We compute and analyze the dependence of excitonic second-and third-harmonic generation (SHG/THG) as a function of the optical excitation intensity in the presence of static electric fields by solving the semiconductor Bloch equations. Our simulations are performed for excitation of the strongly bound intralayer exciton of an inversion-symmetric homobilayer of MoS2 with in-plane electric fields. We demonstrate that for resonant excitation at the 1s K-exciton the SHG and the THG show complex dependencies on both the strength of the static field and the peak amplitude of the optical pulse. For sufficiently intense optical excitation, the THG increases and the SHG increases superlinearly with the amplitude of the static field as long as exciton ionization is not yet dominating. Microscopic simulations demonstrate that these dependencies arise from an interplay between several effects including static and transient Stark shifts, exciton ionization, off-resonant Rabi oscillations, and a modified interference between optical nonlinearities induced by the intraband acceleration. Our findings offer several new possibilities for controlling the strong-field dynamics of systems with strongly bound excitons.

Static electric fields lead to Stark shifts and ionization of excitons. For a bi-layer of MoS 2 we demonstrate that electric fields of intermediate strength can significantly increase excitonic third harmonic generation before ionization dominates.

We compute and analyze the dependence of excitonic second- and third-harmonic generation (SHG/THG) as a function of the optical excitation intensity in the presence of static electric fields by solving the semiconductor Bloch equations. Our simulations are performed for excitation of the strongly bound intralayer exciton of an inversion-symmetric homobilayer of MoS2 with in-plane electric fields. We demonstrate that for resonant excitation at the 1s K-exciton the SHG and the THG show complex dependencies on both the strength of the static field and the peak amplitude of the optical pulse. For sufficiently intense optical excitation, the THG increases and the SHG increases superlinearly with the amplitude of the static field as long as exciton ionization is not yet dominating. Microscopic simulations demonstrate that these dependencies arise from an interplay between several effects including static and transient Stark shifts, exciton ionization, Wannier-Stark localization, off-resonant Rabi oscillations, and a modified interference between optical nonlinearities induced by the intraband acceleration. Our findings offer several new possibilities for controlling the strong-field dynamics of systems with strongly bound excitons.

Dataset of the publication “Excitonic anomalous currents in semiconductor quantum wells”, by C. Ngo, S. Priyadarshi, H. T. Duc, M. Bieler, and T. Meier, published in Physical Review B 108, 165302 (2023) ( https://doi.org/10.1103/PhysRevB.108.165302 )The zip file includes a brief description and the data on which the plots of figures 2 – 10 are based, and the codes used for the numerical evaluations (k.p and semiconductor Bloch equations).

Anomalous currents refer to electronic currents that flow perpendicularly to the direction of the accelerating electric field. Such anomalous currents can be generated when Terahertz fields are applied after an optical interband excitation of GaAs quantum wells. The underlying processes are investigated by numerical solutions of the semiconductor Bloch equations in the length gauge. Excitonic effects are included by treating the manybody Coulomb interaction in time-dependent Hartree-Fock approximation and additionally also carrier-phonon scattering processes are considered. The band structure and matrix elements are obtained from a 14-band k · p model within the envelope function approximation. The random phase factors of the matrix elements that appear due to the separate numerical diagonalization at each k-point are treated by applying a smooth gauge transformation. We present the macroscopic Berry curvature and anomalous current transients with and without excitonic effects. It is demonstrated that the resonant optical excitation of excitonic resonances can significantly enhance the Berry curvature and the anomalous currents.

It is argued that the dynamic core-electron polarization (DCEP) in polar molecules primarily affects harmonic processes at the ionization step only. This manifestation can also be understood in view of the strong-field assumption that the parent ion's potential becomes irrelevant when the electron is accelerated in the continuum-energy region. However, the scenario becomes vastly different, especially in the case of long-wavelength lasers as shown in this paper, where we demonstrate a complete physical picture of the DCEP on the harmonic process from asymmetric carbon monoxide (CO) molecules comprising the propagation step. To do so, we develop a visualization method for the harmonic process with and without DCEP based on Bohmian mechanics. As tracer particles evolving along quantum trajectories, Bohmian trajectories provide an intuitive picture of the ``harmonic process from the CO molecules. Remarkably, when the change of the harmonic intensity with respect to the DCEP inclusion cannot be explained by the instantaneous ionization rate, the Bohmian trajectories can attribute this change to the difference in the number of returning events and returning time of the electron after the propagation stage. By analyzing the dynamics of individual Bohmian trajectories (the acceleration and the time-frequency profile), we show that the DCEP alters nonlocally the innermost trajectories, which encode all the dynamics of the harmonic process. This insight into the DCEP effect necessitates a careful reinvestigation into other strong-field physics theories on the role of the target over the propagation stage.

The nonlinear optical response of quantum well excitons is investigated experimentally using polarization resolved four wave mixing, optical-pump optical-probe, and optical-pump Terahertz-probe spectroscopy. The four-wave mixing data reveal clear signatures of coherent biexcitons which concur with straight-forward polarization selection rules at the Γ point. The type-I samples show the well-established time-domain beating signatures in the transients as well as the corresponding spectral signatures clearly. The latter are also present in type-II samples; however, the smaller exciton and biexciton binding energies in these structures infer longer beating times which, in turn, are accompanied by faster dephasing of the type-II exciton coherences. Furthermore, the THz absorption following spectrally narrow, picosecond excitation at energies in the vicinity of the 1s exciton resonance are discussed. Here, the optical signatures yield the well-established redshifts and blueshifts for the appropriate polarization geometries in type-I quantum well samples also termed “AC Stark Effect”. The THz probe reveals intriguing spectral features which can be ascribed to coherent negative absorption following an excitation into a virtual state for an excitation below the 1s exciton resonance. Furthermore, the scattering and ionization of excitons is discussed for several excitation geometries yielding control rules for elastic and inelastic quasiparticle collisions.

The nonlinear optical response of quantum well excitons excited by optical fields is analyzed by numerical solutions of the semiconductor Bloch equations. Differential absorption spectra are computed for resonant pumping at the exciton resonance and the dependence of the absorption changes on the polarization directions of the pump and probe pulses is investigated. Coherent biexcitonic many-body correlations are included in our approach up to third-order in the optical fields. Results are presented for spatially-direct type-I and spatiallyindirect type-II quantum well systems. Due to the spatial inhomogeneity, in type-II structures a finite coupling between excitons of opposite spins exists already on the Hartree-Fock level and contributes to the absorption changes for the case of opposite circularly polarized pump and probe pulses.

The semiconductor Bloch equations provide a very versatile and microscopic approach to compute and analyze optical and electronic properties of semiconductors. Here, we focus on high harmonic generation arising from the driving of crystalline systems with very strong optical and Terahertz pulses. Implementing a proper gauge allows us to solve the semiconductor Bloch equations in the length gauge. The length gauge turns out to be advantageous since it converges for a smaller number of bands than the velocity gauge and, in addition, enables a unique distinction between inter- and intraband contributions. Besides odd harmonics polarized parallel to the incoming field our approach also describes even harmonics which originate from the Berry curvature and are polarized perpendicular to the incident field. Next, we demonstrate that the electron and hole collision/recombination dynamics is mainly responsible for the anisotropy of the interband high harmonic generation. Our findings connect the electron/hole backward scattering to van Hove singularities and the forward scattering with critical lines in the band structure and we show that this dynamics can be controlled by properly designed two-color fields. Furthermore, we consider excitonic effects within a two-band model and show that they can strongly enhance the high harmonic emission intensity for suitably chosen incident pulses. When an odd-order harmonic corresponds to the energy of the 1s exciton this harmonic is several orders of magnitude larger than the emission from non-interacting electrons and holes.

It has been known that the broadband of continuum harmonics, a regular periodicity or a wide smooth range, is essential for generating attosecond pulses. However, the high-order rescatterings of electrons (HOR) can significantly affect this important part of high-order harmonic spectra. In the present work, we apply the method suggested in our previous studies to limit the HOR effect on the continuum harmonics by using up-chirped pulses with frequency increasing in time to regulate the high-order harmonic generation of an asymmetric molecule such as CO subjected to a near-infrared laser. To do so, we numerically calculate the high-order harmonic spectra using the time-dependent wave functions obtained within the framework of the single-active electron approximation. To analyze and regulate the HOR effect, we use the time-frequency analysis together with the kinetic energy maps obtained from the equation of electron motion in the laser electric field. These techniques reveal the high-order harmonic dynamics, especially the effect of chirped pulse on the manifestation of continuum harmonics. Based on this, we release the notice on choosing appropriate parameters to obtain the optimal continuum range of harmonics. Although the detailed analysis is given for the CO molecule, the method suggested is applicable for other polar molecules.

A wide range of harmonics especially continuum harmonics is a prerequisite for attosecond pulse generation. One can use longer-wavelength lasers to push the cutoff to a higher order. However, this does not translate to the same amount of continuum range extension because multiple rescattering phenomena are also enhanced in the process, potentially affecting the lower end of the continuum harmonics. It is then important to understand exactly how multiple rescatterings affect the harmonic structure and their response to various laser parameters, which is the main theme of this paper. Particularly, by applying the synchrosqueezed time-frequency transform and classical electron trajectory analysis to the asymmetric molecule carbon monoxide (CO), we justify that the multiple rescatterings indeed influence the periodicity of the harmonic spectra and the stable periodicity is, in fact, bounded by the first- and third-order returns. Moreover, for the first time, we find that the high-order rescatterings are asymmetric regarding the molecular rotation of 180°, but always correlate with the first-order returns. Our last result is that by breaking the laser symmetry in an appropriate way, the contribution of multiple rescatterings is removed so that the continuum region is entirely defined by the first-order return energies.

Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well known that numerical band structure calculations typically provide electronic wave functions with an undetermined $k$-dependent phase which results in matrix elements which contain arbitrary $k$-dependent phases. In addition, such approaches usually mix degenerate bands and bands with an energy difference smaller than the numerical precision in an arbitrary way for each point in $k$ space. These ambiguities are problematic if one considers the dynamics induced by electric fields since the matrix elements of the position operator involve a derivative of the wave functions with respect to $k$. When the light-matter interaction is described in the length gauge, the problem of arbitrary phases and degenerate subspace mixing of Bloch states is solved by adopting a smooth gauge transformation along the field direction. The results obtained within this method are validated by comparing with calculations in the velocity gauge. Although we obtain in both gauges the same overall result, the length gauge is advantageous since it converges with a smaller number of bands and thus requires significantly less numerical effort than the velocity gauge. Also a unique distinction between inter- and intraband contributions and thus an instructive physical interpretation is possible in the length gauge whereas in the velocity gauge this is unclear. The computed polarization-direction-dependent high-harmonic spectra agree well with experimental data reported for GaAs. Furthermore, it is demonstrated that, under proper conditions, the Berry curvature is largely responsible for the even-order harmonics which are polarized perpendicular to the driving field.

Photocurrent induced by ultrashort laser pulses in [100]-oriented GaAs quantum wires with square cross section is investigated using the multiband semiconductor Bloch equations with the inclusion of electron-hole interaction. Influences of excitonic effects and quantum confinement effects on the photocurrent are evaluated and discussed.

We theoretically investigate the generation and dynamics of photocurrents induced by linearly polarized single-frequency light pulses in GaAs quantum wells. Our approach is based on the multiband semiconductor Bloch equations (SBE) formulated in the basis of eigenfunctions on the 14-band k . p model and includes excitonic effects and carrier longitudinal-optical-phonon scattering processes. By solving the SBE, we obtain both shift and ballistic currents. For a particular excitation geometry, we obtain a ballistic current which is absent if the electron-hole attraction is neglected. Whereas in other cases excitonic effects quantitatively modify photocurrents that originate from single-particle properties, here we demonstrate the existence of a ballistic current which is absent in single-particle calculations. This photocurrent is of second order in the light-matter interaction and is purely caused by the asymmetric electron-hole Coulomb attraction that results from the inversion asymmetry of GaAs. Furthermore, we show that the coherent dynamics of excitonic wave packets gives rise to oscillations in the photocurrent transients.

The laser-induced dynamic core-electron polarization (DCEP) was known critical in the ionization of polar molecules such as CO, but less relevant in that of nonpolar ones, such as CO2, N-2, or O-2. For the harmonic process, the DCEP is proven to play an essential role for the polar molecule CO; it affects the harmonic intensity through the ionization at a specific instant. However, the influence of DCEP on the harmonic process of nonpolar molecules is still questionable. In this paper, we show that DCEP can affect the high-order harmonic generation (HHG) through a different mechanism-suppressing the distortion of the laser field on the highest occupied molecular orbital (HOMO) during the recombination phase, thus partially recovering the HOMO symmetry. Consequently, this shifts and sharpens the minima in the HHG spectra, which arise from the two-center interference. To support our point, we provide reliable numerical simulation by solving the time-dependent Schrodinger equation of the coupled CO2 molecule-laser field within the single active electron framework. From the minima location, we also extract the internuclear separation O-O of CO2, which is more accurate if including the DCEP in the simulation.