High Harmonic Generation Spectra Research Articles

Ultrafast dephasing in solid-state high harmonic generation: macroscopic origin revealed by real-space dynamics [Invited

Using a fully real-space perspective on high harmonic generation (HHG) in solids, we examine the relationship between microscopic response, macroscopic propagation of this response to the far-field, and the extremely short dephasing times routinely used in the theoretical simulations of experimentally measured solid-state HHG spectra. We find that far-field propagation naturally reduces the contribution to the observed HHG emission from electrons that do not return to the lattice site where they have been injected into the conduction band. We then show that extremely short dephasing times routinely used in microscopic simulations suppress many electron trajectories that contribute to the far-field spectra, leading to significant distortions of the true high harmonic response. We show that a real-space based dephasing mechanism, which preferentially suppresses trajectories that veer too far away from their original lattice site, yields HHG spectra that faithfully retain those trajectories that contribute to the far-field spectra while filtering out those that do not, already at the microscopic level. Our findings emphasize the similarities between atomic and solid-state HHG by highlighting the importance of the intensity-dependent phase of HHG emission and address the longstanding issue regarding the origin of extremely short dephasing times in solid-state HHG.

Extracting correlation length in Mott insulators by strong-field driving

The breakdown of a Mott-insulator when subjected to intense laser fields is characterized by the formation of doublon-hole pairs. This breakdown is furthermore evidenced by the production of high harmonics that can be experimentally measured. Here, we present an approach for extracting the doublon-hole correlation length of a Mott insulator. The method is based on a dynamical calculation of the Mott insulator’s rate of charge production in response to an applied strong-field laser pulse. We find that coupling the Mott insulator to a metal drastically increases the correlation length, in support of our recent hypothesis [Phys. Rev. B 108, 144434 (2023)2469-995010.1103/PhysRevB.108.144434] that coupling to a metal enhances the charge fluctuations in the insulator. We confirm our conclusions using density matrix renormalization group (DMRG) calculations. The proposed method can be applied to experimentally measured observables, such as differential reflectivity or the high harmonic generation (HHG) spectrum to extract doublon-hole correlation length.

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods.

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

High-Harmonic Generation Spectroscopy of Gas-Phase Bromoform.

High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions.

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.

Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra.

Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.

Role of Inner Molecular Orbitals in High-Harmonic Generation Spectra of Aligned Uracil.

In this work, we decompose the high-harmonic generation (HHG) signal of aligned gas-phase uracil into single molecular-orbital (MO) contributions. We compute HHG spectra for a pulse linearly polarized perpendicular to the molecular plane, with an intensity of 0.6 and 0.85 × 1014 W/cm2 and a wavelength of 800 nm. We use the real-time time-dependent Configuration Interaction with singles method, coupled to a Gaussian-based representation of the time-dependent wavefunction. The strong-field dynamics is affected by the energy of the ionization/recombination channels and by the coupling between the orbital symmetry and laser polarization. In the configuration studied here, we expect that π-type MOs favorably couple with the incoming pulse and play a substantial role in generating the HHG spectrum. Indeed, we show that HOMO, HOMO - 1, and HOMO - 4, which all are π-like, determine the intensity of harmonic peaks at different energies, while HOMO - 2 and HOMO - 3 provide a smaller contribution. It is worth mentioning that HOMO - 4 produces a stronger signal than that from HOMO - 1, even though the corresponding ionization energy, in an one-electron picture, is around 2.5 eV larger and more than 4 eV larger than the HOMO one.

Tunability of Half Cycle Cutoff Harmonics with Inhomogeneously Enhanced Laser Pulse

For homogeneous driving, half cycle harmonics and its corresponding half cycle cutoff (HCO) show prominent spectral features, allowing one to produce an isolated attosecond pulse with suitable filtering, or vice versa the retrieval of the driving pulse itself. The temporal profile and spatial dependence of the inhomogeneously enhanced field are two important factors that determine the high harmonic generation (HHG) near a plasmonic nanostructure. This leads us to the question of how the HHG spectra and, in particular, the corresponding half cycle harmonics modify with different types of inhomogeneously enhanced fields. To elucidate this, we have made a comparative study of the HHG in three different types of inhomogeneously enhanced laser pulses by employing the time-dependent Schrödinger equation in one dimension. Within our chosen parameter range, the HCO in cutoff and mid-plateau regimes shift towards higher order with the increase of strength of the inhomogeneity in isotropic case. In anisotropic inhomogeneity, the cutoff HCO shifts towards the higher order but the mid-plateau HCO shifts towards lower order with the increase of strength of inhomogeneity. With increasing carrier envelope phase (CEP), the enhanced HCO in the lower-order harmonic region shifts towards higher orders. This shift is nearly linear from near the above threshold to mid-plateau region and becomes saturated in the near cutoff region. The harmonic spectra is modulo-π periodic for the isotropic inhomogeneity and it is modulo-2π periodic for the anisotropic inhomogeneity. This extension of periodicity increases the tunability of the enhanced HCO harmonics with CEP in the anisotropic inhomogeneity than the CEP tuning of the HCO harmonics in the isotropic inhomogeneity or vice versa the retrieval of CEP.

Direct reconstruction of isolated XUV or soft x-ray attosecond pulses from high-harmonic generation streaking spectra

Characterization of an isolated attosecond pulse (IAP) in the extreme ultraviolet (XUV) or soft x-ray (SXR) region is essential for its applications. Here we propose to retrieve an IAP in the time domain directly through the modulation of high-harmonic generation (HHG) spectra in the presence of a time-delayed intense few-cycle infrared or mid-infrared laser. The retrieval algorithm is derived based on the strong-field approximation and an extended quantitative rescattering model. We show that both isolated XUV pulses with a narrow spectral bandwidth and isolated SXR pulses with a broad bandwidth can be well characterized through the HHG streaking spectra. Such an all-optical method for characterizing the IAP differs from the commonly used approach based on the streaked photoelectron spectra that would require electron spectrometers. We check the robustness of the retrieval method by changing the dressing laser or by adjusting the steps of time delay. We also show that the XUV pulse can be accurately retrieved by treating the HHG streaking spectra calculated from solving the time-dependent Schrödinger equation for single atoms as the ‘experimental’ data.

Approximation Schemes to Include Nuclear Motion in Laser-Driven Ab Initio Electron Dynamics: Application to High Harmonic Generation.

The quantum mechanical description of many-electron dynamics in molecules driven by short laser pulses is at the heart of theoretical attochemistry. In addition to the formidable time-dependent electronic structure problem, the field faces the challenge that nuclear motion, ideally also treated quantum mechanically, may not be negligible, but scales enormously in effort. As a consequence, most first-principles calculations on ultrafast electron dynamics in molecules are done within the fixed-nuclear approximation. For laser-pulse excitation in H2+, where an "exact" treatment of the coupled nuclear-electron dynamics is possible, it has been shown that nuclear motion can have a nonnegligible impact on high harmonic generation (HHG) spectra (Witzorky et al., J. Chem. Theor. Comput. 2021, 17, 7353-7365). It is not so clear, however, how to include (quantum) nuclear motion also for more complicated molecules, with more electrons and/or nuclei, in particular when the electronic structure is described by correlated, multistate wavefunction methods such as the time-dependent configuration interaction (TD-CI). In this work, we suggest a scheme in which the Born-Oppenheimer potential energy surfaces of a molecule are approximated by model potentials (harmonic and asymptotic, as an expansion in 1/R), obtained from only a few ab initio calculations, with the prospect to treat complex molecular systems. The method is tested successfully for HHG by few-cycle laser pulses for the "exact" H2+ reference. It is then applied for diatomic molecules with more electrons and for a two-dimensional model of the water molecule using TD-CIS (S = single) for the electronic structure part.

Modelling intensity volume averaging in ab initio calculations of high harmonic generation

We present an approach to assess the survival of single-atom effects in the macroscopic high-harmonic generation (HHG) spectrum, by accounting for focal volume averaging. We apply this technique to R-matrix with time-dependence (RMT) studies, which are designed to include the full multielectron response of an atom. Such an approach allows the assessment of which features of an experimentally-measured HHG spectrum of diffuse gases may be traced directly to single-atom effects and vice-versa. While accounting for the phase of harmonics produced at different locations in the focal volume gives the most accurate results, a simplified approach, using a smaller number of RMT calculations, is found to provide comparable conclusions. We apply these approaches to compute intensity-averaged harmonic spectra in two different experimental regimes.

Assessment of tight-binding models for high-harmonic generation in zinc blende materials.

Using a simulator for semiconductor Bloch equations (SBEs) accounting for the entire Brillouin zone, we examine the tight-binding (TB) description for zinc blende structure as a model for high-harmonic generation (HHG). We demonstrate that TB models of GaAs and ZnSe exhibit second-order nonlinear coefficients that compare favorably with measurements. For the higher-order portion of the spectrum, we use the results published by Xia et al. in Opt. Express26, 29393 (2018)10.1364/OE.26.029393 and show that the HHG spectra measured in reflection can be closely reproduced by our simulations free of adjustable parameters. We conclude that despite their relative simplicity, the TB models of GaAs and ZnSe represent useful tools to study both the low- and higher-order harmonic response in realistic simulations.

Time‐dependent coupled‐cluster theory

AbstractRecent years have witnessed an increasing interest in time‐dependent coupled‐cluster (TDCC) theory for simulating laser‐driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time‐dependent bivariational principle, we review different flavors of single‐reference TDCC theory with either orthonormal static, orthonormal time‐dependent, or biorthonormal time‐dependent spin orbitals. The time‐dependent extension of equation‐of‐motion coupled‐cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low‐order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite‐temperature many‐body quantum mechanics is briefly described along with a few other application areas.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

Multiphoton excitation and high harmonic generation in rectangular graphene quantum dot

The multiphoton excitation and high harmonic generation (HHG) processes are considered using the microscopic quantum theory of nonlinear interaction of strong coherent electromagnetic (EM) radiation with rectangular graphene quantum dot (RGQD). The dynamic Hartree–Fock approximation is developed for the consideration of the quantum dot-laser field nonlinear interaction at the nonadiabatic multiphoton excitation regime. The many-body Coulomb interaction is described in the extended Hubbard approximation. By numerical results, we show the significance of the RGQD lateral size, shape, and EM wavefield orientation in RGQD of the zigzag edge compear to the armchair edge in the HHG process allowing for increasing the cutoff photon energy and the quantum yield of higher harmonics. The differences via edge on the elongated side of the RGQD have been explained by the investigation of the dipole momentum in both cases. Numerical results have shown that the HHG spectra have a strong anisotropy depending on the orientation of the laser wave, and the cutoff photon energy shifts toward blue with an increase in the transverse size of the RGQD.

Potential energy surfaces for electron dynamics from a model of localized Gaussian wave packets with valence-bond spin-coupling: High-harmonic generation spectra from H and He atoms

Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic generation (HHG) spectra of hydrogen and helium atoms induced by intense laser pulses. The dynamics of the single electron on the ePES is calculated by numerically solving the time-dependent Schrödinger equation. The results reasonably reproduce previous studies. The dynamics of the electron wave function, dipole moment and dipole acceleration were analyzed by comparing one- and two-dimensional calculations. It was found that the main part of the wave function remains within a few Bohrs of the nuclear position, while the part of the wave function that is several orders of magnitude smaller in probability density, which escapes the laser-induced potential barrier by quantum tunneling effect, mainly contributes to the HHG.

Phase-Matched High-Harmonic Generation under Nonadiabatic Conditions: Model and Experiment

Nonadiabatic phase matching of high-harmonic generation (HHG) driven by few-cycle laser pulses is essential for extending harmonic energy and generating isolated attosecond pulses. However, understanding nonadiabatic HHG is challenging due to the complex interplay of various optical phases driven by temporally and spatially varying laser fields. Theoretical calculations typically rely on computationally demanding 3-dimensional simulations, which can make it difficult to extract the essential features of nonadiabatic HHG. In this work, we develop a computationally efficient 2-dimensional model that directly considers various phase contributions of HHG. Our model can well explain the experimentally observed pressure- and intensity-dependent behaviors of different harmonic orders. By appropriately parameterizing the single-atom response, our model can also estimate the variation of HHG spectra under different driving conditions. Our model can provide an efficient tool for the design and optimization of HHG-based applications.

Theory for all-optical responses in topological materials: The velocity gauge picture

High Harmonic Generation (HHG), which has been widely used in atomic gas, has recently expanded to solids as a means to study highly nonlinear electronic response in condensed matter and produce coherent high frequency radiation with new properties. Most recently, attention has turned to Topological Materials (TMs) and the use of HHG to characterize topological bands and invariants. Theoretical interpretation of nonlinear electronic response in TMs, however, presents many challenges. In particular, the Bloch wavefunction phase of TMs has undefined points in the Brillouin Zone. This leads to singularities in calculating the inter-band and intra-band transition dipole matrix elements of Semiconductor Bloch Equations (SBEs). Here, we use the laser-electromagnetic velocity gauge ${\boldsymbol p}\cdot {\bf A}(t)$ to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra. We use a prototype of Chern Insulators (CIs), the Haldane model, to demonstrate our approach. We find good qualitative agreement of the velocity gauge compared to the length gauge and the Time-Dependent Density Functional theory in the case of topologically trivial materials such as MoS$_2$. For velocity gauge and length gauge, our two-band Haldane model reproduces key HHG spectra features: ($\textit i$) The selection rules for linear and circular light drivers, ($\textit ii$) The linear cut-off law scaling and ($\textit iii$) The anomalous circular dichroism. We conclude that the velocity-gauge approach captures experimental observations and provides theoretical tools to investigate topological materials.

Doping effects in high-harmonic generation from correlated systems

Using the one-dimensional Hubbard model, which is commonly used for describing, e.g., high-${T}_{c}$ superconducting cuprates, we study high-harmonic generation (HHG) from doped, correlated materials. Doping is modeled by changing the number of electrons in the lattice from the conventional half-filling case. For relatively small Hubbard $U$, i.e., small electron-electron correlation, we find little to no effect of doping on the dynamics and the HHG spectra. For increasing $U$ the degree of doping has a marked effect on the dynamics and spectra. We explain these findings through the quasiparticle-based doublon-holon picture. The dynamics are separated into two types, first, doublon and holon movement, and, second, doublon-holon pair creation and annihilation. Doping results in all configurations containing doublons or holons. Those quasiparticles can move at no extra cost in energy regardless of the correlation level. This motion at no energy cost increases the high-harmonic gain for low- and medium-harmonic orders. We discuss that in the high-$U$ limit, antiferromagnetic ordering becomes increasingly unlikely with increasing doping rates and explain an associated drop in the high-order harmonics relative to the case of half-filling.

High harmonic generation spectrum of energetic molecule nitromethane

Understanding the interaction between strong laser field and energetic molecules is an important task for practical implementation of the laser-induced ignition for high energy propulsion applications. One of the generic consequences of the interaction of a strong laser field with molecules is high harmonic generation (HHG). Thus far, high harmonic generation has not been observed from any energetic molecule. The purpose of this paper is to present an HHG spectrum obtained for a simple energetic molecule, nitromethane, at various gas cell pressures and laser beam intensities. The experimental spectrum is compared and contrasted with the theoretical one obtained under the approximation of single active electron in molecular electrostatic potential. We believe that the present work would open door to the further investigation of the laser ignition chemistry of energetic molecules from an HHG point of view.

A TD-CIS study of high-harmonic generation of uracil cation fragments

High-harmonic generation (HHG) spectroscopy was investigated from laser ablation plasmas of uracil targets in the experimental work of Hutchinson et al., [Phys. Chem. Chem. Phys. Comparison of high-order harmonic generation in uracil and thymine ablation plumes, 2013, 15, 12308] and of Lopez-Quintas et al., [Appl. Surf. Sci., Characterization of laser-induced plasmas of nucleobases: Uracil and thymine, 2014, 302, 299]. Inspired by these works we computed HHG spectra of uracil cation fragments by means of real-time time-dependent configuration interaction with single excitations (RT-TD-CIS) and continuum-optimal Gaussian basis sets. We calculated the rotationally-averaged HHG spectra of different cation fragments analysing the relation between HHG, geometry of the fragments (linear/nonlinear) and electron dynamics (bound and continuum energy states). Moreover, to simulate the complexity of a sample containing fragments upon ablation, we calculated weighted-rotationally-averaged HHG spectra where the contribution of each fragment is included through weights assigned accordingly to the experimental mass spectra.