Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES.

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

High-harmonic spectroscopy of low-energy electron-scattering dynamics in liquids.

High-harmonic spectroscopy is an all-optical nonlinear technique with inherent attosecond temporal resolution. It has been applied to a variety of systems in the gas phase and solid state. Here we extend its use to liquid samples. By studying high-harmonic generation over a broad range of wavelengths and intensities, we show that the cut-off energy is independent of the wavelength beyond a threshold intensity and that it is a characteristic property of the studied liquid. We explain these observations with a semi-classical model based on electron trajectories that are limited by the electron scattering. This is further confirmed by measurements performed with elliptically polarized light and with ab-initio time-dependent density functional theory calculations. Our results propose high-harmonic spectroscopy as an all-optical approach for determining the effective mean free paths of slow electrons in liquids. This regime is extremely difficult to access with other methodologies, but is critical for understanding radiation damage to living tissues. Our work also indicates the possibility of resolving subfemtosecond electron dynamics in liquids offering an all-optical approach to attosecond spectroscopy of chemical processes in their native liquid environment.

Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization.

Ultrafast nonlinear optical phenomena in solids have been attracting a great deal of interest as novel methodologies for the femtosecond spectroscopy of electron dynamics and control of the properties of materials. Here, we theoretically investigate strong-field nonlinear optical transitions in a prototypical two-dimensional material, hBN, and show that the k-resolved conduction band charge occupation patterns induced by an elliptically polarized laser can be understood in a multiphoton resonant picture, but, remarkably, only if using the Floquet light-dressed states instead of the undressed matter states. Our work demonstrates that Floquet dressing affects ultrafast charge dynamics and photoexcitation even from a single pump pulse and establishes a direct measurable signature for band dressing in nonlinear optical processes in solids, opening new paths for ultrafast spectroscopy and valley manipulation.

Tunable Tesla-Scale Magnetic Attosecond Pulses through Ring-Current Gating.

Coherent control over electron dynamics in atoms and molecules using high-intensity circularly polarized laser pulses gives rise to current loops, resulting in the emission of magnetic fields. We propose, and demonstrate with ab initio calculations, "current-gating" schemes to generate direct or alternating-current magnetic pulses in the infrared spectral region, with highly tunable waveform and frequency, and showing femtosecond-to-attosecond pulse duration. In optimal conditions, the magnetic pulse can be highly isolated from the driving laser and exhibits a high flux density (∼1 T at a few hundred nanometers from the source, with a pulse duration of 787 attoseconds) for application in forefront experiments of ultrafast spectroscopy. Our work paves the way toward the generation of attosecond magnetic fields to probe ultrafast magnetization, chiral responses, and spin dynamics.

High-harmonic generation in liquids with few-cycle pulses: effect of laser-pulse duration on the cut-off energy.

High-harmonic generation (HHG) in liquids is opening new opportunities for attosecond light sources and attosecond time-resolved studies of dynamics in the liquid phase. In gas-phase HHG, few-cycle pulses are routinely used to create isolated attosecond pulses and to extend the cut-off energy. Here, we study the properties of HHG in liquids, including heavy water, ethanol and isopropanol, by continuously tuning the pulse duration of a mid-infrared driver from the multi- to the two-cycle regime. Similar to the gas phase, we observe the transition from discrete odd-order harmonics to continuous extreme-ultraviolet emission. However, the cut-off energy is shown to be entirely independent of the pulse duration. These observations are confirmed by ab-initio simulations of HHG in large liquid clusters. Our results support the notion that the cut-off energy is a fundamental property of the liquid, independent of the driving-pulse properties. Our work implies that few-cycle mid-infrared laser pulses are suitable drivers for generating isolated attosecond pulses from liquids and confirm the capability of high-harmonic spectroscopy to determine the mean-free paths of slow electrons in liquids.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light.

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Multiscale dynamical symmetries and selection rules in nonlinear optics.

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

Ab Initio Cluster Approach for High Harmonic Generation in Liquids.

High harmonic generation (HHG) takes place in all phases of matter. In gaseous atomic and molecular media, it has been extensively studied and is very well understood. In solids, research is ongoing, but a consensus is forming for the dominant microscopic HHG mechanisms. In liquids, on the other hand, no established theory yet exists, and approaches developed for gases and solids are generally inapplicable, hindering our current understanding. We develop here a powerful and reliable ab initio cluster-based approach for describing the nonlinear interactions between isotropic bulk liquids and intense laser pulses. The scheme is based on time-dependent density functional theory and utilizes several approximations that make it feasible yet accurate in realistic systems. We demonstrate our approach with HHG calculations in water, ammonia, and methane liquids and compare the characteristic response of polar and nonpolar liquids. We identify unique features in the HHG spectra of liquid methane that could be utilized for ultrafast spectroscopy of its chemical and physical properties, including a structural minimum at 15-17 eV that is associated solely with the liquid phase. Our results pave the way to accessible calculations of HHG in liquids and illustrate the unique nonlinear nature of liquid systems.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy.

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

Selection rules in symmetry-broken systems by symmetries in synthetic dimensions.

Selection rules are often considered a hallmark of symmetry. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions to demonstrate that symmetry-broken systems systematically exhibit a specific class of symmetries and selection rules. These selection rules constrain the scaling of a system's observables (non-perturbatively) as it transitions from symmetric to symmetry-broken. Specifically, we drive bi-elliptical high harmonic generation (HHG), and observe that the scaling of the HHG spectrum with the pump's ellipticities is constrained by selection rules corresponding to symmetries in synthetic dimensions. We then show the generality of this phenomenon by analyzing periodically-driven (Floquet) systems subject to two driving fields, tabulating the resulting synthetic symmetries for (2 + 1)D Floquet groups, and deriving the corresponding selection rules for high harmonic generation (HHG) and other phenomena. The presented class of symmetries and selection rules opens routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, symmetry-protected dark bands, and more.

Detecting multiple chiral centers in chiral molecules with high harmonic generation.

Characterizing chiral is highly important for applications in the pharmaceutical industry, as well as in the study of dynamical chemical and biological systems. However, this task has remained challenging, especially due to the ongoing increasing complexity and size of the molecular structure of drugs and active compounds. In particular, large molecules with many active chiral centers are today ubiquitous, but remain difficult to structurally analyze due to their high number of stereoisomers. Here we theoretically explore the sensitivity of high harmonic generation (HHG) to the chiral of molecules with a varying number of active chiral centers. We find that HHG driven by bi-chromatic non-collinear lasers is a sensitive probe for the stereo-configuration of a chiral molecule. We first show through calculations (from benchmark chiral molecules with up to three chiral centers) that the HHG spectrum is imprinted with information about the handedness of each chiral center in the driven molecule. Next, we show that using both classical- and deep-learning-based reconstruction algorithms, the composition of an unknown mixture of stereoisomers can be reconstructed with high fidelity by a single-shot HHG measurement. Our work illustrates how the combination of non-linear optics and machine learning might open routes for ultra-sensitive sensing in chiral systems.

Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents.

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material's structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (∼10^{13} W/cm^{2}) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.

The quantum-optical nature of high harmonic generation.

High harmonic generation (HHG) is an extremely nonlinear effect generating coherent broadband radiation and pulse durations reaching attosecond timescales. Conventional models of HHG that treat the driving and emitted fields classically are usually very successful but inherently cannot capture the quantum-optical nature of the process. Although prior work considered quantum HHG, it remains unknown in what conditions the spectral and statistical properties of the radiation depart considerably from the known phenomenology of HHG. The discovery of such conditions could lead to novel sources of attosecond light having squeezing and entanglement. Here, we present a fully-quantum theory of extreme nonlinear optics, predicting quantum effects that alter both the spectrum and photon statistics of HHG, thus departing from all previous approaches. We predict the emission of shifted frequency combs and identify spectral features arising from the breakdown of the dipole approximation for the emission. Our results show that each frequency component of HHG can be bunched and squeezed and that each emitted photon is a superposition of all frequencies in the spectrum, i.e., each photon is a comb. Our general approach is applicable to a wide range of nonlinear optical processes, paving the way towards novel quantum phenomena in extreme nonlinear optics.

Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy.

We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and molecules, based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-symmetric laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented atomic or molecular media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible physical mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calculations.

Floquet group theory and its application to selection rules in harmonic generation.

Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation.

Optical chirality (OC)-one of the fundamental quantities of electromagnetic fields-corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

Selective suppression of high-order harmonics within phase-matched spectral regions.

Phase matching in high-harmonic generation leads to enhancement of multiple harmonics. It is sometimes desired to control the spectral structure within the phase-matched spectral region. We propose a scheme for selective suppression of high-order harmonics within the phase-matched spectral region while weakly influencing the other harmonics. The method is based on addition of phase-mismatched segments within a phase-matched medium. We demonstrate the method numerically in two examples. First, we show that one phase-mismatched segment can significantly suppress harmonic orders 9, 15, and 21. Second, we show that two phase-mismatched segments can efficiently suppress circularly polarized harmonics with one helicity over the other when driven by a bi-circular field. The new method may be useful for various applications, including the generation of highly helical bright attosecond pulses.

Play the heavy: An effective mass study for α-Fe2O3 and corundum oxides.

Iron(iii) oxide (α-Fe2O3) is a known water splitting catalyst commonly used in photoelectrochemical cells. These cells are severely impaired by poor conductivity in α-Fe2O3, and resolving the conductivity issue is therefore crucial. One of the most intrinsic properties of matter, which governs conductivity, is the carrier effective masses. In this work, we investigate the carrier effective masses in α-Fe2O3 and other corundum oxides, including Al2O3, Cr2O3, Ga2O3, and In2O3 with different theoretical constructs: density functional theory (DFT), DFT+U, hybrid DFT, and G0W0. We find DFT sufficiently describes the carrier masses and a quasi-particle theory is only required for accuracies better than 30% for the conduction band effective mass. Additionally, we compare the density of states (DOS) and band effective mass approximations and conclude the DOS effective mass provides poor results whenever the band structure is anisotropic. We find that the charge carriers in Fe2O3 "play the heavy" since they have large effective masses that reduce conductivity and device efficiency. Finally, we conclude that the less heavy electron effective masses of other corundum oxides studied relative to Fe2O3 could contribute to efficiency improvements in Fe2O3 upon Al2O3, Ga2O3, and In2O3 coverage.

Novel High-Throughput Screening Approach for Functional Metal/Oxide Interfaces.

Metal/oxide interfaces have long been studied for their fundamental importance in material microstructure as well as their broad applicability in electronic devices. However, the challenge involved in characterizing the relation between structure and electron transport of a large number of metal/oxide combinations inhibits the search for interfaces with improved functionality. Therefore, we develop a novel high-throughput screening approach that combines computational and theoretical techniques. We use a Density Functional Theory + U (DFT+U) quantum mechanical formalism to produce effective Schrödinger equations, which are solved by wave packet propagation to simulate charge transport across the metal/oxide interface. We demonstrate this method on α-Fe2O3/Mt interfaces, for Mt = Ag, Al, Au, Ir, Pd, or Pt metals. We use this novel method to screen for binary alloys of these metals at the α-Fe2O3/Mt interface and perform a successful validation test of the methodology. Finally, we correlate the interface potential energy and the charge transport permeability through the interface. Counterintuitively, among the interfaces studied, we find that higher mismatch interfaces have better charge transport permeability. We anticipate that this method will be useful as a computationally tractable strategy to perform high-throughput screening for new metal/oxide interfaces.

Can we judge an oxide by its cover? The case of platinum over α-Fe2O3 from first principles.

Metal/metal-oxide interfaces appear in a wide variety of disciplines including electronics, corrosion, electrochemistry, and catalysis. Specifically, covering a metal-oxide with a metal is often thought to enhance solar energy absorption and to improve photocatalytic activity. For example, the platinum/hematite (Pt/α-Fe2O3) interface has demonstrated improved functionality. In order to advance our understanding of how metal coverage over an oxide helps performance, we characterize the geometry and electronic structure of the Pt/α-Fe2O3 interface. We investigate the interface using density functional theory +U, and find a stable crystallographic orientation relationship: Fe2O3(0001)[11[combining macron]00]∥Pt(111)[101[combining macron]] that agrees with experiment. Furthermore, there are significant changes in the electronic structure of α-Fe2O3 as a result of Pt coverage. We therefore suggest the concept of "judging" the electronic properties of an oxide only with its cover. Specifically, covering Fe2O3 with Pt reduces carrier effective mass and creates a continuum of states in the band gap. The former could be beneficial for catalytic activity, while the latter may cause surface recombination. In order to circumvent this problem, we suggest putting metal coverage behind the oxide and far from the electrolyte in a photoelectrochemical device in order to quickly collect electron carriers and avoid recombination with vulnerable holes accumulating as a result of catalysis at the surface.