Control of Ultrafast (Attosecond and Strong Field) Processes Using Structured Light

In extreme nonlinear optics, matter is illuminated by intense light, which results in electronic quiver motion. For a free electron, the cycle-averaged energy of such a quiver motion is known as the ponderomotive energy. However, as they are currently formulated, these concepts are not applicable to charged particles driven by bright squeezed vacuum, and more generally, by light fields with a vanishing coherent electric field amplitude. In this talk, I will present a detailed numerical & analytical study of the motion of free and bound electrons driven by quantum light, focusing on multi-mode squeezed vacuum state. This study resolves many aspects of the dynamics, including bound and unbound free-electron width oscillations & their ponderomotive energy, Rabi-like oscillations between bound states, and the sub-cycle structure of tunnel ionization rates induced by squeezed vacuum. I will show that all these effects stem from an effective photon-statistics force, and discuss its implications on three-step trajectories in high harmonic generation.

The structure of bulk liquid systems is long-range disordered, and the mechanism of high-order harmonic generation (HHG) in liquids is difficult to be interpreted by the existing models about HHG in gases and solid crystals. We developed a new model by introducing the statistical methods. It is found that the finite coherence distance (cask effect) plays a very important role in liquid HHG. Dephasing is naturally included, which will filter the long trajectories. This model could quantitatively reproduce the cutoff energy of HHG as a function of laser field strength measured by recent experiments. Its prediction on the independence of driving laser wavelength is also confirmed by recent experiments. It provides us a new method to measure the degree of disorder in the liquid system.

If we stack up two layers of graphene while changing their respective orientation by some twisting angle, we end up with a system that has striking differences when compared to single-layer graphene. For a very specific value of this twist angle, known as magic angle, twisted bilayer graphene displays a unique phase diagram that cannot be found in other systems. In parallel, high harmonic generation spectroscopy has been successfully applied to elucidate the electronic properties of quantum materials. The purpose of the present work is to exploit the nonlinear optical response of magic-angle twisted bilayer graphene to unveil its electronic properties. We show that the band structure of magic-angle twisted bilayer graphene is imprinted onto its high-harmonic spectrum. Specifically, we observe a drastic decrease of harmonic signal as we approach the magic angle. Our results show that high harmonic generation can be used as a spectroscopy tool for measuring the twist angle and also the electronic properties of twisted bilayer graphene, paving the way for an all-optical characterization of moire materials.

Experimental and most of the theoretical investigations on high-order harmonic generation (HHG) in solids up to now were focused on the dependence of the emission spectrum upon the laser polarization (orientation of the linear polarization with respect to symmetry directions or ellipticity) and the laser intensity. Surprisingly, the dependence of HHG on such important parameter as the laser wavelength remains essentially unexplored. In this contribution, we present a rigorous experimental and theoretical study of the wavelength dependence of HHG in solids. To disentangle the complex contribution of linear and nonlinear propagation effects, the experiments are conducted with different single atomic layer TMDC crystals. We report on two major observables. First, we demonstrate an exponential decrease in harmonic yield with increasing the wavelength. This observation sheds light on the problem of the dephasing time – an empirical and disputable concept introduced originally to match numerically simulated HHG spectra to the experimentally measured ones. As a reference, we show that a similar exponential drop in efficiency is observed in a bulk semiconductor thin film. Our measurements and numerical simulations, based on real-time time dependent density functional theory and semiconductor Bloch equations, strongly support the concept of dephasing. Second, we investigated the effect of selective enhancement of even order harmonics in single layer 2D materials. By tuning the laser wavelength at a fixed laser intensity, we show that the enhancement occurs only for even order harmonics that fall in a specific, relatively narrow spectral range, while odd-order harmonics possess a standard plateau-cutoff behaviour. This enhancement is orientational and material dependent, suggesting the role of multi-band effects.

The control of ultrafast and strong field processes using structured light with orbital angular momentum (OAM) requires the most detailed knowledge of the physical properties of these light waves, and in particular, the amount of OAM carried by these waves and their propagation behavior. While experiments of high harmonic and attosecond pulse generation with longitudinal OAM are made routinely in diverse experimental configurations, it is not yet completely clear the limits of the amount of OAM that the driving pulses can carry. Also, numerical studies of second and higher order harmonic generation using pulses with transverse OAM are being conducted, and experiments are planned, but at present there is a lack of knowledge about their propagation properties, and a hot debate on the amount of transverse OAM they carry, and hence transfer to the harmonics. In this talk recent theoretical developments aimed at clarifying these issues will be exposed.

Discoveries of topological materials, such as topological insulators, Dirac and Weyl semimetals, have revolutionised contemporary physics. Moreover, these materials hold promises for upcoming technologies based on quantum science and electronics. The transition from Dirac to Weyl semimetal requires the breaking of either inversion or time-reversal symmetry. The present work shows that the laser-driven electron dynamics in a Weyl semimetal with broken time-reversal symmetry has intriguing features in its high-harmonic spectrum [1]. It is found that the parity and magnitude of the non-zero Berry curvatures components control the direction and strength of the anomalous current, which leads to the generation of the anomalous odd harmonics. We show that the non-trivial topology of the Berry curvature in time-reversal symmetry broken quantum materials can be probed by measuring the polarisation of the emitted anomalous odd harmonics. Density matrix based approach is used to investigate laser-driven electron dynamics in Weyl semimetal [2] [3]. Our findings unequivocally illustrate that the laser-driven electron dynamics leads to the generation of nonlinear anisotropic anomalous Hall effect in time-reversal symmetry broken quantum materials on ultrafast timescale. Present work opens a new avenue for studying strong-field driven electron dynamics and high-harmonic generation in systems with broken TRS, such as exotic magnetic and topological materials, and tailoring the polarization of the emitted harmonics. References [1] Amar Bharti, M. S. Mrudul, and Gopal Dixit, Phys. Rev. B 105, 155140 (2022). [2] Mrudul MS and Gopal Dixit, Phy. Rev. B 103,arXiv 2112.01745 (2021) 094308 (2021). [3] M. S. Mrudul, lvaro Jimnez-Galn, Misha Ivanov, and Gopal Dixit, Optica 8, 422-427 (2021).

Traditional all-optical enantiosensitive techniques arise due to the interference of electric dipole transitions (E1) with magnetic dipole (M1) or electric quadrupole (E2) transitions [1]; they are thus rather inefficient due to the relative weakness of the M1 and E2 transitions with respect to the E1 ones. Recently, a new enantiosensitive method based on enantiosensitive interference of E1-only transitions was proposed in Ref. [2]. The method is based on the transitions being driven by synthetic chiral light (SCL), i.e. light that displays chirality in time and not in space. The chirality is encoded in the Lissajous curve drawn by the electric field vector over one optical cycle, rather than in its propagation in space as in E1-M1 or E1-E2 techniques [1], leading to particularly strong enantiosensitive signals [2]. Here we combine the concept of SCL with the one of structured light [1], creating structured chiral light (SSCL) with spatially varying handedness, and use SSCL to drive HHG in molecular enantiomers, resulting in enantiosensitive far-field interference of the emitted light [2]. To create SSCL, we use two tightly focused $\omega-2\omega$ beams. By using two circularly polarized Laguerre-Gaussian beams carrying orbital angular momentum (OAM), we create chiral vortices, i.e. beams with azimuthally varying handedness characterized by a topological charge $\chi=(\ell_{2\omega}+m_{2\omega})-2(\ell_\omega+m_\omega)$, where $\ell$ is the OAM and $m$ is the spin-angular momentum (SAM) of the beams. The topological charge $\chi$ is directly reflected in the enantiosensitive response of a chiral molecule to the SSCL field, leading to enantiosensitive rotations of the far-field spatial profile of HHG radiation. The spatial rotation of the HHG radiation is robust against noise, and can be used also to reconstruct magnitude and phases of the multiphoton pathways leading to the emission of a harmonic photon. [1] K. A. Forbes and D. L. Andrews, ``Orbital angular momentum of twisted light: chirality and optical activity'', J. Phys. Photonics, 3, 022007, 2021. [2] D. Ayuso et al., ``Synthetic chiral light for efficient control of chiral light–matter interaction,'' Nat. Photon., 13, 866-871, 2019. [3] N. Mayer et al., ``Imprinting Chirality on Atoms Using Synthetic Chiral Light Fields,'' Phys. Rev. Lett., 24, 129, 243201, 2022. [4] R. Dorn et al., ``Sharper Focus for a Radially Polarized Light Beam,'' Phys. Rev. Lett., 91, 23, 233901, 2003.

Chiral molecules exist in pairs of mirror-reflected versions: the left and right enantiomers, which behave identically unless they interact with another chiral object. Opposite enantiomers can behave very differently, e.g. in biochemical contexts, making chiral discrimination vital. Traditional chiral spectroscopy relies on the spatial helix of circularly polarised light, but its pitch is orders-of-magnitude larger than the molecule, which leads to tiny sensitivity ($<0.1\%$). To overcome this limitation, one can shape light's local polarization in time to drive chiral effects via electric-dipole interactions in the strong-field regime [1-3] ($100\%$ enantio-sensitivity). Here we bring this giant sensitivity to the perturbative regime, by combining third harmonic generation (THG) with sum-frequency generation (SFG). SFG [4] uses two incident laser beams with frequencies $\omega_1\neq\omega_2$, wave vectors $\mathbf{k}_1$ and $\mathbf{k}_2$, and polarisation $\hat{\mathbf{e}}_1$ and $\hat{\mathbf{e}}_2$, which drive a second-order response with frequency $\omega_3=\omega_1+\omega_2$ and polarisation $\hat{\mathbf{e}}_3=\hat{\mathbf{e}}_1\times\hat{\mathbf{e}}_2$, leading to light emission with $\mathbf{k}_3=\mathbf{k}_1+\mathbf{k}_2$. SFG exclusive of chiral media, and driven by purely electric-dipole interactions. However, the intensity of SFG is not enantio-sensitive, the molecular handedness remains hidden in the phase of the signal [4]. Here we show how, by making the driving field locally chiral, we can achieve full control over the intensity of SFG in randomly oriented chiral molecules. The proposed optical setup combines two laser beams and two optical frequencies, and it leads to emission of SFG and THG radiation in the same direction, so they can efficiently interfere. By controlling the two-colour phase delay, we control the field's chirality, and thus the enantio-sensitive interference. As a result, we can maximise emission of light at 266nm in one enantiomer while fully quenching it in its mirror twin. Imaging molecular chirality on ultrafast time scales via low-order nonlinear processes, which requires gentle laser intensities, creates exciting opportunities for efficient chiral recognition in the liquid phase, the natural medium of biological molecules, or in amorphous chiral solids. [1] Ayuso et al, Nat Photon 13, 866 (2019) [2] Ayuso et al, Nat Commun 12, 3951 (2021) [3] Ayuso et al, Optica 8, 1243 (2021) [4] Fischer and Hache, Chirality 17, 421 (2005)

Increasing the speed limits of conventional electronics requires innovative approaches to manipulate other quantum properties of electrons besides their charge. An alternative approach utilizes the valley degree of freedom in low-dimensional semiconductors. Here we demonstrate that the valley degeneracy of exciton energies in transition metal dichalcogenide monolayers may be lifted by coherent optical interactions on timescales corresponding to a few tens of femtoseconds. The optical Stark and Bloch-Siegert effects generated by strong nonresonant circularly-polarized light induce valley-selective blue shifts of exciton quantum levels by more than 30 meV. We show these phenomena by studying the two most intensive exciton resonances in transition metal dichalcogenide monolayers and comparing the results with the theoretical model, which properly includes the effects of screened Coulomb interaction in the monolayers. These results open the door for ultrafast valleytronics working at multiterahertz frequencies.

The recent development of strong lasers in the THz and midinfrared regimes enables us to study various nonlinear optical phenomena. One fundamental and technologically important example is high-harmonic generation (HHG). HHG was first observed and studied in gases. After the first observation of HHG in semiconductors, its scope has been extended to condensed matter (CM). Although the major target of the HHG research in CM so far has been semiconductors and band insulators, more recently, the scope is further extended to strongly correlated electron systems (SCESs). SCESs are a potentially interesting playground for the HHG research since i) the excitation structures cannot be described by independent electrons and holes unlike conventional semiconductors, ii) various degrees of freedom (charge, spin and orbitals) can be strongly intertwined in SCESs and iii) SCESs show various phases that can be controlled by modulating system parameters such as temperatures. Due to these properties, HHG in SCESs may show peculiar properties absent in HHG in semiconductors. In this presentation, we discuss the basic feature and origin of HHG in Mott insulators described by the single-band Hubbard model, a standard model for SCESs [1-3]. In the Mott insulating phase of this model, each site is occupied by a single electron, and it cannot move due to the strong on-site Coulomb interaction. Photo-excitation creates doubly occupied sites (doublons) and no occupied sites (holons). They are charge carriers of this system and their dynamics leads to the emission of light. In the first part, we focus on the one-dimensional system, where the information of many body elemental excitations is exactly known, and reveal the relation between these excitations and HHG. We show that the semi-classical three step model for these many body excitations works well to describe the HHG process in this system. This is in a stark contrast to the case of semiconductors, where the three-step model combined with the information of the single particle excitations works well. Our results suggest the potential application of HHG to detect many body excitations in SCESs. In the second part, we focus on the systems in higher dimensions and discuss the effects of the spin-charge coupling on HHG. In higher dimensions than one, dynamics of doublons and holons always disturbs the spin background, which leads to the strong spin-charge coupling. We show that this strong spin-charge coupling leads to the intriguing temperature (or band-gap) dependence of HHG as has been recently reported in the experiment on a Mott insulator Ca2RuO4 [4]. Our results tell the importance of correlations between different degrees of freedom in understanding HHG in SCESs. [1] Y. Murakami, M. Eckstein and P. Werner, Phys. Rev. Lett. 121, 057405 (2018). [2] Y. Murakami, S. Takayoshi, A. Koga, and P. Werner, Phys. Rev. B 103, 035110 (2021). [3] Y. Murakami, K. Uchida, A. Koga, K. Tanaka and P. Werner, Phys. Rev. Lett. 129, 157401 (2022). [4] K. Uchida, et. al., Phys. Rev. Lett. 128, 127401 (2022).

I will present investigations on extreme nonlinear optics driven by quantum light, including squeezed coherent and bright squeezed vacuum.

Light beams may carry both a spin and an orbital angular momentum (SAM & OAM). While the former is associated to their polarization state, the latter stems from the geometrical properties of their wavefront. Over the past decade, great progress has been made to control separately the SAM and the OAM during High Harmonic Generation (HHG), yielding eXtreme UltraViolet (XUV) light beams with femtosecond to attosecond duration with monitorable SAM and OAM values [1-3]. These developments progressed in tandem with the design and validation of new measurement methods, adapted to the XUV domain. In particular, it was shown that HHG driven by a single beam with well-defined non zero OAM, yields XUV radiation with a spatio-temporal structure showing a double helix; whose pitch is half the wavelength of the driving laser [1]. These new XUV sources long remained a solution looking for a problem. Over the past two years, a few applications emerged, in molecular physics and condensed matter. In particular, we investigated the reflexion of such light beams off magnetic structures, and discovered that the OAM content of the outgoing light beam directly depends on the coefficients of the azimuthal Fourier transform of the magnetization. We named this effect Magnetic Helicoidal Dichroism, and recently reported on its observation at FERMI FEL [4-5]. It allows to shape XUV beams in OAM content, or alternatively gives access, with a minimal number of acquisitions, to the symmetries of a, possibly evolving, magnetic structure. In the paraxial approximation, both SAM and OAM add up to form the total angular momentum associated to the photons. However, SAM and OAM are just the two peculiar angular momenta adapted to the symmetries of beams with respectively well-defined OAM, and well-defined SAM. In more general cases, for instance when a beam is made of two sub-beams carrying different OAM and SAM, they may be ill-defined. Thus, coordinated symmetries acting on both polarization and space may leave the beam invariant, suggesting to introduce a generalized angular momentum (GAM), linear combination of OAM and SAM, to describe their angular momentum. Interestingly, the eigenvalues of this GAM may take any fractional value. Using two beams with opposite SAM and OAM values of respectively ℓ=0 and ℓ=1, we formed a “polarization Möbius strip”, whose GAM shows half integer eigenvalues. Through HHG, this GAM was linearly up-scaled to the XUV, yielding harmonics with half integer GAM values [6]. The unique properties of these beams, which show entangled SAM and OAM values, are foreseen to be of interest in quantum optics or for imaging applications. In this talk, we will summarize our recent progress on the synthesis of such structured beams, and give an overview of applications to Magnetic Helicoidal Dichroism. References [1] Géneaux, R. et al., 2016. Nature Communications, 7, 12583. http://dx.doi.org/10.1038/ncomms12583 [2] Géneaux, R. et al., 2017. Phys Rev A, 95, 051801. http://dx.doi.org/10.1103/PhysRevA.95.051801 [3] Gauthier, D. et al., 2017. Nature Communications, 8, 14971. http://dx.doi.org/10.1038/ncomms14971 [4] Fanciulli, M. et al., 2021. Physical Review A, 103(1). http://dx.doi.org/10.1103/physreva.103.013501 [5] Fanciulli, M. et al., 2022. Physical Review Letters, 128(7), 077401. http://dx.doi.org/10.1103/physrevlett.128.077401 [6] Luttmann, M. et al., 2022. In press at Science Advances http://dx.doi.org/10.1126/sciadv.adf3486

Superconductors (SCs) support a variety of sub-gap collective modes such as amplitude (Higgs) mode (massive excitations of the SC order parameter) or Bardasis-Schriffer modes (fluctuations of subdominant order parameters) and others (1). In recent years, number of studies on these modes have been carried out using electromagnetic pulses (2). Generally, however the coupling to far-zone transverse electromagnetic waves is weak and one has to resort to near (plasmonic) fields (3). Thus, it is desirable to envision ways to enhance the coupling of electromagnetic fields to SCs especially in the non-linear regime and ideally for nanostructured SCs. In this talk, we will discuss how the topology and the vectorial texture of structured fields help enhance and tune at the sub-wavelength scale the coupling of photonic fields to SCs. In particular, results from material-specific numerical simulations will be presented for high-harmonic generation from SC nanostructures with a size below the SC phase-coherence length resulting in fully phase-matched harmonics. 1. Brusov, P. N. Collective excitations in unconventional superconductors and superfuids; World Scientific: New Jersey, 2010. 2. Schwarz, L et al. D. Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors. Nature Communications 2020, 11, 287; Vaswani et al Light quantum control of persisting Higgs modes in iron-based superconductors Nature Communications 2021, 12, 258. 3. Sun, Z. et al. Collective modes and terahertz near-field response of superconductors.Phys. Rev. Research 2020, 2, 023413.

During the last decade there has been a considerable interest in exploiting HHG as a new route for the production of structured high-frequency harmonic radiation. One interesting aspect in HHG from crystalline targets is to study the interplay of the target symmetries with the topological characteristics of structured driving fields. We shall demonstrate that graphene’s non-linear anisotropy, arising from its crystalline structure, couples with the driving field's topology to produce harmonic fields composed by a cluster of diverging light vortices. We show that the structural analysis of this cluster, i.e. the shape and position of the vortices, yields valuable information of the macroscopic optical response of graphene.

We report on coherent control of nonperturbative high harmonic generation in silicon crystal by two-color $\omega$-3$\omega$ fields. We observe a strong modulation of the high harmonic emission yield as a function of the relative phase between the two pulses at different frequencies even for a very small ratio between the 3$\omega$ and $\omega$ field amplitudes of the order of 0.5%. Besides the amplitude modulation of the emitted harmonics we apply spectral interferometry techniques to characterize attosecond emission delays induced by the modulated two-color waveform.

Observing and clocking non-equilibrium electronic dynamics in real time has developed into one of the key areas of attosecond physics. Attosecond chronoscopy, originally developed for atomic systems, holds the promise to provide novel information on many-electron systems complementary to conventional spectroscopy. Its extension to condensed matter opens up new opportunities to explore electronic band structures and topology, electron transport, and decoherence. We will illustrate the timing of electronic processes in solids with the help of a few prototypical examples. They include the Eisenbud-Wigner-Smith (EWS) and transport time delay in layered materials [1, 2], the influence of the collective screening response on electron timing, the quest for identifying the speed limit of optoelectronics [3], and time-resolved valleytronics in graphene. [4] References [1] M. Ossiander et al., Nature 561, 374, (2018). [2] M. Schnitzenbauer et al., submitted to PRL. [2] M. Ossiander et al., Nature 13, 1620, (2022). [2] T. Fabian et al., Phys. Rev. B. 106, 125419, (2022).

The fundamental polarization singularities of light are generally symmetric under coordinated rotations: that is, transformations which rotate the spatial dependence of the fields by an angle $\theta$ and the field polarization by a fraction $\gamma\theta$ of that angle, as generated by 'mixed' angular momenta of the form $J_\gamma = L + \gamma S$. Generically, the coordination parameter $\gamma$ has been thought to be restricted to integer or half-integer values. In this talk I will show that this constraint is an artifact of the restriction to monochromatic fields, and that a much wider variety of optical singularities is available when one considers polychromatic beam combinations that contain more than one frequency. Building upon this I will show that these new optical singularities present novel field topologies, isomorphic to torus knots, and I will show how they can be characterized both analytically and experimentally. I will also show that the generator for the symmetry group of these singularities, whose algebraic structure is deeply related to the torus-knot topology of the beams, is conserved in nonlinear optical interactions. I will also report on recent work that constructs explicit three-dimensional versions of these topologies, providing an explicit embedding in real space. On the more physical side, I will also describe how these optical singularities behave once we introduce nonlinear optical interactions - and, specifically, high-harmonic generation - and I will show that the new symmetry of these singularities is associated with the conservation of the new 'mixed' angular momentum $J_\gamma$. References:  - E. Pisanty et al. Knotting fractional-order knots with the polarization state of light. Nature Photonics 13 569 (2019).  - E. Pisanty et al. Conservation of torus-knot angular momentum in high-order harmonic generation. Physical Review Letters 122 203201 (2019).

Radiative recombination of electrons with protons and dissociative recombination of electrons with molecular ions can be controlled by external laser fields of a moderate intensity in the range of 0.1 GW/cm$^2$ to 100 GW/cm$^2$. The Coulomb focusing effect plays a crucial role in these processes by strongly extending the range of impact parameters for which recombination is possible. To incorporate this effect we treat these processes semiclassically. For radiative recombination we extend the old Kramers' theory to the case when the laser field is present. For dissociative recombination we use the classical trajectory approach in the outer region of the interaction zone, and then match them with quantum probabilities for recombination in the inner zone. The results of calculations show a strong enhancement of cross sections as compared to the zero-field case.

TBC

Enantio-selective photochemistry relies on the ability to induce different electronic transitions in left and right handed versions (opposite enantiomers) of a chiral molecule using light. This is challenging because i) opposite enantiomers share the same energy spectrum and ii) excitation with circularly polarized light is very weakly enantio-selective. Highly enantio-selective photochemistry is very attractive because it would provide a laser-based alternative to the usual chemical methods for enantiomeric purification and enantio-selective synthesis. These are tasks of immense importance in the chemical industry, where the objective is to produce samples with only one of the two enantiomers starting from 50:50 mixtures. In this talk I will discuss how to tailor the polarization and the spectrum of the light to induce highly enantio-selective population transfer between electronic states using intense femto-second pulses. Our results are supported by an analytical model and by numerical simulations based on direct integration of the time-dependent Schrödinger equation.

Over the last few decades, the generation, detection, and application of structured light fields (i.e, light with nontrivial, but programmable, polarization, intensity, and phase) have revolutionized our ability to control and enhance light-matter interactions, enabling a myriad of technological breakthroughs in super-resolution microscopy, telecommunications, optical manipulation, attosecond physics, and even forensic science. In particular, light waves with programmable spin and orbital angular momentum (SAM and OAM, related to the polarization and spatial phase of a light beam, respectively) have sparked a revolution in attosecond science, owing to their potential to resolve ultrafast chiral and topological dynamics at the nano-femto scale. In the first half of this talk, I highlight progress on the generation of structured extreme ultraviolet (EUV) beams —and attosecond pulses— with designer SAM and OAM that have been realized by harnessing the quantum physics of high-harmonic generation (HHG). The unique mapping of lower-frequency laser properties to the emitted EUV beams in an HHG process has enabled the realization of exquisitely tailored ultrafast waveforms that even possess new properties not present in the lower-frequency driving laser fields. These new sources of structured EUV light have the potential to enable new paradigms in nanoscale, ultrafast spectro-microscopies. The second half of this talk will then focus on industrial applications of ultrafast EUV spectroscopies and imaging at imec, with a perspective on the use of structured EUV light for advanced imaging and spectroscopy of materials and structures at the forefront of semiconductor innovation.

tbd

Manifestations of and possibilities related to vortex electrons in strong-field physics are discussed. We present a theory which extends the foundation of a powerful method of target structure and dynamics imaging to vortex electrons. The theory enables one to extract the differential cross section (DCS) for elastic scattering of a vortex electron on the parent ion—a collision property introduced here—from the observable photoelectron momentum distribution (PEMD). We illustrate this by considering strong-field ionization from π orbitals in two atoms, Xe and He$^+$, and a molecule, O$_2$. The vortex DCS is shown to be sensitive to the target structure. The PEMDs formed by vortex electrons are predicted to be sensitive to the chirality of the target. Extracting vortex DCSs from experimental PEMDs may open a new avenue for rescattering photoelectron spectroscopy.

Since their theoretical proposal [1] and their first experimental demonstration [2], free electron vortices have attracted much attention. Experimental results on the generation and manipulation of photoelectron vortices by multiphoton ionization (MPI) have been reviewed recently in [4,5]. In our experiments, we combine supercontinuum polarization pulse shaping with high-resolution photoelectron tomography [6] to map the atomic MPI dynamics. Recently, we have extended our previous scheme towards multichromatic polarization shaping. In this talk, we report on the experimental observation of free electron vortices, relevant physical mechanisms, and the properties of multicolor free electron vortices. In addition, we introduce a holographic method for extracting the phases in the photoelectron momentum distributions [7,8]. So far, most of the theoretical and all of the experimental investigations were performed on atoms. Here, we present the first experimental demonstration of free electron vortices by MPI of molecules. Specifically, we investigate the creation of molecular vortices on C60 fullerenes by counter rotating circularly polarized femtosecond laser pulse sequences. Since the discovery of the C60 molecule, it has served as a benchmark system for studying photo-induced dynamics in complex systems. Due to its symmetry, the C60 molecule is an ideal system to bridge the gap between atoms and more complex systems such as polyatomic molecules and clusters. It has been shown that C60 has various atom-like electronic orbitals, termed superatomic molecular orbitals (SAMOS) [9], which play an important role in the MPI of fullerenes. By tomographic reconstruction of the three-dimensional photoelectron momentum distribution, we show that ionization from a SAMO with the polarization-tailored laser field creates a six-armed free electron vortex. [1] J. M. Ngoko Djiokap, S. X. Hu, L. B. Madsen, N. L. Manakov, A. V. Meremianin, and A. F. Starace, Phys. Rev. Lett. 115, 113004 (2015). [2] D. Pengel, S. Kerbstadt, D. Johannmeyer, L. Englert, T. Bayer, and M. Wollenhaupt, Phys. Rev. Lett. 118, 053003 (2017). [3] S. Kerbstadt, K. Eickhoff, T. Bayer, and M. Wollenhaupt, Nat. Comm. 10, 658 (2019). [4] K. Eickhoff, L. Feld, D. Köhnke, L. Englert, T. Bayer, and M. Wollenhaupt, Journal of Physics B: Atomic, Molecular and Optical Physics 54, 164002 (2021). [5] K. Eickhoff, L. Englert, T. Bayer, and M. Wollenhaupt, Front. Phys. 9, 444 (2021). [6] M. Wollenhaupt, M. Krug, J. Köhler, T. Bayer, C. Sarpe-Tudoranand T. Baumert, Applied Physics B 95, 647 (2009) [7] K. Eickhoff, L. Feld, D. Köhnke, T. Bayer, and M. Wollenhaupt, Phys. Rev. A 104, 052805 (2021). [8] D. Köhnke, K. Eickhoff, T. Bayer and M. Wollenhaupt, J. Phys. B.: At. Mol. Opt. Phys. 55, 184003 (2022). [9] M. Feng, J. Zhao and H. Petek, Science 359, 320 (2008)

Kerr-type nonlinearities form the basis of our physical understanding of nonlinear optical phenomena in moderately intense fields. In strong laser fields, additional higher-order nonlinearities enable high-harmonic generation, which is currently understood as the interplay of light-driven intraband charge dynamics and interband recombination. Remarkably, the nonlinear response emerging from the subcycle injection dynamics of electrons into the conduction band, i.e. from ionization, has been almost completely overlooked in solids and only partially investigated in the gas phase. In the talk I will illustrate the significance and impact of this ionization-induced nonlinearity in SiO2 as a typical wide-bandgap dielectric and will show that, close to the material damage threshold, the so far unexplored injection current provides the leading contribution [1]. The ultrafast plasma dynamics following massive ionization can be traced via time-resolved coherent-diffractive imaging, as will be discussed for the case of SiO$_2$ nanospheres [2]. References [1] P. Jürgens, B. Liewehr, B. Kruse, C. Peltz, D. Engel, A. Husakou, T. Witting, M. Ivanov , M. J. J. Vrakking, T. Fennel, A. Mermillod-Blondin, Origin of strong-field induced low-order harmonic generation in amorphous solids, Nat. Phys. 16, 1035 (2020) [2] C. Peltz, J. A. Powell, P. Rupp, A. Summers, T. Gorkhover, M. Gallei, I. Halfpap, E. Antonsson, B. Langer, C. Trallero-Herrero, C. Graf, D. Ray, Q. Liu, T. Osipov, M. Bucher, K. Ferguson, S. Möller, S. Zherebtsov, D. Rolles, E. Rühl, G. Coslovich, R. N. Coffee, C. Bostedt, A. Rudenko, M. F. Kling and T. Fennel, Few-femtosecond resolved imaging of laser-driven nanoplasma expansion, New J. Phys. 24, 043024 (2022)

The structure of isolated molecules can be probed with electron diffraction, however, when the molecules are randomly oriented only 1D information is accessible. Controlling the angular distribution of the molecules enables the retrieval of 3D structural information. We have recently shown that ultrafast electron diffraction can be used to characterize the time-dependent angular distribution of the molecules, and to retrieve 3D structural information. Molecules in a gas beam are impulsively aligned with a femtosecond laser pulse, and probed with a femtosecond electron pulse. Here we will show recent examples that demonstrate the retrieval of rotational wavepacket dynamics and 3D structural information.

We demonstrate that polarization control and characterization of high-harmonic generation in non-collinear geometry performs as an excellent ellipsometry that can fully retrieve the amplitude and phase of ultrafast dipole response, advancing high harmonic spectroscopy.

Computational imaging is an elegant approach to microscopy, in which the image formation is achieved using computer algorithms rather than optical components. This approach is particularly interesting for wavelengths at which imaging optics are challenging to manufacture, such as the extreme ultraviolet (EUV) and soft-X-ray spectral ranges, as it allows high-resolution imaging even without using lenses. Advanced computational imaging approaches such as ptychography even enable simultaneous reconstruction of both the object structure and the complex light field that was used to image it. This ability opens up the possibility for EUV imaging with structured light fields, which provides opportunities for exploring new contrast mechanisms and optimizing image information content. We have recently developed methods to produce coherent EUV and soft-X-ray beams with complex spatial structure, using diffractive optical components. This has enabled e.g. simultaneous focusing of multiple wavelengths from a broadband high-harmonic generation (HHG) source, as well as the generation of soft-X-ray vortex beams consisting of superpositions of orbital angular momentum states. To characterize these structured beams, we exploit ptychographic imaging methods as a means for high-resolution wavefront sensing. In this way we are able to retrieve the complex spatial light field of such beams for multiple harmonics in parallel, and reconstruct their structural variations as they propagate through a focus.

We observe experimentally, for the first time to our knowledge, a secondary plateau in UV-driven high harmonic generation in the X-ray regime, extending the conventional cutoff from 130 eV to 300 eV, due to emission of a single photon in double recombination of highly-correlated electrons in helium atoms. The double electron recombination plateau exhibits a stronger dependence on the ellipticity of the driving UV laser, compared to the conventional cutoff from He atoms and He+ ions, and obeys a favorable cutoff scaling of approximately 5.5 times the pondermotive electron energy. Coherent X-ray generation from Ne and Ar atoms and ions, with a lower level correlation of electrons in the outermost shells, does not produce emission with characteristic double-electron recombination signatures. This observation establishes a straightforward way to detect highly correlated femtosecond-to-attosecond electron-electron dynamics in atomic, molecular systems, and materials by using high harmonic electron-correlation spectroscopy.

On-demand modification of quantum material properties is one of the holy grails of material science. The demonstrated feasibility to apply intense light fields, controlled at the level of individual oscillations [1], to 2D materials without optical damage [2], opened the opportunity to induce and control quantum properties that can be manipulated on the timescales of coherent electron motion. One of the most relevant quantum properties of 2D semiconductors is their ability to host two valleys in the band structure, at K and K′ crystal momenta, that can be selected via circularly-polarized light fields resonant with the excitonic band gap, i.e., valleytronics [3]. Yet, to be of practical use, such valley initialization must be accompanied by ultrafast valley manipulation and reading. The one-photon resonant fields that are currently used in valleytronics preclude ultrafast valley switching on timescales shorter than valley lifetime and decoherence (around 100fs in the 100K temperature range [4]), limiting their use for future technological applications. Here, we show how the use of polarization-tailored fields allows for a new regime of band structure engineering and valleytronics. First, we use a strong, non-resonant field with polarization tailored to the spatial symmetry of the crystal lattice to modify the topological properties of a 2D material, allowing to controllably lift the valley degeneracy on few-cycle timescales [5]. This scheme allows for the realization of the topological model of Haldane in monolayer, multi-layer and bulk hexagonal semiconductors with few-femtosecond control [6,7]. Second, we use a train of polarization- and time-controlled weak femtosecond pulses to switch on and off the valley state in transition metal dichalcogenides on less than 100fs [8]. Finally, we introduce an orbital perspective of high-harmonic generation in solids which allows to identify the atomic contributions to the high-harmonic emission, as well as to suppress or enhance the contribution of particular atoms in the lattice. We validate our theory with intensity- and angle-dependent high-harmonic measurements in ReS$_2$ [9]. [1] A. Wirth et al., Science 334 6053 (2011) [2] H. Liu et al., Nat. Phys. 13 262 (2017) [3] J. Schaibley et al., Nat. Rev. Mat. 1 16055 (2016) [4] K. Hao et al., Nat. Phys. 12 677 (2016) [5] A. Jimenez-Galan et al. Nat. Photonics 14 728 (2022) [6] I. Tyulnev et al., arXiv 2302.12564 (2023) [7] S. Mitra et al., to be sumbitted (2023) [8] A. Jimenez-Galan et al., Opt. Express 30 30347 (2022) [9] A. Jimenez-Galan et al., submitted (2023)

TBA

The recent discovery of high harmonic generation in solids [1], merging the fields of strong field and condensed matter physics, opened the door for the direct observation of Bloch oscillations [1], all-optical reconstruction of the band structure [2] and direct observation of the influence of the Berry curvature in the optical response [3]. In this work, we will focus on high harmonic generation in strongly correlated and topological materials. First, I will show how high harmonic spectroscopy can be used to induce and time resolve insulator-to-metal transitions in strongly correlated materials, using the Hubbard model [4]. I will further demonstrate how high harmonic spectroscopy can be used to identify topological phases of matter and how the Berry curvature leaves its fingerprint in the nonlinear optical response of the material [5]. Using a combination of w-2w counter-rotating strong circular fields, we demonstrate that we are able to induce valley polarization in hexagonal 2D materials and use HHG spectroscopy to read the valley polarization [6]. I will also show how non-linear optical spectroscopy can be used to image the electronic structure of twisted bilayer graphene near the magic angle [8]. At last, I will show how the use of Wannier orbitals can be useful in the calculation of the nonlinear optical response of solids [7]. References: [1] S. Ghimire et al., Nat. Phys., 7 138-141 (2011 [2] G. Vampa et al., Phys. Rev. Lett., 115 193603 (2015) [3] H. Liu et al., Nat. Phys., 13 262-265 (2017) [4] R. E. F. Silva, I. Blinov, A. Rubtsov, O. Smirnova and M. Ivanov, Nat. Phot., 12 266-270 (2018) [5] R. E. F. Silva, Á. Jiménez-Galán, B. Amorim, O. Smirnova, M. Ivanov, Nat. Phot., 13 849-854 (2019) [6] Á. Jiménez-Galán, R. E. F. Silva, O. Smirnova, M. Ivanov, Nat. Phot. Nat. Phot. 14 728-732 (2020) [7] R. E. F. Silva, F. Martin, M. Ivanov, Phys. Rev. B, 100 195201 (2019) [8] E. B. Molinero et al. arXiv.2302.04127 (2023)

Lightwave electronics has pushed the control of condensed matter to record short time scales. By harnessing the carrier wave of intense phase-locked light pulses as an alternating voltage [1-16], electrons can be driven faster than a cycle of light, opening up a fascinating coherent quantum world. Phase-stable multi-terahertz (THz) pulses have been uniquely adapted to the energy scales of delocalized Bloch electrons in crystalline solids, enabling dynamical Bloch oscillations [3-6], quasiparticle collisions [7-10], all-optical band-structure reconstruction [9], and subcycle Dirac currents [11,12]. THz fields can also switch the spin [13] and the valley pseudospin [8,14] and drive atomically resolved ultrafast currents [15] and forces [16]. Yet, resolving the influence of many-body correlations on the trajectories of delocalized Bloch electrons directly in the time domain has remained an open challenge. Here, we use THz fields to force electron–hole pairs in crystalline semiconductors onto closed trajectories and clock the delay between separation and recollision with a 300 as precision, corresponding to 0.7\% of the driving field’s oscillation period. We detect that strong Coulomb correlations emergent in atomically thin WSe\textsubscript{2} shift the optimal timing of recollisions by up to 1.2 fs compared to the bulk material [10]. Also valley-specific phase-space filling, Pauli-repulsion and screening influence the dynamics of the charge carriers. The resulting attosecond chronoscopy of delocalized electrons could revolutionize our understanding of phase transitions and emergent quantum-dynamic phenomena for future electronic, optoelectronic, and quantum-information technologies. Most recently, we also succeeded in utilizing topologically non-trivial trajectories of quasi-relativistic electrons, to optically engineer Floquet-Bloch bands. In the first-ever subcycle band-structure videography in the strong-field limit, we directly visualize the birth of Floquet-Bloch states within a single oscillation cycle of the carrier field and witness their collapse by scattering [12]. These results mediate a direct time-domain view of Floquet physics, explore the fundamental frontiers of ultrafast band-structure engineering, and pave the way for the investigation of novel exotic phases of matter. [1] P. B. Corkum and F. Krausz, Nat. Phys. 3, 381 (2007) and references therein. [2] D. Shafir et al., Nature 485, 343 (2012). [3] O. Schubert et al., Nat. Photon. 8, 119 (2014). [4] M. Hohenleutner et al., Nature 523, 572 (2015). [5] Y. S. You et al., Nat. Commun. 8, 724 (2017). [6] C. P. Schmid et al., Nature 593, 385 (2021). [7] F. Langer et al., Nature 533, 225 (2016). [8] F. Langer et al., Nature 557, 76 (2018). [9] M. Borsch et al., Science 370, 1204 (2020). [10] J. Freudenstein et al., Nature 610, 290-295 (2022). [11] J. Reimann et al., Nature 562, 396 (2018). [12] S. Ito, et al., in press (2023). [13] S. Schlauderer et al., Nature 569, 383 (2019). [14] Á. Jiménez-Galán et al., Nat. Photon. 14, 728 (2020). [15] T. L. Cocker, D. Peller et al., Nature 539, 263 (2016). [16] D. Peller et al., Nature 585, 58 (2020).J. Freudenstein\textsuperscript{1}, M. Meierhofer\textsuperscript{1}, S. Ito\textsuperscript{3}, M. Borsch\textsuperscript{2}, M. Schüler\textsuperscript{4}, J. Güdde\textsuperscript{3}, M. Sentef\textsuperscript{5}, U. Höfer\textsuperscript{3}, M. Kira\textsuperscript{2}, and R. Huber\textsuperscript{1}\\ \textsuperscript{1}Department of Physics, University of Regensburg, Regensburg, Germany\\ \textsuperscript{2}Department of Electrical Engineering and Computer Science, University of Michigan, Michigan, USA\\ \textsuperscript{3}Department of Physics, Philipps-University of Marburg, Marburg, Germany\\ \textsuperscript{4}Condensed Matter Theory Group, Paul Scherrer Institute, Villigen PSI, Switzerland\\ \textsuperscript{5}Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany\\

TBA

Through the application of intertwined wavefronts to an intense femtosecond pulse we can create two XUV pulses that are separated in space and yet have a phase jitter of 0.1mrad or 6zs at ~80nm of center wavelength. High harmonic generation creates XUV pulses between the 7th and the 17th harmonic of the fundamental 800nm . We perform single-, and two-photon interferometric experiments to show that each photon carries the full high harmonic spectrum. This was established by collapsing the wavefunction of the first XUV photon followed by a measurement of a second XUV photon. Both measurements are spatially and spectrally resolved. The presence of spatial interference in this case, shows that while highly coherent, the two photons are not entangled. The delay between the pulses can be controller with a resolution of <100zs. We discuss applications to molecular dynamics spectroscopy.

In extreme nonlinear optics, matter is illuminated by intense light, which results in electronic quiver motion. For a free electron, the cycle-averaged energy of such a quiver motion is known as the ponderomotive energy. However, as they are currently formulated, these concepts are not applicable to charged particles driven by bright squeezed vacuum, and more generally, by light fields with a vanishing coherent electric field amplitude. In this talk, I will present a detailed numerical & analytical study of the motion of free and bound electrons driven by quantum light, focusing on multi-mode squeezed vacuum state. This study resolves many aspects of the dynamics, including bound and unbound free-electron width oscillations & their ponderomotive energy, Rabi-like oscillations between bound states, and the sub-cycle structure of tunnel ionization rates induced by squeezed vacuum. I will show that all these effects stem from an effective photon-statistics force, and discuss its implications on three-step trajectories in high harmonic generation.

Trajectory models for the observables in strong-field induced dynamics of atoms and molecules work are astonishingly useful for extracting space and time information about the electron dynamics. Along these lines, in high-harmonic generation, orthogonal two-color fields with variable delay can measure the exit time of electrons with few-attosecond precision if the electron-core interaction is properly taken into account in the modeling. In photoelectron emission from polar molecules, we show that molecular properties such as the polarizability tensor and the dipole moment can be extracted from the dependence of the photoelectron momentum distribution on the orientation of the molecule. In this case, it is useful to tailor a two-dimensional field to be transiently linearly polarized to have a well-defined angle between the electric field and the molecule, while the overall shape of the field is not linear, thus avoiding complications due to rescattering.

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is a powerful photoelectron spectroscopy, offering direct access to internal dynamics of the target. It is being increasingly applied to molecular systems, but a general, computationally tractable theory of RABBITT spectra in molecules has so far been lacking. I show that under quite general assumptions, RABBITT spectra in molecules can be expressed as a convolution of the vibronic cross-correlation functions and two-electron photoionization matrix elements. The general expressions allow simplification and specialization to the commonly-encountered special cases, some of which I will present. I will illustrate the theory using the example of simulating RABBITT spectra in methane and deuteromethane.

When atoms and molecules (the building block of matter) is exposed to and ionized using ultrashort and intense laser pulses in the perturbative and multiphoton regime, manipulating the polarization state of light opens the possibility of exploring a variety of novel physical phenomena inaccessible for linear polarization. In this talk, we will consider one of such phenomena, electron matter-wave vortices seen as spiral patterns in the photoelectron momentum distribution thanks to the broad bandwidth characteristic of ultrashort laser pulses, which we discovered and was confirmed experimentally. Different aspects of this interference and polarization effect to be discussed include their generation, origin, control by means of the target and light configuration dependences, electron-electron correlation, classification and potential applications. This electron effect has created a new subfield in physics for searches and applications of this wave property of matter for different processes, targets, and regimes.

Resolving the real-time motion of electrons in complex systems is a key to enhancing the functionality and understanding the underlying mechanism of modern materials. Future studies using ultrafast capabilities with attosecond x-ray pulses brings closer the possibility of following electron dynamics with site specificity. In this context, we develop a numerical code in order to describe the optical response in real time. Here we will show some preliminary calculations in which we are able to resolve the laser-driven electron dynamics in realistic materials. The description of structured light can be further implemented by the integration of the code with a light propagation framework.

Attosecond science and strong field physics are rapidly progressing toward a world-changing goal to control the electron motion in matters and, ultimately, chemical reaction. To theoretically investigate attosecond and strong field processes, we have developed various cost-effective wavefunction-based methods such as time-dependent multiconfiguration self-consistent-field (TD-MCSCF) methods, the time-dependent optimized coupled-cluster (TD-OCC) methods using time-varying orbitals, and the gauge-invariant time-dependent configuration-interaction-singles (TDCIS) method. In this talk, we report their formulations, numerical implementations, and comparison with experimental results as well as simulations using quantum computers.

We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit (U=0), the model admits both localized and delocalized phases depending on the strength of the incommensurate potential V0. We show that the particle current contains only odd harmonics in the delocalized phase in contrast to the localised phase where both even and odd harmonics are identified. The relative magnitudes of these even and odd harmonics and sharpness of the peaks can be tuned by varying frequency and the number of cycles of the applied pulse, respectively. In the presence of repulsive interactions, the amplitudes of the even and odd harmonics further depend on the relative strengths of the interaction U and the potential V0. We illustrate that the disorder and interaction-induced phases can be distinguished and characterized through the particle current. Finally, we discuss the dynamics of field induced excitation responsible for exhibiting higher harmonics in the current spectrum.

Since the early days of strong-field physics and attoscience it has been recognized that intense-laser-field-driven processes can be significantly modified in the presence of static fields [1]. Nowadays terahertz fields are strong enough to mimic such static fields [2]. The THz field wavelength is hundreds of times longer than that of the usual laser fields, so that a THz field can be considered as constant during the laser pulse. The vector potential amplitude is proportional to the wavelength and to the strength of the used field, so that the THz pulse vector potential can be comparable to that of the laser field even in the case when the THz field intensity is much lower than the laser field intensity. Since the dynamics of the strong-field processes is governed by the vector potential, these processes can be significantly modified in the presence of a THz field. And, really, it has recently been shown that the laser-induced ionization drastically changes in the presence of a strong THz pulse [3]. In the present contribution I will show how the ionization probability and the maximum photoelectron energy can be changed by an order of magnitude by changing the time delay between the THz and laser pulses. I will also show how the nondipole effects modify this process [4]. Experimental results for the THz-pulse-assisted above-threshold ionization may be shown if the suggested experiment is performed at the ELI ALPS facility in Szeged by the time of the conference. [1] D. B. Milošević and A. F. Starace, Phys. Rev. Lett. 81, 5097 (1998); ibid. 82, 2653 (1999). [2] X. C. Zhang, A. Shkurinov, and Y. Zhang, Nat. Photonics 11, 16 (2017); D. Matte et al., Phys. Rev. Research 3, 013137 (2021). [3] D. B. Milošević, Opt. Lett. 47, 1669 (2022); Phys. Rev. A 105, 053111 (2022). [4] D. B. Milošević and D. Habibović, Opt. Express 30, 29979 (2022).

Attosecond (as) pulse generation is temporally constrained by the attochirp inherent to the high-order harmonic generation (HHG) process. In the extreme ultraviolet, near Fourier-limited as-pulses are obtained compensating the attochirp using dispersive materials like metallic filters. The shortest as-pulse record used a Zr-filter to compress the pulse down to just 43 as [1]. However, at the soft x-rays regime, chirp compensation optics is inefficient and the generation of near Fourier-limited pulses has become a great challenge. We identify a promising scenario to suppress the attochirp assisting HHG with a strong fast oscillating magnetic field (B-field), up to tens of kT, than can be obtained from structured beams or stationary configurations of state-of-the-art Petawatt laser systems. [2] We spot a situation where a strong B-field assists the HHG process creating a transverse harmonic oscillator-like potential acting as an energy reservoir and as a confinement of the free electron wavepacket after the ionization step. Whereas HHG driven by a circularly-polarized (CP) laser is not efficient by the ineffective recollision with the parent ion [3], this no longer holds if assisted by a B-field. We numerically show how CP drivers not only result in a broad spectra beyond the classical limit, but also form near Fourier-limited as-pulses. We compare the HHG spectra, driven by a $|E_0|^2 = 1.6\times10^14$ W/cm2 laser at 0.8 μm, with the standard scheme of HHG (linearly-polarized (LP) driver and no B-field), and our proposed configuration (CP driver assisted by a $2.8\times10^4$ T B-field at 1.6 μm). In the new setup, the spectrum is extended to 310 eV, hundreds of harmonic orders above the classical cutoff energy. Remarkably, the radiation arises as a few-cycle near Fourier-limited 27 as full-width half maximum pulse. To understand the intrinsic physics, we develop a unidimensional model for the transverse component of the free wavepacket. From the interplay between the trapping potential and the transverse component of the CP driver, the wavepacket follows a quivering trajectory together with a lateral breathing cycle. If the maximum wavepacket compression is synchronized with the ion recollision, the effective rescattering time is minimized leading to a chirp-free emission. We foresee a new scenario where Petawatt lasers may be vital in an attochirp-free x-ray HHG process, paving the way to the generation of few-cycle Fourier-limited as-pulses. [4] References: ------------------------------ [1] T. Gaumnitz et al., Streaking of 43-attosecond soft-x-ray pulses generated by a passively CEP-stable mid-infrared driver, Opt. Express, 25, 27506 (2017). [2] M. Blanco et al., Ultraintense Femtosecond Magnetic Nanoprobes Induced by Azimuthally Polarized Laser Beams, ACS Photonics, 6, 38 (2019). [3] K. S. Budil et al., Influence of ellipticity on harmonic generation Phys. Rev. A, 48, R3437 (1993). [4] R. Mart ́ın-Herna ́ndez et al., Fourier-Limited Few-Cycle Attosecond Pulses from High-Order Harmonic Generation Assisted by an Ultraintense Ultrafast Magnetic Field, in preparation.

When atoms and molecules are shined by photons with large energies or intense lasers in the long wavelength, various new phenomena will arise due to the nondipole effects, in which case the magnetic component of the laser pluse can not be completely neglected. In this talk, we will first briefly review several popular theoretical methods and relevant concepts in strong field and attosecond physics beyond the dipole approximation. Physical phenomena stemming from the breakdown of the dipole approximation are then discussed in various topics, including the radiation pressure and photon-momentum transfer, the atomic stabilization, the dynamic interference, and the electron-electron correlation, etc.