Theory of high-harmonic generation by low-frequency laser fields

Harnessing collisional nonlinearity for enhanced harmonic generation by ultraviolet plasmonic nanoparticles

We investigate the contribution of inelastic electron collisions to nonlinear (NL) dynamics in ultraviolet plasmonic nanoparticles, exploring their potential for harmonic generation. Employing the Landau weak coupling formalism to model radiation-driven electron dynamics in sodium and aluminum, we account for both electron-electron and electron-phonon scattering processes by a set of hydrodynamic equations, which we solve perturbatively to obtain third-order NL susceptibilities. Furthermore, we model high harmonic generation enhanced by localized surface plasmons in nanospheres composed of such poor metals, demonstrating their efficient operation for extreme ultraviolet generation. Our investigation reveals that plasmonic nanospheres composed of sodium and aluminum produce a large field intensity enhancement of ≃103-105, boosting the harmonic generation process. Our findings indicate that poor metals hold great promise for advanced extreme ultraviolet nano-sources with potential applications in nano-spectroscopy.

Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets

Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation.

Many-body enhancement of high-harmonic generation in monolayer MoS2

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green's function with the GW self energy. We calculate the HHG of monolayer MoS2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.

Benchmarking Functionals for Strong-Field Light-Matter Interactions in Adiabatic Time-Dependent Density Functional Theory

In recent years, time-dependent density functional theory (TDDFT) has been extensively employed for highly nonlinear optics in molecules and solids, including high harmonic generation (HHG), photoemission, and more. TDDFT exhibits a relatively low numerical cost while still describing both light-matter and electron-electron interactions ab initio, making it highly appealing. However, the majority of implementations of the theory utilize the simplest possible approximations for the exchange-correlation (XC) functional-either the local density or generalized gradient approximations, which are traditionally considered to have rather poor chemical accuracy. We present the first systematic study of the XC functional effect on molecular HHG, testing various levels of theory. Our numerical results suggest justification for using simpler approximations for the XC functional, showing that hybrid and meta functionals (as well as Hartree-Fock) can, at times, lead to poor and unphysical results. The specific source of the failure in more elaborate functionals should be topic of future work, but we hypothesize that its origin might be connected to the adiabatic approximation of TDDFT.

Ultrafast Picometer-Resolved Molecular Structure Imaging by Laser-Induced High-Order Harmonics

Real-time visualization of molecular transformations is a captivating yet challenging frontier of ultrafast optical science and physical chemistry. While ultrafast x-ray and electron diffraction methods can achieve the needed subangstrom spatial resolution, their temporal resolution is still limited to hundreds of femtoseconds, much longer than the few femtoseconds required to probe real-time molecular dynamics. Here, we show that high-order harmonics generated by intense femtosecond lasers can be used to image molecules with few-ten-attosecond temporal resolution and few-picometer spatial resolution. This is achieved by exploiting the sensitive dependence of molecular recombination dipole moment to the geometry of the molecule at the time of harmonic emission. In a proof-of-principle experiment, we have applied this high-harmonic structure imaging (HHSI) method to monitor the structural rearrangement in NH_{3}, ND_{3}, and N_{2} from one to a few femtoseconds after the molecule is ionized by an intense laser. Our findings establish HHSI as an effective approach to resolve molecular dynamics with unprecedented spatiotemporal resolution, which can be extended to trace photochemical reactions in the future.

Attosecond chronoscopy of the photoemission near a bandgap of a single-element layered dielectric

We report on the energy dependence of the photoemission time delay from the single-element layered dielectric HOPG (highly oriented pyrolytic graphite). This system offers the unique opportunity to directly observe the Eisenbud-Wigner-Smith (EWS) time delays related to the bulk electronic band structure without being strongly perturbed by ubiquitous effects of transport, screening, and multiple scattering. We find the experimental streaking time shifts to be sensitive to the modulation of the density of states in the high-energy region (E ≈ 100 eV) of the band structure. The present attosecond chronoscopy experiments reveal an energy-dependent increase of the photoemission time delay when the final state energy of the excited electrons lies in the vicinity of the bandgap providing information difficult to access by conventional spectroscopy. Accompanying simulations further corroborate our interpretation.

High-Order Harmonics Generation Using Spherical and Non-Spherical Nanoparticles

The conversion efficiency of 800 nm, 65 fs radiation toward high-order harmonic generation (HHG) in laser-induced plasmas containing spherical and non-spherical nanoparticles (NPs) produced during the laser ablation of different metals in water using 1064 nm, 70 ps pulses was analyzed. Non-spherical NPs of different forms (triangle, cubic, bowtie, rod, rectangular, ellipsoid, etc.) were synthesized during the aging of some spherical NPs (In, Al, and Cu) in water. These NPs were then dried on the glass substrates and ablated to produce plasmas comprising nanostructured species of different morphologies. It was shown that harmonic generation in all synthesized non-spherical NPs was less efficient by a factor of at least five than in the initial spherical NP. Meanwhile, the spherical NPs that maintained the morphology state during aging (Ni, Ag, Mn, and Au) showed almost similar HHG conversion efficiency compared to the fresh spherical NPs. In all cases, the HHG conversion efficiency using spherical and non-spherical nanoparticles was notably larger compared to the atomic and ionic single-particle plasmas of the same elemental composition. NP plasmas demonstrated featureless harmonic distributions, contrary to the indium and manganese atomic/ionic plasmas, when the resonance enhancement of harmonics was observed.

Coulomb-induced emission time shifts in high-order harmonic generation from H2

Accurate emission times of high-order harmonic generation (HHG) are vital for high-precision ultrafast detection in attosecond science, but a quantitative analysis of Coulomb effects on this time is absent in the molecular HHG. Here, we investigate the Coulomb-induced emission-time shift in HHG of H2+ with two different internuclear distances R, where the times obtained via the Gabor transform of numerical data from solving the time-dependent Schrödinger equation are used as simulation experiment results. Based on the molecular strong-field approximation, we develop a trajectory-resolved classical model that takes into account the molecular two-center structure. By selecting appropriate electron trajectories and including Coulomb interactions, the classical trajectory method can reproduce Gabor emission times well. This consistence reveals that Coulomb tails cause an emission-time shift of ∼35 as at the R = 2.0 a.u. case and of ∼40-60 as at the R = 2.6 a.u. case under the present laser parameters when compared to the Coulomb-free quantum-orbit model. Our results are of significance to probe the attosecond dynamics via two-center interference.

Entanglement in photo-ionization process

We report a study of the entanglement between the quantized photon field and an atom arising in the photo-ionization process. Our approach is based on an ab initio solution of the time-dependent Schrödinger equation (TDSE) describing the quantum evolution of a bipartite system consisting of the atom and the quantized electromagnetic field. Using the solution of the TDSE, we calculate the reduced photon density matrix, which we subsequently use to compute entanglement entropy. We explain some properties of the entanglement entropy and propose an approximate formula for the entanglement entropy based on the analysis of the density matrix and its eigenvalues. We present the results of a comparative study of the entanglement in the photo-ionization process for various ionization regimes, including the tunneling and the multiphoton ionization regimes.

Strong-field photoelectron holography in the subcycle limit

Strong-field photoelectron holography is promising for the study of electron dynamics and structure in atoms and molecules, with superior spatiotemporal resolution compared to conventional electron and X-ray diffractometry. However, the application of strong-field photoelectron holography has been hindered by inter-cycle interference from multicycle fields. Here, we address this challenge by employing a near-single-cycle field to suppress the inter-cycle interference. We observed and separated two distinct holographic patterns for the first time. Our measurements allow us not only to identify the Gouy phase effect on electron wavepackets and holographic patterns but also to correctly extract the internuclear separation of the target molecule from the holographic pattern. Our work leads to a leap jump from theory to application in the field of strong-field photoelectron holography-based ultrafast imaging of molecular structures.

Focal cone high harmonic generation driven by a 400 TW laser

The generation of self-focusing beams of extreme ultraviolet (XUV) radiation using the focal cone high harmonic generation (FCHHG) technique is examined for high energy lasers. The FCHHG geometry is created by passing a focusing laser beam through a gas sheet prior to reaching focus and thus creating a converging beam of high harmonic radiation. This leads to a larger interaction area that increases the total area of XUV emission while not exceeding the saturation intensity of the target atoms or increasing the density of the atoms. Such a method allows for scaling of HHG to any incident laser power. An experiment was conducted demonstrating such scaling to incident 400 TW pulses, showing both the expected spectral signature of HHG and the converging cone of XUV radiation. It was found that this technique is very sensitive to spatial non-uniformity in the driving laser, which has become more prevalent in high energy laser systems.

Sub-cycle strong-field tunneling dynamics in solids

Tunneling ionization is a crucial process in the interaction between strong laser fields and matter which initiates numerous nonlinear phenomena including high-order harmonic generation, photoelectron holography, etc. Both adiabatic and nonadiabatic tunneling ionization are well understood in atomic systems. However, the tunneling dynamics in solids, especially nonadiabatic tunneling, has not yet been fully understood. Here, we study the sub-cycle resolved strong-field tunneling dynamics in solids via a complex saddle-point method. We compare the instantaneous momentum at the moment of tunneling and the tunneling distances over a range of Keldysh parameters. Our results demonstrate that for nonadiabatic tunneling, tunneling ionization away from Γ point is possible. When this happens the electron has a nonzero initial velocity when it emerges in the conduction band. Moreover, consistent with atomic tunneling, a reduced tunneling distance as compared to the quasi-static case is found. Our results provide remarkable insight into the basic physics governing the sub-cycle electron tunneling dynamics with significant implications for understanding subsequent strong-field nonlinear phenomena in solids.

Multiple plateaus of high-sideband generation from Floquet matters

We theoretically report that high-order sideband generation (HSG) from Floquet matters driven by a strong terahertz light while engineered by weak infrared light can achieve multiple plateau HSG. The Floquet-engineering systems exhibit distinctive spectroscopic characteristics that go beyond the HSG processes in field-free band-structure systems. The spatial-temporal dynamics analyses under Floquet-Bloch and time-reversal-symmetry theories clarify the spectra and its odd-even characteristics in the HSG spectrum. Our work demonstrates the HSG of Floquet matters via Floquet engineering and indicates a promising way to extract Floquet material parameters in future experiments.

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.

Vibronic Correlations in Molecular Strong-Field Dynamics

We investigate the ultrafast vibronic dynamics triggered by intense femtosecond infrared pulses in small molecules. Our study is based on numerical simulations performed with 2D model molecules and analyzed in the perspective of the renowned Lochfrass and bond-softening models. We give a new interpretation of the observed nuclear wave packet dynamics with a focus on the phase of the bond oscillations. Our simulations also reveal intricate features in the field-induced nuclear motion that are not accounted for by existing models. Our analyses assign these features to strong dynamical correlations between the active electron and the nuclei, which significantly depend on the carrier envelope phase of the pulse, even for relatively "long" pulses, which should make them experimentally observable.

Entanglement and Squeezing of the Optical Field Modes in High Harmonic Generation

Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.

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.

Vortex harmonic generation in indium tin oxide thin film irradiated by a two-color field

When a two-color Laguerre-Gaussian laser beam propagates through an indium tin oxide (ITO) material, the spatial distributions of odd- and even-order vortex harmonics carrying orbital angular momentum (OAM) are studied. The origin of vortex harmonics can be directly clarified by investigating their dependence on the incident laser field amplitude and frequency. In addition, it is shown that the spectral intensities of vortex harmonics are sensitive to the epsilon-near-zero nonlinear enhancing effects and the thickness of ITO materials. Thus the vortex harmonics can be conveniently tunable, which provides a wider potential application in optical communications based on high-order OAM coherent vortex beams.

Motion of charged particles in bright squeezed vacuum

The motion of laser-driven electrons quivers with an average energy termed pondermotive energy. We explore electron dynamics driven by bright squeezed vacuum (BSV), finding that BSV induces width oscillations, akin to electron quivering in laser light, with an equivalent ponderomotive energy. We identify closed and open trajectories of the electronic width that are associated with high harmonic generation and above-threshold ionization, respectively, similarly to trajectories of the electron position when its motion is driven by coherent light. In the case of bound electrons, the width oscillations may lead to ionization with noisy sub-cycle structure. Our results are foundational for strong-field and free-electron quantum optics, as they shed light on ionization, high harmonic generation, and nonlinear Compton scattering in BSV.

Tunnelling of electrons via the neighboring atom

As compared to the intuitive process that the electron emits straight to the continuum from its parent ion, there is an alternative route that the electron may transfer to and be trapped by a neighboring ionic core before the eventual release. Here, we demonstrate that electron tunnelling via the neighboring atomic core is a pronounced process in light-induced tunnelling ionization of molecules by absorbing multiple near-infrared photons. We devised a site-resolved tunnelling experiment using an Ar-Kr+ ion as a prototype system to track the electron tunnelling dynamics from the Ar atom towards the neighboring Kr+ by monitoring its transverse momentum distribution, which is temporally captured into the resonant excited states of the Ar-Kr+ before its eventual releasing. The influence of the Coulomb potential of neighboring ionic cores promises new insights into the understanding and controlling of tunnelling dynamics in complex molecules or environment.

Spectral splitting in phase mismatched harmonics

Spectral splitting of high harmonic radiation is observed when a gas target is irradiated with a high-energy laser pulse, having an extreme amount of frequency chirp. The phenomenon, which may be observed only by using a multi-TW laser system, originates from the temporal evolution of the phase-matching conditions. We illustrate how these conditions are mapped to the spectral domain, and present experimental evidence which is validated by our model.

Propagation effects in polarization-gated attosecond soft-X-ray pulse generation

Accurate estimation of the duration of soft-x-ray pulses from high-harmonic generation (HHG) remains challenging given their higher photon energies and broad spectral bandwidth. The carrier-envelope-phase (CEP) dependence of generated soft-x-ray spectra is indicative of attosecond pulse generation, but advanced simulations are needed to infer the pulse duration from such data. Here, we employ macroscopic propagation simulations to reproduce experimental polarization-gated CEP-dependent soft-x-ray spectra. The simulations indicate chirped pulses, which we theoretically find to be compressible in hydrogen plasmas, suggesting this as a viable compression scheme for broadband soft-x-rays from HHG.

Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density functional theory. CM + FMSS is a pump-probe scheme that uses a frequency-matched high harmonic generation (HHG)-driving laser as an independent probe step, following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with a negligible contribution from the ionization step.

High-harmonic spectroscopy of impulsively aligned 1,3-cyclohexadiene: Signatures of attosecond charge migration

High-harmonic spectroscopy is an all-optical technique with inherent attosecond temporal resolution that has been successfully employed to reconstruct charge migration, electron-tunneling dynamics, and conical-intersection dynamics. Here, we demonstrate the extension of two key components of high-harmonic spectroscopy, i.e., impulsive alignment and measurements with multiple driving wavelengths to 1,3-cyclohexadiene and benzene. In the case of 1,3-cyclohexadiene, we find that the temporal sequence of maximal and minimal emitted high-harmonic intensities as a function of the delay between the alignment and probe pulses inverts between 25 and 30 eV and again between 35 and 40 eV when an 800-nm driver is used, but no inversions are observed with a 1420-nm driver. This observation is explained by the wavelength-dependent interference of emission from multiple molecular orbitals (HOMO to HOMO-3), as demonstrated by calculations based on the weak-field asymptotic theory and accurate photorecombination matrix elements. These results indicate that attosecond charge migration takes place in the 1,3-cyclohexadiene cation and can potentially be reconstructed with the help of additional measurements. Our experiments also demonstrate a pathway toward studying photochemical reactions in the molecular frame of 1,3-cyclohexadiene.

Phase-matching of high-order harmonic generation in the extreme ultraviolet region with orbital angular momentum

High-order harmonics can generate vortex beams with orbital angular momentum (OAM) in the extreme ultraviolet region. However, experimental research on their phase-matching (PM) characteristics is limited. In this study, vortex high-order harmonic generation (HHG) in the extreme ultraviolet region was generated with Ar gas. Phase-matched HHG with OAM was obtained by optimizing the focus position, laser energy, and gas pressure. The dependence of the PM characteristics on these parameters was analyzed. In addition, we conducted an experimental analysis of the dimensional properties of vortex harmonics under PM conditions. This study is a contribution towards the intense vortex high-order harmonic light sources and their applications.

Orbital perspective on high-harmonic generation from solids

High-harmonic generation in solids allows probing and controlling electron dynamics in crystals on few femtosecond timescales, paving the way to lightwave electronics. In the spatial domain, recent advances in the real-space interpretation of high-harmonic emission in solids allows imaging the field-free, static, potential of the valence electrons with picometer resolution. The combination of such extreme spatial and temporal resolutions to measure and control strong-field dynamics in solids at the atomic scale is poised to unlock a new frontier of lightwave electronics. Here, we report a strong intensity-dependent anisotropy in the high-harmonic generation from ReS2 that we attribute to angle-dependent interference of currents from the different atoms in the unit cell. Furthermore, we demonstrate how the laser parameters control the relative contribution of these atoms to the high-harmonic emission. Our findings provide an unprecedented atomic perspective on strong-field dynamics in crystals, revealing key factors to consider in the route towards developing efficient harmonic emitters.

Control of the annular spatial profile of high harmonics using a Bessel-Gaussian beam carrying the nonzero orbital angular momentum

We propose to generate vortex high harmonics in the extreme ultraviolet (XUV) with a controllable spatial profile by using a Bessel-Gaussian (BG) beam carrying a nonzero orbital angular momentum (OAM). Such BG beam has quite a different intensity profile at the focus compared to the generally used BG beam without carrying the OAM. We show that the BG beam is capable of generating single-ring structured high harmonics, which is quite different from an Laguerre-Gaussian (LG) beam with a similar intensity distribution at the laser focus. We reveal that favorable phase-matching conditions can be achieved off-axis and away from the laser focus because a single-atom intrinsic phase due to the short electron trajectory can be well compensated by a geometric phase of the BG beam. We thus give a general rule that vortex high harmonics with a single annular profile can be efficiently generated when a gas medium is located at 1.5zred to 2.0zred before or after the laser focus of the BG beam, here zred is a reduced length. We also show the validity of this rule when the BG beam carries a higher OAM. This work is expected to be useful for synthesizing attosecond vortex pulses.

Magnetic optical rotation from real-time simulations in finite magnetic fields

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

Time-resolving state-specific molecular dissociation with XUV broadband absorption spectroscopy

The electronic and nuclear dynamics inside molecules are essential for chemical reactions, where different pathways typically unfold on ultrafast timescales. Extreme ultraviolet (XUV) light pulses generated by free-electron lasers (FELs) allow atomic-site and electronic-state selectivity, triggering specific molecular dynamics while providing femtosecond resolution. Yet, time-resolved experiments are either blind to neutral fragments or limited by the spectral bandwidth of FEL pulses. Here, we combine a broadband XUV probe pulse from high-order harmonic generation with an FEL pump pulse to observe dissociation pathways leading to fragments in different quantum states. We temporally resolve the dissociation of a specific O2+ state into two competing channels by measuring the resonances of ionic and neutral fragments. This scheme can be applied to investigate convoluted dynamics in larger molecules relevant to diverse science fields.

Photon Pathways and the Nonperturbative Scaling Law of High Harmonic Generation

High harmonic generation (HHG) has become a core pillar of attosecond science. Traditionally described with field-based models, HHG can also be viewed in a parametric picture, which predicts all properties of the emitted photons, but not the nonperturbative efficiency of the process. Driving HHG with two noncollinear beams and deriving analytically the corresponding yield scaling laws for any intensity ratio, we herein reconcile the two interpretations, introducing a generalized photonic description of HHG. It is in full agreement with field-based simulations and experimental data, opening the route to smart engineering of HHG with multiple driving beams.

Harmonic Suppression Induced by Three-Electron Dynamics of Li in Strong Laser Fields

We build a model to elucidate the high harmonic generation in combined EUV and midinfrared laser fields by embodying the spin-resolved three-electron dynamics. The EUV pulse ionizes an inner-shell electron, and the midinfrared laser drives the photoelectron and steers the electron-ion rescattering. Depending on the spin of the photoelectron, the residual ion including two bound electrons can be either in a single spin configuration or in a coherent superposition of different spin configurations. In the latter case, the two electrons in the ion swap their orbits, leading to a deep valley in the harmonic spectrum. The model results agree with the time-dependent Schrödinger equation simulations including three active electrons. The intriguing picture explored in this work is fundamentally distinguished from all reported scenarios relied on spin-orbit coupling, but originates from the exchanges asymmetry of two-electron wave functions.

Circularly polarized attosecond light generation from OCS molecules irradiated by the combination of linear polarized infrared and orthogonal terahertz fields

Researching ultrafast dynamics and creating coherent light sources will both benefit significantly from the establishment of polarization control in high-order harmonic generation (HHG). By employing the time-dependent density functional theory method, we investigate HHG of carbonyl sulfide molecules using a combination of a linear polarized infrared (IR) laser and a weaker orthogonal Terahertz (THz) field. Our findings show that by adjusting the amplitude of the THz field, the movement scale of electrons in the THz direction can be tuned, thereby one can control the harmonic intensity in the IR laser direction. This method allows for the creation of near-circularly polarized attosecond pulses. Furthermore, the ellipticity of the attosecond pulse may be changed by modifying the carrier-envelope phase of the IR laser pulse.

Real-Time Extension of TAO-DFT

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Enhancing harmonic brightness near the cutoff region by using laser pulses with a small positive chirp

Efficient enhancement of harmonic brightness near the cutoff region is achieved by employing laser pulses with a small positive chirp in theory, where the laser intensity and frequency near the peak of the laser pulse are almost unchanged relative to the chirp-free field. The improvement of harmonic brightness is achieved under the condition that the ionization probability is almost unchanged. Through the analysis of the harmonics contributed by the rising and falling parts of the laser pulse, we have uncovered a "frequency compensation" mechanism that leads to an enhanced harmonic brightness near the cutoff region. Under appropriate chirp parameters, the harmonics contributed by the rising and falling parts can be constructively interfered in a smaller frequency range with greater intensity, thereby obtaining harmonics with good monochromaticity and high brightness. This study explains the mechanism of harmonic brightness enhancement from a new perspective, and provides a new idea for harmonic regulation without changing the ionization.

Reduced Scaling Real-Time Coupled Cluster Theory

Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation of complex spectroscopies that are unreachable using frequency-domain approaches. Due to the high-order polynomial scaling, the required numerical time propagation of the CC residual expressions is a computationally demanding process. This scaling may be reduced by local correlation schemes, which aim to reduce the size of the (virtual) orbital space by truncation according to user-defined parameters. We present the first application of local correlation to real-time CC. As in previous studies of locally correlated frequency-domain CC, traditional local correlation schemes are of limited utility for field-dependent properties; however, a perturbation-aware scheme proves promising. A detailed analysis of the amplitude dynamics suggests that the main challenge is a strong time dependence of the wave function sparsity.

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.

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.

Generation of high-order harmonics and attosecond pulses in the water window via nonlinear propagation of a few-cycle laser pulse

We theoretically and computationally study the generation of high-order harmonics in the water window from a semi-infinite gas cell where a few-cycle, carrier-envelope-phase-controlled 1.7-µm driving laser pulse undergoes nonlinear propagation via optical Kerr effect (self-focusing) and plasma defocusing. Our calculation shows that high harmonic signals are enhanced for extended propagation distances and furthermore, isolated attosecond pulses in the water window can be generated from the semi-infinite gas cell. This enhancement is attributed mainly to better phase matching for extended propagation distances achieved via nonlinear propagation and resulting intensity stabilization.

Two phase-matching regimes in high-order harmonic generation

High-order harmonic generation (HHG) provides scalable sources of coherent extreme ultraviolet radiation with pulse duration down to the attosecond time scale. Efficient HHG requires the constructive interplay between microscopic and macroscopic effects in the generation volume, which can be achieved over a large range of experimental parameters from the driving field properties to those of the generating medium. Here, we present a systematic study of the harmonic yield as a function of gas pressure and medium length. Two regimes for optimum yield are identified, supporting the predictions of a recently proposed analytical model. Our observations are independent on the focusing geometry and, to a large extent, on the pulse duration and laser intensity, providing a versatile approach to HHG optimization.

Higher harmonics and supercontinuum generated from the Kerr response time in different states of matter from a universal electromagnetic model

There is a need for a universal model to describe higher harmonic generation (HHG) in different states of matter. Based on an electromagnetic model (EM), the generation of odd higher harmonic (HHG) and supercontinuum (SC) from intense fs and ps pulses for visible, NIR, and MIR lasers is simulated based on the parameters from experimental observation. HHG and SC depend critically on the different Kerr material response times τ from the ultrafast on the order of 100 as for electronic cloud distortion to fast ~ 10 fs from plasma and molecular redistribution and to the slower picoseconds rotational and vibrational molecular processes. The number of odd HHG generated is shown to depend critically on the fastest Kerr response time on the order of ~ 1 fs from electronic self-phase modulation (ESPM). In this study, different states of matter from noble gas Argon to condensed matter ZnO and LBG are simulated showing the dependence on the Kerr response time to produce HHG for various applications in Physics, Chemistry, Biology, and Engineering. The EM model is universal to produce HHG and SC in different states of matter.

Minimum structure of high-order harmonic spectrum from molecular multi-orbital effects involving inner-shell orbitals

The spectral features of high-order harmonic spectra can provide rich information for probing the structure and dynamics of molecules in intense laser fields. We theoretically study the high harmonic spectrum with the laser polarization direction perpendicular to the N2O molecule and find a minimum structure in the plateau region of the harmonic spectrum. Through analyzing the time-dependent survival probability of different electronic orbitals and the time-dependent wave packet evolution, it is found that this minimum position is caused by the harmonic interference of HOMO a, HOMO-1, and HOMO-3 a orbitals. Moreover, this interference minimum is discovered over a wide frequency range of 0.087 a.u. to 0.093 a.u., as well as a range of driving laser intensities with peak amplitudes between 0.056 a.u. and 0.059 a.u.. This study sheds light on the multi-electron effects and ultrafast dynamics of inner-shell electrons in intense laser pulses, which are crucial for understanding and controlling chemical reactions in molecules.

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.

Enabling elliptically polarized high harmonic generation with short cross polarized laser pulses

Enabling elliptically polarized high-order harmonics overcomes a historical limitation in the generation of this highly nonlinear process in atomic, molecular and optical physics with applications in other branches. Here, we shed new light on a controversy between experimental observations and theoretical predictions on the possibility to generate harmonics with large ellipticity using two bichromatic laser pulses which are linearly polarized in orthogonal directions. Results of numerical calculations confirm the previous experimental data that in short laser pulses even harmonics with large ellipticity can be obtained for the interaction of such cross-polarized laser pulses with atoms initially in a s- or p-state, while odd harmonics have low ellipticity. The amount of the ellipticity can be controlled via the relative carrier-envelope phase of the pulses, their intensity ratio and the duration of the pulses.

High-order harmonics generation in Cd and Pd laser-induced plasmas

We demonstrate the generation of high-order harmonics of laser pulses in palladium and cadmium plasmas. We adjusted the wavelength of driving pulses to investigate the resonance enhancement in different ranges of extreme ultraviolet region. The summation of incommensurate waves during the two-color pump of Pd and Cd plasmas allowed the generation of a broader range of harmonics. The theoretical aspects of the two-color pump of the laser-induced plasma are discussed.

Frequency shift of even-order high harmonic generation in monolayer MoS2

Sub-optical-cycle electron dynamics in materials driven by intense laser fields can be investigated by high harmonic generation. We observed frequency shift of high harmonic spectrum near the band gap of monolayer MoS2 experimentally. Through semi-classical quantum trajectory analysis, we demonstrated that the phase of transition dipole moment varies according to the recombination timing and momentum of tunneled electrons. It results in either blue- or red-shift of harmonic frequencies, determined by the modulated energy gap by transition dipole phases (TDPs) and Berry connections. Our finding reveals the effect of TDPs on high harmonic frequency in non-central symmetric materials.

49 W carrier-envelope-phase-stable few-cycle 2.1 µm OPCPA at 10 kHz

We demonstrate a mid-infrared optical parametric chirped pulse amplifier (OPCPA), delivering 2.1 µm center wavelength pulses with 20 fs duration and 4.9 mJ energy at 10 kHz repetition rate. This self-seeded system is based on a kW-class Yb:YAG thin-disk amplifier driving a CEP stable short-wavelength-infrared (SWIR) generation and three consecutive OPCPA stages. Our SWIR source achieves an average power of 49 W, while still maintaining excellent phase and average power stability with sub-100 mrad carrier-envelope-phase-noise and 0.8% average power fluctuations. These parameters enable the OPCPA setup to drive attosecond pump probe spectroscopy experiments with photon energies in the water window.

X-FAST: A versatile, high-throughput, and user-friendly XUV femtosecond absorption spectroscopy tabletop instrument

We present the X-FAST (XUV Femtosecond Absorption Spectroscopy Tabletop) instrument at the University of Wisconsin-Madison. The instrument produces femtosecond extreme ultraviolet photon pulses via high-harmonic generation in the range of 40-72 eV, as well as optical pump pulses for transient-absorption experiments. The system implements a gas-cooled sample cell that enables studying the dynamics of thermally sensitive thin-film samples. This paper provides potential users with specifications of the optical, vacuum, data acquisition, and sample cooling systems of the X-FAST instrument, along with performance metrics and data of an ultrafast laser-induced phase transition in a Ni2MnGa Heusler thin film.

Two-color attosecond chronoscope

We study ionization of atoms in strong orthogonal two-color (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like one and a shoulder-like one, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived. Through these mappings, we are able to establish a two-color attosecond chronoscope for timing electron emission, which is essential for OTC-based precise manipulation.