Propagation Induced Dephasing in Semiconductor High-Harmonic Generation

Toward Complete All-Optical Intensity Modulation of High-Harmonic Generation from Solids

Optical modulation of high-harmonics generation in solids enables the detection of material properties, such as the band structure, and promising new applications, such as super-resolution imaging in semiconductors. Various recent studies have shown optical modulation of high-harmonics generation in solids, in particular, suppression of high-harmonics generation has been observed by synchronized or delayed multipulse sequences. Here we provide an overview of the underlying mechanisms attributed to this suppression and provide a perspective on the challenges and opportunities regarding these mechanisms. All-optical control of high-harmonic generation allows for femtosecond, and in the future possibly subfemtosecond, switching, which has numerous possible applications: These range from super-resolution microscopy to nanoscale controlled chemistry and highly tunable nonlinear light sources.

High harmonic generation in graphene quantum dots

We study theoretically the generation of high harmonics in disk graphene quantum dots placed in linearly polarized short pulse. The quantum dots (QD) are described within an effective model of the Dirac type and the length gauge was used to describe the interaction of quantum dots with an optical pulse. The generated radiation spectra of graphene quantum dots can be controlled by varying the quantum dot size, i.e. its radius. With increasing the quantum dot radius, the intensities of low harmonics mainly decrease, while the cutoff frequency increases. The sensitivity of the cutoff frequency to the QD size increases with the intensity of the pulse.

Dephasing Dynamics Accessed by High Harmonic Generation: Determination of Electron-Hole Decoherence of Dirac Fermions

We reveal the critical effect of ultrashort dephasing on the polarization of high harmonic generation in Dirac fermions. As the elliptically polarized laser pulse falls in or slightly beyond the multiphoton regime, the elliptically polarized high harmonic generation is produced and exhibits a characteristic polarimetry of the polarization ellipse, which is found to depend on the decoherence time T2. T2 could then be determined to be a few femtoseconds directly from the experimentally observed polarimetry of high harmonics. This shows a sharp contrast with the semimetal regime of higher pump intensity, where the polarimetry is irrelevant to T2. An access to the dephasing dynamics would extend the prospect of high harmonic generation into the metrology of a femtosecond dynamic process in the coherent quantum control.

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.

Pure Dephasing of Light-Matter Systems in the Ultrastrong and Deep-Strong Coupling Regimes

Pure dephasing originates from the nondissipative information exchange between quantum systems and environments, and plays a key role in both spectroscopy and quantum information technology. Often pure dephasing constitutes the main mechanism of decay of quantum correlations. Here we investigate how pure dephasing of one of the components of a hybrid quantum system affects the dephasing rate of the system transitions. We find that, in turn, the interaction, in the case of a light-matter system, can significantly affect the form of the stochastic perturbation describing the dephasing of a subsystem, depending on the adopted gauge. Neglecting this issue can lead to wrong and unphysical results when the interaction becomes comparable to the bare resonance frequencies of subsystems, which correspond to the ultrastrong and deep-strong coupling regimes. We present results for two prototypical models of cavity quantun electrodynamics: the quantum Rabi and the Hopfield model.

Review on the Reconstruction of Transition Dipole Moments by Solid Harmonic Spectrum

In the process of intense laser–matter interactions, the transition dipole moment is a basic physical quantity at the core, which is directly related to the internal structure of the solid and dominates the optical properties of the solid in the intense laser field. Therefore, the reconstruction of the transition dipole moment between solid energy bands is extremely important for clarifying the ultrafast dynamics of carriers in the strong and ultrashort laser pulse. In this review, we introduce recent works of reconstructing transition dipole moment in a solid, and the advantages and drawbacks of different works are discussed.

Onset of Bloch oscillations in the almost-strong-field regime

In the field of high-order harmonic generation from solids, the electron motion typically exceeds the edge of the first Brillouin zone. In conventional nonlinear optics, on the other hand, the excursion of band electrons is negligible. Here, we investigate the transition from conventional nonlinear optics to the regime where the crystal electrons begin to explore the first Brillouin zone. It is found that the nonlinear optical response changes abruptly already before intraband currents due to ionization become dominant. This is observed by an interference structure in the third-order harmonic generation of few-cycle pulses in a non-collinear geometry. Although approaching Keldysh parameter γ = 1, this is not a strong-field effect in the original sense, because the iterative series still converges and reproduces the interference structure. The change of the nonlinear interband response is attributed to Bloch motion of the reversible (or transient or virtual) population, similar to the Bloch motion of the irreversible (or real) population which affects the intraband currents that have been observed in high-order harmonic generation.

Proposal for High-Energy Cutoff Extension of Optical Harmonics of Solid Materials Using the Example of a One-Dimensional ZnO Crystal

We propose a novel approach based on the subcycle injection of carriers to extend the high-energy cutoff in solid-state high harmonics. The mechanism is first examined by employing the standard single-cell semiconductor Bloch equation (SC SBE) method for one-dimensional (1D) Mathieu potential model for ZnO subjected to the intense linearly polarized midinfrared laser field and extreme-ultraviolet pulse. Then, we use coupled solution of Maxwell propagation equation and SC SBE to propagate the fundamental laser field through the sample, and find that the high-harmonics pulse train from the entrance section of the sample can inject carriers to the conduction bands with attosecond timing, subsequently leading to a dramatic extension of high-energy cutoff in harmonics from the backside. We predict that for a peak intensity at 2×10^{11}  W/cm^{2}, as a result of the self-seeding, the high-energy cutoff shifts from 20th (7.75 eV) order to around 50th (19.38 eV) order harmonics.

Anomalous Temperature Dependence of High-Harmonic Generation in Mott Insulators

We reveal the crucial effect of strong spin-charge coupling on high-harmonic generation (HHG) in Mott insulators. In a system with antiferromagnetic correlations, the HHG signal is drastically enhanced with decreasing temperature, even though the gap increases and the production of charge carriers is suppressed. This anomalous behavior, which has also been observed in recent HHG experiments on Ca_{2}RuO_{4}, originates from a cooperative effect between the spin-charge coupling and the thermal ensemble, as well as the strongly temperature-dependent coherence between charge carriers. We argue that the peculiar temperature dependence of HHG is a generic feature of Mott insulators, which can be controlled via the Coulomb interaction and dimensionality of the system. Our results demonstrate that correlations between different degrees of freedom, which are a characteristic feature of strongly correlated solids, have significant and nontrivial effects on nonlinear optical responses.

Signatures of Multiband Effects in High-Harmonic Generation in Monolayer MoS_{2}

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS_{2}, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. This observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multiband recombination dipoles.

All-optical valley switch and clock of electronic dephasing

2D materials with broken inversion symmetry posses an extra degree of freedom, the valley pseudospin, that labels in which of the two energy-degenerate crystal momenta, K or K', the conducting carriers are located. It has been shown that shining circularly-polarized light allows to achieve close to 100% of valley polarization, opening the way to valley-based transistors. Yet, switching of the valley polarization is still a key challenge for the practical implementation of such devices due to the short valley lifetimes. Recent progress in ultrashort laser technology now allows to produce trains of attosecond pulses with controlled phase and polarization between the pulses. Taking advantage of such technology, we introduce a coherent control protocol to turn on, off and switch the valley polarization at faster timescales than electron-hole decoherence and valley depolarization, that is, an ultrafast optical valley switch. We theoretically demonstrate the protocol for hBN and MoS₂ monolayers calculated from first principles. Additionally, using two time-delayed linearly-polarized pulses with perpendicular polarization, we show that we can extract the electronic dephasing time T₂ from the valley Hall conductivity.

Multiscale numerical tool for studying nonlinear dynamics in solids induced by strong laser pulses

Strong-field phenomena in solids exhibit extreme high-order nonlinear optical effects, which have triggered many theoretical and experimental investigations. However, there is still a lack of highly efficient numerical tools to simulate the relevant phenomena. In this paper, a versatile multiscale numerical tool set is developed for studying high-order nonlinear optical effects in solids, generated by ultrafast strong laser pulses. This tool is based on the tight-binding model approximation of the crystal structure, the related parameters of which are obtained from the density functional theory calculations. And the nonlinear effects are explored by solving the Maxwell equations coupled with the semiconductor Bloch equations. Our numerical tool can provide not only basic electronic structures and optical responses of the crystal, but also the real-time evolution of the macroscopic electromagnetic fields and the current density. The high-performance parallel computing and the interpolation method in our tool make it possible to study the strong-field nonlinear responses and propagation effects on a large spatial and temporal scale. Finally, three theoretical or experimental results published recently are satisfactorily reproduced, showing a good performance of the current toolbox.

Ultrafast transverse and longitudinal response of laser-excited quantum wires

We couple 1D pulse propagation simulations with laser-solid dynamics in a GaAs quantum wire, solving for the electron and hole populations and the interband and intraband coherences between states. We thus model not only the dynamical dipole contributions to the optical polarization (interband bound-charge response) but also the photo-generation and back-action effects of the net free-charge density (intraband free-charge response). These results show that solving for the dynamic electron and hole intraband coherences leads to plasma oscillations at THz frequencies, even in a 1D solid where plasma screening is small. We then calculate the transverse and longitudinal response of the quantum wire and characterize the dispersion relation for the e-h plasma. This approach allows one to predict the optoelectronic response of 1D semiconductor devices during and after exposure to resonant ultrashort pulses.

Coherence in macroscopic high harmonic generation for spatial focal phase distributions of monochromatic and broadband Gaussian laser pulses

Efficient application of ultrafast laser sources from high harmonic generation requires an understanding of how the spectrum can be controlled - the extent of the highest harmonics and the strength and cleanness of the harmonic lines. We study one important aspect in the coherent build-up of macroscopic high-order harmonic generation, namely the impact of different phase distributions in the focal area on the features of the generated radiation. Specifically, we compare the high harmonic signals for the commonly-used Gouy distribution of a monochromatic beam with those for the phase distribution of a short broadband Gaussian pulse. To this end, we apply a theoretical model in which the microscopic yields are obtained via interpolation of results of the time-dependent Schrödinger equation, which are then used in an individual-emitter approach to determine the macroscopic signals. Regions of poor and good coherent build-up as a function of the position of the gas jet are identified using measures for the strength of the harmonic lines and for the impact of off-harmonic radiation. While the largest extent of the spectra as well as the strongest contribution of off-harmonic radiation is found for positioning the gas jet after the focus for both distributions, the relative strength of the harmonics is overall weaker for the short Gaussian pulse distribution and the spectra differ for a gas jet positioned at the focus. These differences are mainly caused by the additional dependence of the focal phase in the transverse direction for the short Gaussian pulse distribution.

Spectral caustics of high-order harmonics in one-dimensional periodic crystals

We theoretically investigate the spectral caustics of high-order harmonics in solids. We analyze the one-dimensional model of high-order harmonic generation (HHG) in solids and find that apart from the caustics originating from the van Hove singularities in the energy band structure, another kind of catastrophe enhancement also emerges in solids when the different branches of electron-hole trajectories generating high-order harmonics coalesce into a single branch. We solve the time-dependent Schrödinger equation in terms of the periodic potential and demonstrate the control of this kind of singularity in HHG with the aid of two-color laser fields. The diffraction patterns of the harmonic spectrum near the caustics agree well with the interband electron-hole recombination trajectories predicted by the semiconductor semiclassical equation. This work is expected to improve our understanding of the HHG dynamics in solids and enable us to manipulate the harmonic spectrum by adjusting the driving field parameters.