High-harmonic Generation Spectroscopy Research Articles

High-harmonic generation with a twist: all-optical characterization of magic-angle twisted bilayer graphene

If we stack up two layers of graphene while changing their respective orientation by some twisting angle, we end up with a strikingly different system 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. Recently, 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 moiré materials.

Terahertz-slicing - an all-optical synchronization for 4th generation light sources.

A conceptually new approach to synchronizing accelerator-based light sources and external laser systems is presented. The concept is based on utilizing a sufficiently intense accelerator-based single-cycle terahertz pulse to slice a thereby intrinsically synchronized femtosecond-level part of a longer picosecond laser pulse in an electro-optic crystal. A precise synchronization of the order of 10 fs is demonstrated, allowing for real-time lock-in amplifier signal demodulation. We demonstrate successful operation of the concept with three benchmark experiments using a 4th generation accelerator-based terahertz light source, i.e. (i) far-field terahertz time-domain spectroscopy, (ii) terahertz high harmonic generation spectroscopy, and (iii) terahertz scattering-type scanning near-field optical microscopy.

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.

Efficient attosecond pulse generation from WS2 semiconductor by tailoring the driving laser pulse

High harmonic generation in semiconductor materials with ultra-short pulses of the femtosecond order provides a promising approach to generate attosecond pulses and control the electron dynamics. In this study, an accurate time dependent density functional theory model describing high-order harmonic generation in WS2 bulk is investigated. The effect of driving laser specifications such as ellipticity and chirp rate on producing attosecond pulse is studied. The results show that using a nonlinearly chirped laser can lead to generation of harmonics up to 50 eV, and consequently, production of an attosecond pulse with duration of 440 as. Moreover, a two-color chirped driving laser is proposed which is capable of increasing harmonics up to 63 eV with a slight decrease in the intensity, and reducing the output attosecond pulse duration to 310 as. Our results offer a valuable route towards development of solid-state high harmonic generation spectroscopy and high-performance attosecond source applications.

Ultrafast laser-driven many-body dynamics and Kondo coherence collapse

Ultrafast laser pulse has provided a systematic way to inspect the dynamics of electrons in condensed matter systems. In this paper, by means of time-dependent density matrix renormalization group, we study an ultrafast laser driven Kondo lattice model, in which conduction electrons are strongly coupled with magnetically local moments. The single-particle spectral function due to strong correlation effects and photon emission in the non-equilibrium states under laser driving are calculated. We find laser field excited collective doublon-hole pairs and an associated transient melting of Kondo coherence phase, signifying the collapse of Kondo energy gap. Moreover, we show that the photon emission, induced by a strong laser field, exhibits a different intensity characteristics than in the equilibrium Kondo insulator, which could be explained by the Kondo collapse and related suppression of both intra-band and inter-band contribution in Kondo melting liquid. These theoretical insight is accessible with time- and angle-resolved photoemission spectroscopy and high-harmonic generation spectroscopy, and will stimulate the investigation of nonequilibrium dynamics and nonlinear phenomenon in heavy fermion systems.

Visualization of two-dimensional transition dipole moment texture in momentum space using high-harmonic generation spectroscopy

Highly nonlinear optical phenomena can provide access to properties of electronic systems which are otherwise difficult to access through conventional linear optical spectroscopies. In particular, high harmonic generation (HHG) in crystalline solids is strikingly different from that in atomic gases, and it enables us to access electronic properties such as the band structure, Berry curvature, and valence electron density. Here, we show that polarization-resolved HHG measurements can be used to probe the transition dipole moment (TDM) texture in momentum space in two dimensional semiconductors. TDM is directly related to the internal structure of the electronic system and governs the optical properties. We study HHG in black phosphorus, which offers a simple two-band system, with bandgap resonant excitation. We observed a unique crystal-orientation dependence of the HHG yields and polarizations and succeeded in reconstructing the TDM texture related to the inter-atomic bonding structure. Our results demonstrate the potential of high harmonic spectroscopy for probing electronic wavefunctions in crystalline solids.

Role of exchange and correlation in high-harmonic generation spectra of H2, N2, and CO2: Real-time time-dependent electronic-structure approaches.

This study arises from the attempt to answer the following question: how different descriptions of electronic exchange and correlation affect the high-harmonic generation (HHG) spectroscopy of H2, N2, and CO2 molecules? We compare HHG spectra for H2, N2, and CO2 with different ab initio electronic structure methods: real-time time-dependent configuration interaction and real-time time-dependent density functional theory (RT-TDDFT) using truncated basis sets composed of correlated wave functions expanded on Gaussian basis sets. In the framework of RT-TDDFT, we employ Perdew-Burke-Ernzerhof (PBE) and long-range corrected Perdew-Burke-Ernzerhof (LC-ωPBE) functionals. We study HHG spectroscopy by disentangling the effect of electronic exchange and correlation. We first analyze the electronic exchange alone, and in the case of RT-TDDFT with LC-ωPBE, we use ω = 0.3 and ω = 0.4 to tune the percentage of long-range Hartree-Fock exchange and short-range exchange PBE. Then, we added the correlation as described by the PBE functional. All the methods give very similar HHG spectra, and they seem not to be particularly sensitive to the different description of exchange and correlation or to the correct asymptotic behavior of the Coulomb potential. Despite this general trend, some differences are found in the region connecting the cutoff and the background. Here, the harmonics can be resolved with different accuracy depending on the theoretical schemes used. We believe that the investigation of the molecular continuum and its coupling with strong fields merits further theoretical investigations in the near future.

Probing the molecular frame of uracil and thymine with high-harmonic generation spectroscopy.

In this work, we present the computed high-harmonic generation (HHG) spectra of uracil and thymine molecules, by means of the real-time time-dependent formulation of Gaussian-based configuration interaction with single excitations (RT-TD-CIS). According to the experimental work [Hutchison et al., Comparison of high-order harmonic generation in uracil and thymine ablation plumes, Phys. Chem. Chem. Phys., 2013, 15, 12308], a pulse wavelength of 780 nm has been used, together with an intensity of 1014 W cm-2 and a pulse duration of 23 optical cycles. In order to examine the effect of pulse polarisation, rotationally averaged (to mimic the gas-phase sample) and single-polarisations have been computed for both molecules. Our results show that the HHG signal for both molecules possibly originates from different ionisation channels, involving HOMO, HOMO-1, HOMO-2 and HOMO-3 orbitals, which lie within 4 eV. We characterize the HHG spectrum of thymine, supporting the idea that the absence of the thymine signal in the original work does not depend on the single-molecule behaviour. Present results for uracil are consistent with the experimental data. Moreover, we have observed that states below and above the chosen ionisation threshold provide different contributions to the HHG spectrum in averaged and single-polarisation calculations.

Circular dichroism in higher-order harmonic generation: Heralding topological phases and transitions in Chern insulators

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

Attosecond spectral singularities in solid-state high-harmonic generation

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.

Shaping electron-hole trajectories for solid-state high harmonic generation control.

Solid-state high-harmonic generation (HHG) by an intense infra-red (IR) laser field offers a new route to generate coherent attosecond light pulses in the extreme ultraviolet regime. The propagation of the IR driving field in the dense solid medium is accompanied by non-linear processes which shape the generating waveform. In this work, we introduce a monolithic scheme in which we both exploit the non-linear propagation to manipulate a two color driving field, as well as generate high harmonics within a single crystal. We show that the resulting non-commensurate, bi-chromatic, generating field provides precise control over the periodicity of the HHG process. This control enables us to manipulate the spectral positions of the discrete harmonic peaks. Our method advances solid-state HHG spectroscopy, and offers a simple route towards tunable, robust XUV sources.

Discriminating organic isomers by high harmonic generation: A time-dependent configuration interaction singles study.

High Harmonic Generation (HHG) is a nonlinear optical process that provides a tunable source for high-energy photons and ultrashort laser pulses. Recent experiments demonstrated that HHG spectroscopy may also be used as an analytical tool to discriminate between randomly oriented configurational isomers of polyatomic organic molecules, namely, between the cis- and trans-forms of 1,2-dichloroethene (DCE) [M. C. H. Wong et al., Phys. Rev. A 84, 051403 (2011)]. Here, we suggest as an economic and at the same time a reasonably accurate method to compute HHG spectra for polyatomic species, Time-Dependent Configuration Interaction Singles (TD-CIS) theory in combination with extended atomic orbital bases and different models to account for ionization losses. The HHG spectra are computed for aligned and unaligned cis- and trans-DCE. For the unaligned case, a coherent averaging over possible rotational orientations is introduced. Furthermore, using TD-CIS, possible differences between the HHG spectra of cis- and trans-DCE are studied. For aligned molecules, spectral differences between cis and trans emerge, which can be related to their different point group symmetries. For unaligned, randomly oriented molecules, we also find distinct HHG spectra in partial agreement with experiment. In addition to HHG response in the frequency space, we compute time-frequency HHG spectra to gain insight into which harmonics are emitted at which time. Further differences between the two isomers emerge, suggesting time-frequency HHG as another tool to discriminate configurational isomers.

The Role of Electron Trajectories in XUV-Initiated High-Harmonic Generation

High-harmonic generation spectroscopy is a powerful tool for ultrafast spectroscopy with intrinsic attosecond time resolution. Its major limitation—the fact that a strong infrared driving pulse is governing the entire generation process—is lifted by extreme ultraviolet (XUV)-initiated high-harmonic generation (HHG). Tunneling ionization is replaced by XUV photoionization, which decouples ionization from recollision. Here we probe the intensity dependence of XUV-initiated HHG and observe strong spectral frequency shifts of the high harmonics. We are able to tune the shift by controlling the instantaneous intensity of the infrared field. We directly access the reciprocal intensity parameter associated with the electron trajectories and identify short and long trajectories. Our findings are supported and analyzed by ab initio calculations and a semiclassical trajectory model. The ability to isolate and control long trajectories in XUV-initiated HHG increases the range of the intrinsic attosecond clock for spectroscopic applications.

Effect of vibrational pre-excitation on sub-femtosecond structural evolution of water cation in 2A1 state

We study the effects of vibrational excitation of neutral water molecule on sub-femtosecond nuclear dynamics of the 2A1 electronic state of cationic water and its isotopomers that are induced by high-harmonic generation (HHG) process. Both the photoelectron spectra and the autocorrelation functions of electronically excited states of M2O+ (M = H, D, and T) that are produced by Franck-Condon ionization of vibrationally pre-excited M2O to its 2A1 electronic state are calculated. HHG signals are also calculated from the square of the absolute value of autocorrelation functions. In addition, the ratio of the HHG signal of D2O+ to that of H2O+ and that between T2O+ and H2O+ are calculated with respect to time, for varying initially prepared vibrational state of the corresponding neutral molecule. Vibrational dynamics are notably strong on the 2A1 state of the cationic species, as the initial vibrational quantum number increases. The HHG signal of a heavier isotopomer is larger than that of water when the initial vibrational state is on its ground state. The expectation values of the bond length and bond angle show quasiperiodic oscillations with respect to time, which are ascribed to the observed overall rise in the HHG signals. Exceptionally strong vibrational dynamics observed on the 2A1 state potential energy surface of the cationic water molecule can be attributed to the excitation of water bending mode upon Franck-Condon ionization of the corresponding neutral molecule. Here, the observed peaks in the ratios of the HHG signals are theoretically explained in terms of time-evolving molecular structures at two different turning points of the 2A1 surface. We anticipate that the present computational method of solving time-dependent Schrödinger equation would be of use to provide explanations on both ultrafast and chiroptical HHG spectroscopy of polyatomic molecules with certain handedness.

Robust enhancement of high harmonic generation via attosecond control of ionization

High-harmonic generation (HHG) is a powerful tool to generate coherent attosecond light pulses in the extreme ultraviolet. However, the low conversion efficiency of HHG at the single atom level poses a significant practical limitation for many applications. Enhancing the efficiency of the process defines one of the primary challenges in the application of HHG as an advanced XUV source. In this work, we demonstrate a new mechanism, which in contrast to current methods, enhances the HHG conversion efficiency purely on a single particle level. We show that using a bichromatic driving field, sub-optical-cycle control and enhancement of the tunnelling ionization rate can be achieved, leading to enhancements in HHG efficiency by up to two orders of magnitude. Our method advances the perspectives of HHG spectroscopy, where isolating the single particle response is an essential component, and offers a simple route toward scalable, robust XUV sources.

An apparatus for quantitative high-harmonic generation spectroscopy in molecular vapours.

We present an apparatus for performing gas phase high-harmonic generation spectroscopy of molecules primarily found in the liquid phase. Liquid molecular samples are heated in a temperature controlled bath and their vapour is used to back a continuous flow gas jet, with vapour pressures of over 1 bar possible. In order to demonstrate the system, we perform high harmonic spectroscopy experiments in benzene with a 1.8 μm driving field. Using the unique capabilities of the system, we obtain spectra that are nearly free from the effects of longitudinal phase-matching, amenable to comparison with advanced numerical modelling.

Optimal-continuum and multicentered Gaussian basis sets for high-harmonic generation spectroscopy

High-harmonic generation (HHG) is used to produce coherent XUV and soft X-ray radiation with attosecond resolution and is a sensitive tool for probing atomic and molecular structures. In this work, we have used time-dependent configuration interaction with a Gaussian basis set to compute the HHG spectrum of the hydrogen atom. To get a correct description of the HHG optical spectrum, the Gaussian basis set has to provide an accurate representation of the bound and the continuum states. Two strategies have been proposed: (1) multicentered (defining ghost atoms around the hydrogen) and (2) optimal-continuum Gaussian basis sets. We have systematically investigated these two approaches for the hydrogen atom, which permits a non-biased analysis of the basis set. Several basis sets have been constructed and tested by combining multicentered and optimal-continuum functions together in order to obtain a reliable and accurate Gaussian basis set to be used for HHG. We have studied the effect of changing the number of ghost atoms and the distance between the ghosts and the hydrogen atom, with and without optimal-continuum Gaussian functions. We conclude that multicentered basis sets are less efficient than basis sets using only optimal-continuum Gaussian functions for a proper description of HHG.

Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO2 molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

Role of tunnel ionization in high harmonic generation from substituted benzenes.

We theoretically study high-harmonic generation in toluene, ortho-xylene and fluorobenzene driven by a 1.8 μm ultrashort pulse. We find that the chemical substitutions have a strong influence on the amplitude and phase of the emission from the highest occupied molecular orbital, despite having a small influence on the orbital itself. We show that this influence is due to the tunnel ionization step, which depends critically on the sign and amplitude of the asymptotic part of the wave function. We discuss how these effects would manifest in phase-sensitive high-harmonic generation spectroscopy experiments.

Studying the universality of field induced tunnel ionization times via high-order harmonic spectroscopy

High-harmonic generation spectroscopy is a promising tool for resolving electron dynamics and structure in atomic and molecular systems. This scheme, commonly described by the strong field approximation, requires a deep insight into the basic mechanism that leads to the harmonic generation. Recently, we have demonstrated the ability to resolve the first stage of the process—field induced tunnel ionization—by adding a weak perturbation to the strong fundamental field. Here we generalize this approach and show that the assumptions behind the strong field approximation are valid over a wide range of tunnel ionization conditions. Performing a systematic study—modifying the fundamental wavelength, intensity and atomic system—we observed a good agreement with quantum path analysis over a range of Keldysh parameters. The generality of this scheme opens new perspectives in high harmonics spectroscopy, holding the potential of probing large, complex molecular systems.