Harmonic Generation Spectra Research Articles

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.

Raman scattering evolution in temperature-induced ferroelectric phase transition of few-layer NbOCl2

NbOCl2 is an emerging layered ferroelectric (FE) material with unique photoelectric properties. However, the phonons and thermal properties of NbOCl2 have remained elusive. Here, we report measurements of Raman and second harmonic generation spectrum of NbOCl2 flakes as a function of temperature (80–500 K). All observed Raman modes exhibit temperature-dependent shift. The first-order temperature coefficients of P1, P2, P3, P4, and P5 modes are 0.001 58, −0.005 21, −0.006 44, −0.012 56, and 0.036 75 cm−1 K−1, respectively. Interestingly, the frequency of the P1 mode changes directly from 161 to 156 cm−1 with increasing temperature, which is attributed to the switching between two independent Raman modes (P1H and P1L). The P1H mode is mainly contributed by the FE phase, while the P1L mode is mainly contributed by the antiferroelectric phase. Our results provide a fundamental understanding and analysis of the thermal–phonon coupling properties of few-layer NbOCl2 and promote the deep exploration of the basic physical properties of few-layer NbOCl2, which is crucial for the design and application of NbOCl2-based thermal and optoelectronic devices in the future.

Measurement of ultrashort laser pulses with a time-dependent polarization state using the d-scan technique

The dispersion scan (d-scan) technique is extended to measurement of the time-dependent polarization state of ultrashort laser pulses. In the simplest implementation for linearly polarized ultrashort pulses, the d-scan technique records the second harmonic generation spectrum as a function of a known spectral phase manipulation. By applying this method to two orthogonally polarized projections of an arbitrary polarized electric field and by measuring the spectrum at an intermediate angle, we can reconstruct the evolution over time of the polarization state. We demonstrate the method by measuring a polarization gate generated from 6fs pulses with a combination of waveplates. The measurements are compared to simulations, showing an excellent agreement.

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.

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.

Nonadiabatic electron dynamics effects on high-harmonic generation spectrum of [formula omitted]: Minima and oscillatory pattern

We numerically solved the full-dimensional electronic time-dependent Schrödinger equation for H2+ with Born-Oppenheimer approximation under different sin2-shaped and trapezoidal laser pulses at some different wavelengths, with I = 1 × 1013, 3 × 1013 and 6 × 1013 Wcm−2 intensity at 4.73 a.u. and 7.0 a.u. internuclear distances. Some structures such as minima and oscillatory patterns appearing in the high-order harmonic generation (HHG) spectra. We evaluate these structures in the HHG spectrum by considering the electron localization, electron nonadiabatic dynamics, and the Rabi oscillation of the population of the ground and excited electronic states. We have explored that these minima originate from the oscillatory patterns and different phase in the Sgω and Suω spectra due to recombination to the 1σg and 2pσu respectively. These oscillatory patterns in turn are due to the nonadiabatic electronic behavior appearing as a slow oscillation pattern in the ground and first excited electronic states populations. We show that the minima of the HHG spectrum are related to Sgω, Suω, and orbital interference.

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

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.

Tunable Nonlinearity and Efficient Harmonic Generation from a Strongly Coupled Light–Matter System

Strong light–matter coupling within electromagnetic environments provides a promising path to modify and control chemical and physical processes. The origin of the enhancement of nonlinear optical processes such as second-harmonic and third-harmonic generation (SHG and THG) due to strong light–matter coupling is attributed to distinct physical effects, which questions the relevance of strong coupling in these processes. In this work, we leverage a first-principles approach to investigate the origins of the experimentally observed enhancement of resonant SHG and THG under strong light–matter coupling. For the proposed system under consideration, we find that the enhancement of the nonlinear conversion efficiency has its origins in a modification of the associated nonlinear optical susceptibilities as polaritonic resonances emerge in the nonlinear spectrum. Further, we find that the nonlinear conversion efficiency can be tuned by increasing the light–matter coupling strength. Finally, we provide an alternative framework to compute the harmonic generation spectra from the displacement field as opposed to the standard approach, which computes the harmonic spectrum from the matter-only induced polarization. Our results provide useful insights that shed light on this key debate in the field and pave the way for predicting and understanding quantum nonlinear optical phenomena in strongly coupled light–matter systems.

High-order harmonic generation in three-dimensional Weyl semimetals with broken time-reversal symmetry

In this paper the nonlinear interaction of a Weyl semimetal (WSM) with a strong driving electromagnetic wave field is investigated. In the scope of the structure-gauge-invariant low-energy nonlinear electrodynamic theory, the polarization-resolved high-order harmonic generation spectra in the WSM with broken time-reversal symmetry are analyzed. The results obtained show that the spectra in the WSM are completely different compared to the two-dimensional graphene case. In particular, at the noncollinear arrangement of the electric and Weyl node momentum separation vectors, anomalous harmonics are generated which are polarized perpendicular to the pump wave electric field. The intensities of anomalous harmonics are quadratically dependent on the momentum space separation of the Weyl nodes. If the right and the left Weyl fermions are merged, we have a four-component trivial massless Dirac fermion and, as a consequence, the anomalous harmonics vanish. In contrast to the anomalous harmonics, the intensities of normal harmonics do not depend on the Weyl nodes' momentum separation vector and the harmonics spectra resemble the picture for a massless three-dimensional Dirac fermion.

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.

Signatures of nonlinear magnetoelectricity in the second harmonic spectra of SU(2) symmetry-broken quantum many-body systems

Quantum mechanical perturbative expressions for second-order dynamical magnetoelectric (ME) susceptibilities have been derived and calculated for a small molecular system using the Hubbard Hamiltonian with SU(2) symmetry breaking in the form of spin–orbit coupling (SOC) or spin–phonon coupling. These susceptibilities will have signatures in second harmonic generation spectra. We show that SU(2) symmetry breaking is the key to generate these susceptibilities. We have calculated these ME coefficients using the full many-body basis and solved the Hamiltonian matrix for low-lying excited states using Lanczos method. Varying the Hubbard term along with SOC strength, we find spin and charge and both spin–charge dominated spectra of dynamical ME coefficients. We have shown that intensities of the peaks in the spectra are the highest when the magnitudes of Hubbard and SOC strengths are in a similar range.

Laser-Dressed Molecular Point Groups in the Kramers-Henneberger Oscillating Frame-of-Reference: Selection Rules for Higher Harmonic Generation.

Point groups of molecules in a laser, within the Kramers-Henneberger (KH) oscillating frame for laser-dressed states, is given in this work. In a Fourier series of the time-dependent potential, the zeroth-order time-average yields the point group of the laser-dressed molecule. Various laser polarizations and relative molecular orientation induce a new point group or retain the original point group. The dynamical Fourier components (KH potentials) classify as irreducibles of this new laser-dressed point group. Recurrence of unique irreducibles in the Fourier expansion dictates the dynamical symmetry of the Floquet Hamiltonian. Hence, selection rules for harmonic generation spectra are Nk ± 1 in harmonic order, where N is the number of unique irreducibles and .

The interfacial structure of super-concentration LiNO3 aqueous electrolyte studied by second harmonic generation.

The interfacial structure of a super-concentration LiNO3 aqueous electrolyte was studied using non-resonant second harmonic generation (SHG) and heterodyne-detected SHG spectra. First, we investigated the electric double layer structure at the air/LiNO3 interface. As the concentration of LiNO3 increased, the SHG intensity first increased and then remained unchanged, while the SHG phase changed by about 5°. These results reveal that there was only a small amount of NO3 - at the interface. The increase of the SHG intensity resulted from the thickening of the interfacial water molecular layer. In addition, we studied the broadening mechanism of the electrochemical stability window (ESW) for the super-concentrated LiNO3 aqueous electrolyte. During cyclic voltammetry scanning, the potential-dependent SHG curves of the Pt/LiNO3 interface verify that at the cathodic end of the ESW, as the concentration of LiNO3 increased, the orientation angle θ of Pt-H changed less and the number density Ns of Pt-H gradually decreased, which indicates the decrease of the number of adsorbed H atoms on the Pt electrode surface. Therefore, the decrease of the number of free water molecules on the Pt electrode surface resulted in an expanded ESW.

A Second Harmonic Wave Angle Sensor with a Collimated Beam of Femtosecond Laser

An optical angle sensor based on the collimated mode-locked femtosecond laser (Fs) beam, in which the angle measurement is carried out by observing the second harmonic wave generated by irradiating the Fs beam towards MgO:LiNbO3 crystal, is proposed. The angle detection is demonstrated by identifying the second harmonic generation (SHG) spectrum peaks against the angular position of the rotating stage-mounted MgO:LiNbO3 crystal that represents the measurement object. The MgO:LiNbO3 with a length of 2 mm, a cut-off angle of 47°, a diameter of 5 mm, and 5% of MgO:LN, is rotated within the phase-matching angle over a wavelength range from 1480 nm to 1640 nm. Angle measurement is also carried out by placing the crystal at different positions along the laser beam propagation direction to confirm the feasibility of the angle sensor where the measurement range, measurement sensitivity, and resolution of the proposed method are also evaluated. The result shows that the proposed angle sensor can overcome the working distance limitation of conventional angle sensors and has no specific material target requirement. Since the configuration of the proposed angle sensor is not limited by the specification of the measurement target, it is expected to have wide potential applications, especially in the manufacturing process and inspection process.

In Situ Probe Supramolecular Self-Assembly Dynamics and Chirality Transfer Mechanism at Air-Water Interface.

The study of supramolecular self-assembly dynamics and the chirality transfer mechanism is of importance to the rational design of potentially functional chiral supramolecular materials and an understanding of the origin of homochirality in biological systems. Herein, we study the supramolecular assemblies constructed by the tetrakis(4-sulfonatophenyl) porphyrin (TPPS) molecules' adsorption on the enantiomer chiral amphiphilic molecules (l-/d-G12) using sum-frequency generation (SFG) and second harmonic generation (SHG) spectra. We first establish a dynamic model that involved adsorption and assembly and obtained the dynamic parameters by fitting this model. We then propose the chiral transfer mechanism from the chiral center of the l-/d-G12 molecule to the whole supramolecular assembly. Finally, we put forward an explanation that the sulfonic acid group and the phenyl group on the TPPS molecule show homochirality, but the porphyrin ring forms J-aggregation and shows mirror-symmetric structural chirality in the l-/d-G12 and TPPS self-assembly at these processes.

Reply to “Comment on ‘Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation’”

In reply to the Comment by O. Neufeld et al. [Phys. Rev. A 105, 047101 (2022)], we argue that the conclusions of Phys. Rev. A 103, 043106 (2021) remain valid. We disprove the claim that the unphysical even-order harmonics originate from convergence issues related to reflections at the boundary of the simulation box. By additional calculations, we show that such reflections perturb the high-order harmonic generation spectra by oscillations with periods much smaller than the distance between the harmonics. We also demonstrate that the convergence argument of the Comment, in contrast to our multielectron excitations argument, cannot explain why there are no unphysical even-order harmonics in one-electron systems. Moreover, we show that the argument put forward in the Comment to conclude that the time-dependent Kohn-Sham equations are superior to the time-dependent natural Kohn-Sham equations is not valid.

High Harmonic Generation from Oriented Asymmetric Molecules in the Presence of Static Electric Field

Abstract We investigate the high harmonic generation during the interaction of the femtosecond laser field with oriented asymmetric diatomic molecules in the presence of an external static electric field. Based on the numerical solution of the time-dependent Schrödinger equation for the model one-electron system, we calculate the high harmonic generation spectrum for a wide range of static-field strengths. The possibilities for visualizing low-frequency (terahertz and mid-infrared) radiation using time-delay measurements of even high harmonics intensities are discussed.

A real-time TDDFT scheme for strong-field interaction in Cartesian coordinate grid

In this communication, we present a new approach towards RT-TDDFT through time-dependent KS equations based on an adiabatic eigenstate subspace (AES) procedure. It introduces a second-order split operator technique in energy representation to implement the approximate TD propagator in AES. Most of the elements in TDKS matrix are directly computed in Cartesian coordinate grid (CCG). To demonstrate the internal consistency of our proposed scheme, we computed the TD dipole moment and high harmonic generation spectra using an adiabatic local density approximation. The comparison with available theoretical results ensures the feasibility of this proposed route.

High harmonic generation spectra for lithium embedded in plasma environment

Effect of plasma on High harmonic generation of Lithium is investigated. Variation of the strength of different harmonics with respect to changes in Debye length is shown. The unperturbed energy eigenvalues and wavefunctions are calculated using the pseudostate summation technique while for the time evolution of wavefunctions the symplectic method is applied. Results for the numerical simulation of High harmonic generation spectra for plasma embedded Lithium are reported.