond timescales by controlling the sub-cycle structure of non-resonant driving fields. We use this method to propose an all-optical, non-element-specific technique, physically transparent in real space, to coherently write, manipulate and read selective valley excitation using fields carried in a wide range of frequencies and on timescales that are orders of magnitude shorter than the valley lifetime, crucial for the implementation of valleytronic devices11,12. A method to control the topological properties of two-dimensional (2D) materials on few-femtosecond timescales is proposed. By controlling the sub-cycle structure of non-resonant driving fields, it may be possible to coherently write, manipulate and read selective valley excitation.

Sub-laser cycle time scale of electronic response to strong laser fields enables attosecond dynamical imaging in atoms, molecules and solids. Optical tunneling and high harmonic generation are the hallmarks of attosecond imaging in optical domain, including imaging of phase transitions in solids. Topological phase transition yields a state of matter intimately linked with electron dynamics, as manifested via the chiral edge currents in topological insulators. Does topological state of matter leave its mark on optical tunneling and sub-cycle electronic response? We identify distinct topological effects on the directionality and the attosecond timing of currents arising during electron injection into conduction bands. We show that electrons tunnel across the band gap differently in trivial and topological phases, for the same band structure, and identify the key role of the Berry curvature in this process. These effects map onto topologically-dependent attosecond delays in high harmonic emission and the helicities of the emitted harmonics, which can record the phase diagram of the system and its topological invariants. Thus, the topological state of the system controls its attosecond, highly non-equilibrium electronic response to strong low-frequency laser fields, in bulk. Our findings create new roadmaps in studies of topological systems, building on ubiquitous properties of sub-laser cycle strong field response - a unique mark of attosecond science.

The reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) is one of the most widely used techniques for resolving ultrafast electronic dynamics in atomic and molecular systems. As it relies on the interference of photo-electrons in vacuum, similar interference has never been contemplated in the bulk of crystals. Using accurate numerical simulations in a realistic system, here we show that the interference of two-photon transitions can be recorded directly in the bulk of solids and read out with standard angle-resolved photo-emission spectroscopy. The phase of the RABBIT beating in the photoelectron spectra coming from the bulk of solids is sensitive to the relative phase of the Berry connection between bands and it experiences a shift of π as one of the quantum paths crosses a band. For resonant interband transitions, the amplitude of the RABBIT oscillation decays as the pump and probe pulses are separated in time due to electronic decoherence, providing a simple interferometric method to extract dephasing times.

Electron correlation and multielectron effects are fundamental interactions that govern many physical and chemical processes in atomic, molecular and solid state systems. The process of autoionization, induced by resonant excitation of electrons into discrete states present in the spectral continuum of atomic and molecular targets, is mediated by electron correlation. Here we investigate the attosecond photoemission dynamics in argon in the 20–40 eV spectral range, in the vicinity of the 3s−1np autoionizing resonances. We present measurements of the differential photoionization cross section and extract energy and angle-dependent atomic time delays with an attosecond interferometric method. With the support of a theoretical model, we are able to attribute a large part of the measured time delay anisotropy to the presence of autoionizing resonances, which not only distort the phase of the emitted photoelectron wave packet but also introduce an angular dependence., Nature Communications, 9, ISSN:2041-1723

We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy for photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal transitions in vanadium dioxide. We benchmark our technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calculations. Tr-HHG allows distinguishing of individual dynamic channels, including a transition to a thermodynamically hidden phase. In addition, the HHG yield is shown to be modulated at a frequency characteristic of a coherent phonon in the equilibrium monoclinic phase over a wide range of excitation fluences. These results demonstrate that tr-HHG is capable of tracking complex dynamics in solids through its sensitivity to the band structure., 20 pages and 4 figures main text, 8 pages and 4 figures supplementary information

Strong-field-driven electric currents in condensed-matter systems are opening new frontiers in petahertz electronics. In this regime, new challenges are arising as the roles of band structure and coherent electron–hole dynamics have yet to be resolved. Here, by using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid-state systems. We demonstrate that when the electron–hole relative velocity approaches zero, enhanced constructive interference leads to the appearance of spectral caustics in the high-harmonic generation spectrum. We introduce the role of the dynamical joint density of states and identify its mapping into the spectrum, which exhibits singularities at the spectral caustics. By studying these singularities, we probe the structure of multiple unpopulated high conduction bands. High-harmonic waves are generated from a MgO crystal under experimental conditions where the simple semi-classical analysis fails. High-harmonic generation spectroscopy directly probes the strong-field attosecond dynamics over multiple bands.

We study fundamental limitations to topological protection induced by increasing the amount of entanglement in nonseparable two-photon states. We identify the physics underlying such vulnerability and the conditions for robust protection of two-photon states.

This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on 354, 11 november 2016, DOI: 10.1126/science.aah5188, The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. However, the rapidity of electron dynamics on the attosecond scale has precluded the complete characterization of electron wave packets in the time domain. Using spectrally resolved electron interferometry, we were able to measure the amplitude and phase of a photoelectron wave packet created through a Fano autoionizing resonance in helium. In our setup, replicas obtained by two-photon transitions interfere with reference wave packets that are formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wave packet released in the continuum. In turn, this resolves the buildup of the autoionizing resonance on an attosecond time scale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave packets, We thank S. Weber for crucial contributions to the PLFA attosecond beamline, D. Cubaynes, M. Meyer, F. Penent, J. Palaudoux, for setup and test of the electron spectrometer, and O. Smirnova, for fruitful discussions. Supported by ITN-MEDEA 641789, ANR-15-CE30-0001-01-CIMBAAD, ANR11-EQPX0005-ATTOLAB, the European Research Council Advanced Grant XCHEM no. 290853, the European COST Action XLIC CM1204, and the MINECO Project no. FIS2013-42002-R. We acknowledge allocation of computer time from CCC-UAM and Mare Nostrum BSC

We develop theoretically and confirm both numerically and experimentally a comprehensive analytical model which describes the propensity rules in the emission of circularly polarized high harmonics by systems driven by two-color counter-rotating fields, a fundamental and its second harmonic. We identify and confirm the three propensity rules responsible for the contrast between the $3N+1$ and $3N+2$ harmonic lines in the HHG spectra of noble gas atoms. We demonstrate how these rules depend on the laser parameters and how they can be used in the experiment to shape the polarization properties of the emitted attosecond pulses.

Recent experiments on measuring time-delays during tunnelling of cold atoms through an optically created potential barrier are reinvigorating the controversial debate regarding possible time-delays during light-induced tunnelling of an electron from an atom. Compelling theoretical and experimental arguments have been put forward to advocate opposite views, confirming or refuting the existence of finite tunnelling time delays. Yet, such a delay, whether present or not, is but a single quantity characterizing the tunnelling wavepacket; the underlying dynamics are richer. Here we propose to augment photo-electron detection in laser-induced tunnelling with detection of light emitted by the tunnelling electron -- the so-called Brunel radiation. Using a combination of single-color and two-color driving fields, we identify the all-optical signatures of the re-shaping of the tunnelling wavepacket as it emerges from the tunnelling barrier and moves away from the core. This reshaping includes not only an effective time-delay but also time-reversal asymmetry of the ionization process, which we describe theoretically and observe experimentally. We show how both delay and reshaping are mapped on the polarization properties of the Brunel radiation, with different harmonics behaving as different hands of a clock moving at different speeds. The all-optical detection paves the way to time-resolving optical tunnelling in condensed matter systems, e.g. tunnelling across bandgaps in solids, on the attosecond time-scale.

International audience; Autoionization, which results from the interference between direct photoionization and photoexcitation to a discrete state decaying to the continuum by configuration interaction, is a well known example of the important role of electron correlation in light–matter interaction. Information on this process can be obtained by studying the spectral, or equivalently, temporal complex amplitude of the ionized electron wave packet. Using an energy-resolved interferometric technique, we measure the spectral amplitude and phase of autoionized wave packets emitted via the sp2+ and sp3+ resonances in helium. These measurements allow us to reconstruct the corresponding temporal profiles by Fourier transform. In addition, applying various time–frequency representations, we observe the build-up of the wave packets in the continuum, monitor the instantaneous frequencies emitted at any time and disentangle the dynamics of the direct and resonant ionization channels.

High-harmonic generation in two-colour ($\omega-2\omega$) counter-rotating circularly polarised laser fields opens the path to generate isolated attosecond pulses and attosecond pulse trains with controlled ellipticity. The generated harmonics have alternating helicity, and the ellipticity of the generated attosecond pulse depends sensitively on the relative intensities of two adjacent, counter-rotating harmonic lines. For the $s$-type ground state, such as in Helium, the successive harmonics have nearly equal amplitude, yielding isolated attosecond pulses and attosecond pulse trains with linear polarisation, rotated by 120$^{{\circ}}$ from pulse to pulse. In this work, we suggest a solution to overcome the limitation associated with the $s$-type ground state. It is based on modifying the three propensity rules associated with the three steps of the harmonic generation process: ionisation, propagation, and recombination. We control the first step by seeding high harmonic generation with XUV light tuned well below the ionisation threshold, which generates virtual excitations with the angular momentum co-rotating with the $\omega$-field. We control the propagation step by increasing the intensity of the $\omega$-field relative to the $2\omega$-field, further enhancing the chance of the $\omega$-field being absorbed versus the $2\omega$-field, thus favouring the emission co-rotating with the seed and the $\omega-$field. We demonstrate our proposed control scheme using Helium atom as a target and solving time-dependent Schr{\"o}dinger equation in two and three-dimensions., Comment: 15 pages, 3 figures

High harmonic generation in multi-color laser fields opens the opportunity of generating isolated attosecond pulses with high ellipticity. Such pulses hold the potential for time-resolving chiral electronic, magnetization, and spin dynamics at their natural timescale. However, this potential cannot be realized without characterizing the exact polarization state of light on the attosecond timescale. Here we propose and numerically demonstrate a complete solution of this problem. Our solution exploits the extrinsic two-dimensional chirality induced in an atom interacting with the chiral attosecond pulse and a linearly polarized infrared probe. The resulting asymmetry in the photoelectron spectra allows to reconstruct the complete polarization state of the attosecond pulse, including its possible time dependence. The challenging problem of distinguishing circularly polarized, partially polarized, or unpolarized pulses in the extreme ultraviolet range is also resolved. We expect this approach to become the core ingredient for attosecond measurements of chiral-sensitive processes in gas and condensed phase., Attosecond pulses are useful in exploring processes involving ultrafast electron motion in atomic and molecular systems. Here the authors discuss a method to characterize the complex time-varying polarization state of broadband attosecond pulses by using asymmetry in photoelectron spectra.

High-order harmonic generation with bicircular fields - the combination of counter-rotating circularly polarized pulses at different frequencies - results in a series of short-wavelength XUV harmonics with alternating circular polarizations, and experiments show that there is an asymmetry in the emission between the two helicities: a slight one in helium, and a larger one in neon and argon, where the emission is carried out by p-shell electrons. Here we analyze this asymmetry by switching to a rotating frame in which the field is linearly polarized; this induces an effective magnetic field which lowers the ionization potential of the $p_+$ orbital that co-rotates with the lower-frequency driver, enhancing its harmonic emission and the overall helicity of the generated harmonics, while also introducing nontrivial effects from the transformation to a non-inertial frame in complex time. In addition, this analysis directly relates the small asymmetry produced by s-shell emission to the imaginary part of the recollision velocity in the standard strong-field-approximation formalism., Comment: Title changed from v1 as enforced by Phys. Rev. A editorial policies

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

Tunnel ionization of noble gas atoms driven by a strong circularly polarized laser field in combination with a counter-rotating second harmonic generates spin-polarized electrons correlated to the spin-polarized ionic core. Crucially, such two-color field can bring the spin-polarized electrons back to the parent ion, enabling the scattering of the spin-polarized electron on the spin-polarized parent ion. Here we show how one can control the degree of spin polarization as a function of electron energy and recollision time by tuning the laser parameters, such as the relative intensities of the counter-rotating fields. The attosecond precision of the control over the degree of spin polarization opens the door for attosecond control and spectroscopy of spin-resolved dynamics. Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659

Complete characterization of attosecond pulses with arbitrary ellipticity and possibly partial polarization is now particularly acute. State-of-the-art experimental setups have provided robust and practical means to generate high harmonics in the XUV and soft-X-ray range with controlled polarization [1]. This opens the way to generate isolated attosecond pulses and attosecond pulse trains with controlled ellipticity [2]. Such pulses will enable time-resolved studies of chiral-sensitive light-matter interaction, from electron dynamics in chiral molecules to ultrafast magnetization and spin transport, with unprecedented temporal resolution.

The photoelectron emission time delay τ associated with one-photon absorption, which coincides with half the Wigner delay τW experienced by an electron scattered off the ionic potential, is a fundamental descriptor of the photoelectric effect. Although it is hard to access directly from experiment, it is possible to infer it from the time delay of two-photon transitions, τ(2), measured with attosecond pump-probe schemes, provided that the contribution of the probe stage can be factored out. In the absence of resonances, τ can be expressed as the energy derivative of the one-photon ionization amplitude phase, τ=∂EargDEg, and, to a good approximation, τ=τ(2)-τcc, where τcc is associated with the dipole transition between Coulomb functions. Here we show that, in the presence of a resonance, the correspondence between τ and ∂EargDEg is lost. Furthermore, while τ(2) can still be written as the energy derivative of the two-photon ionization amplitude phase, ∂EargDEg(2), it does not have any scattering counterpart. Indeed, τ(2) can be much larger than the lifetime of an intermediate resonance in the two-photon process or more negative than the lower bound imposed on scattering delays by causality. Finally, we show that τ(2) is controlled by the frequency of the probe pulse, ωIR, so that by varying ωIR, it is possible to radically alter the photoelectron group delay, We thank M. Dahlström, P. Salières, E. Lindroth, J. Burgdörfer, and R. Pazourek for useful discussions. We acknowledge computer time from the CCC-UAM and Marenostrum Supercomputer Centers and financial support from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement 290853 XCHEM, the MINECO Projects FIS2013-42002-R and FIS2016-77889-R, and the European COST Action XLIC CM1204. L.A. acknowledges support from TAMOP NSF Grant No. 1607588, as well as UCF fundings. A.M., J.C., and R.T. acknowledge financial support from the Agence Nationale de la Recherche through the program ANR-15-CE30-0001-01-CIMBAAD. A.J.G. acknowledges support from DFG QUTIF Grant IV 152/6-1

International audience

We present an analytical model capable of describing two-photon ionization of atoms with attosecond pulses in the presence of intermediate and final isolated autoionizing states. The model is based on the finite-pulse formulation of second-order time-dependent perturbation theory. It approximates the intermediate and final states with Fano's theory for resonant continua, and it depends on a small set of atomic parameters that can either be obtained from separate \emph{ab initio} calculations, or be extracted from few selected experiments. We use the model to compute the two-photon resonant photoelectron spectrum of helium below the N=2 threshold for the RABITT (Reconstruction of Attosecond Beating by Interference of Two-photon Transitions) pump-probe scheme, in which an XUV attosecond pulse train is used in association to a weak IR probe, obtaining results in quantitative agreement with those from accurate \emph{ab initio} simulations. In particular, we show that: i) Use of finite pulses results in a homogeneous red shift of the RABITT beating frequency, as well as a resonant modulation of the beating frequency in proximity of intermediate autoionizing states; ii) The phase of resonant two-photon amplitudes generally experiences a continuous excursion as a function of the intermediate detuning, with either zero or $2\pi$ overall variation., Comment: 23 pages, 13 figures

Nature Communications 7, 10566(2016). doi:10.1038/ncomms10566, Electron dynamics induced by resonant absorption of light is of fundamental importance in nature and has been the subject of countless studies in many scientific areas. Above the ionization threshold of atomic or molecular systems, the presence of discrete states leads to autoionization, which is an interference between two quantum paths: direct ionization and excitation of the discrete state coupled to the continuum. Traditionally studied with synchrotron radiation, the probability for autoionization exhibits a universal Fano intensity profile as a function of excitation energy. However, without additional phase information, the full temporal dynamics cannot be recovered. Here we use tunable attosecond pulses combined with weak infrared radiation in an interferometric setup to measure not only the intensity but also the phase variation of the photoionization amplitude across an autoionization resonance in argon. The phase variation can be used as a fingerprint of the interactions between the discrete state and the ionization continua, indicating a new route towards monitoring electron correlations in time., Published by Nature Publishing Group, London

Time delays of electrons emitted from an isotropic initial state with the absorption of a single photon and leaving behind an isotropic ion are angle independent. Using an interferometric method involving XUV attosecond pulse trains and an IR-probe field in combination with a detection scheme, which allows for full three-dimensional momentum resolution, we show that measured time delays between electrons liberated from the 1s2 spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the common linear polarization axis of the ionizing XUV light and the IR-probing field. Such time delay anisotropy, for which we measure values as large as 60 as, is caused by the interplay between final quantum states with different symmetry and arises naturally whenever the photoionization process involves the exchange of more than one photon. With the support of accurate theoretical models, the angular dependence of the time delay is attributed to small phase differences that are induced in the laser-driven continuum transitions to the final states. Since most measurement techniques tracing attosecond electron dynamics involve the exchange of at least two photons, this is a general and significant effect that must be taken into account in all measurements of time delays involving photoionization processes, S.H, C.C, L.G., and U.K. acknowledge support by the ERC advanced Grant No. ERC-2012-ADG_20120216 within the seventh framework program of the European Union and by the NCCR MUST, funded by the Swiss National Science Foundation. M.L. acknowledges support from the ETH Zurich Postdoctoral Fellowship Program. A.J.G., L.A., and F.M. acknowledge the support from the European Research Council under the ERC Grant No. 290853 XCHEM, from the European COST Action No. CM1204 XLIC, the MINECO Project No. FIS2013-42002-R, the ERA-Chemistry Project No. PIM2010EEC- 00751, and the European Grant No. MC-ITN CORINF. Calculations were performed at the Centro de Computacion Científica of the Universidad Autónoma de Madrid (CC-UAM) and the Barcelona Supercomputing Center (BSC). I.I. and A.S.K. acknowledge support of the Australian Research Council (Grant No. DP120101805) and the use of the National Computational Infrastructure Facility. J.M.D. acknowledges support from the Swedish Research Grants No. 2013-344 and No. 2014-3724. E.L. acknowledges support from the Swedish Research Council, Grant No. 2012-3668. Moreover, this research was supported in part by the Kavli Institute for Theoretical Physics (National Science Foundation under Grant No. NSF PHY11-25915) and by NORDITA, the Nordic Institute for Theoretical Physics

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum (ATAS) of helium dressed by a few-cycle visible pulse [C. Ott, Nature (London) 516, 374 (2014)] provide evidence of the inversion of Fano profiles. With the support of accurate ab initio calculations that reproduce the results of the latter experiment, here we investigate the new physics that arise from ATAS when the laser intensity is increased. In particular, we show that (i) previously unnoticed signatures of the dark 2p2 1S doubly excited state are observed in the experimental spectrum, (ii) inversion of Fano profiles is predicted to be periodic in the laser intensity, and (iii) the ac Stark shift of the higher terms in the sp2,n+ autoionizing series exceeds the ponderomotive energy, which is the result of a genuine two-electron contribution to the polarization of the excited atom, We acknowledge computer time from the CCC-UAM and Marenostrum Supercomputer Centers and financial support from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 290853 XCHEM, the MINECO project FIS2013-42002-R, the ERAChemistry Project PIM2010EEC-00751, the European COST Action XLIC CM1204, the Marie Curie ITN CORINF, and the CAM project NANOFRONTMAG. C.O. and T.P. acknowledge financial support by the Max-Planck Research Group Program of the Max-Planck Gesellschaft (MPG) and the European Research Council (ERC, Grant No. X-MuSiC-616783)

In contrast to expectations, we observe that the photoionization time delay from the 1s2 spherically symmetric ground state of He depend on the electron emission direction with respect to an external reference. We attribute the observed anisotropy to the interplay between different final quantum states, which become accessible once two photons are involved in the photoionization process. This is a universal effect, which needs to be taken into account for any study dealing with photoionization dynamics.

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum (ATAS) of helium dressed by a few-cycle visible pulse [C. Ott et al, Nature 516, 374 (2014)] provide evidence of the inversion of Fano profiles. With the support of accurate ab-initio calculations that reproduce the results of the latter experiment, here we investigate the new physics that arise from ATAS when the laser intensity is increased. In particular, we show that (i) previously unnoticed signatures of the dark 2p2 1S doubly excited state are observed in the experimental spectrum, (ii) inversion of Fano profiles is predicted to be periodic in the laser intensity, and (iii) the ac-Stark shift of the higher terms in the sp+2, n autoionizing series exceeds the ponderomotive energy, which is the result of a genuine two-electron contribution to the polarization of the excited atom.

We present an analytical model that characterizes two-photon transitions in the presence of autoionising states. We applied this model to interpret resonant RABITT spectra, and show that, as a harmonic traverses a resonance, the phase of the sideband beating significantly varies with photon energy. This phase variation is generally very different from the $\pi$ jump observed in previous works, in which the direct path contribution was negligible. We illustrate the possible phase profiles arising in resonant two-photon transitions with an intuitive geometrical representation., Comment: Manuscript for the Proceedings of the XXIX International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC XXIX), held in Toledo (Spain) July 22-28 2015, where \'Alvaro Jim\'enez Gal\'an gave special report presentation with the same title as the manuscript

We present a theoretical study of the photoelectron attosecond beating due to interference of two-photon transitions in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, both the phase shift and frequency of the sideband beating significantly vary with photon energy. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a nonholographic interferometric means to reconstruct coherent metastable wave packets. We characterize these phenomena by means of a general analytical model that accounts for the effect of both intermediate and final resonances on two-photon processes. The model predictions are in excellent agreement with those of accurate ab initio calculations for the helium atom in the region of the N=2 doubly excited states, We acknowledge computer time from the CCCUAM and Marenostrum Supercomputer Centers and financial support from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 290853 XCHEM, the MINECO Project No. FIS2013-42002-R, the ERA-Chemistry Project No. PIM2010EEC-00751, and the European COST Action XLIC CM1204

We use the soft-photon approximation, formulated for finite pulses, to investigate the effects of the dressing pulse duration and intensity on simulated attosecond pump–probe experiments employing trains of attosecond extremeultraviolet pulses in conjunction with an IR probe pulse.We illustrate the validity of the approximation by comparing the modelled photoelectron distributions for the helium atom, in the photon energy region close to the N = 2 threshold, to the results from the direct solution of the time-dependent Schr¨odinger equation for two active electrons. Even in the presence of autoionizing states, the model accurately reproduces most of the background features of the ab initio photoelectron spectrum in the 1s channel. A splitting of the photoelectron harmonic signal along the polarization axis, in particular, is attributed to the finite duration of the probe pulse. Furthermore, we study the dependence of the sideband integrated signal on the pump–probe time delay for increasing IR field strengths. Starting at IR intensities of the order of 1TWcm−2, overtones in the sideband oscillations due to the exchange of three or more IR photons start to appear. We derive an analytical expression in the frequency-comb limit of the soft-photon model for the amplitude of all the sideband frequency components and show that these amplitudes oscillate as a function of the intensity of the IR field. In particular, we predict that the amplitude of the fundamental component with frequency 2!IR, on which the rabitt optical reconstruction technique is based, changes sign periodically, We thank Mare Nostrum BSC and CCC-UAM (Centro de Computación Científica, Universidad Autónoma de Madrid) for allocation of computer time. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 290853, the European COST Actions CM0702 and CM1204, the ERA-Chemistry project number PIM2010EEC-00751, the Marie Curie ITN CORINF and the MICINN projects numbers FIS2010-15127 and CSD 2007-00010 (Spain)

So far, it has been assumed that selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has to rely on using circularly polarized fields. We theoretically demonstrate a way to control the valley excitation in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier–envelope phase. The valley polarization is mapped onto the strength of the perpendicular harmonic signal of a weak, linearly polarized pulse, which allows to read this information all-optically without destroying the valley state and without relying on the Berry curvature, making our approach potentially applicable to inversion-symmetric materials. We show applicability of this method to hexagonal boron nitride and M o S 2 .