Search

In a previous publication [J. Chem. Phys., 161, 044105 (2024)], it has been shown that Rothe's method can be used to solve the time-dependent Schr\"odinger equation (TDSE) for the hydrogen atom in a strong laser field using time-dependent Gaussian wave packets. Here, we generalize these results, showing that Rothe's method can propagate arbitrary numbers of thawed, complex-valued, explicitly correlated Gaussian functions (ECGs) with dense correlation matrices for systems with varying dimensionality. We consider the multidimensional Henon-Heiles potential, and show that the dynamics can be quantitatively reproduced using only 30 Gaussians in 2D, and that accurate spectra can be obtained using 20 Gaussians in 2D and 30 to 40 Gaussians in 3D and 4D. Thus, the relevant multidimensional dynamics can be described at high quality using only a small number of ECGs that give a very compact representation of the wave function. This efficient representation, along with the demonstrated ability of Rothe's method to propagate Gaussian wave packets in strong fields and ECGs in complex potentials, paves the way for accurate molecular dynamics calculations beyond the Born-Oppenheimer approximation in strong fields., Comment: 15 pages, 11 figures

We introduce a simple definition of the weight of any given Slater determinant in the coupled-cluster state, namely as the expectation value of the projection operator onto that determinant. The definition can be applied to any coupled-cluster formulation, including conventional coupled-cluster theory, nonorthogonal orbital-optimized coupled-cluster theory, and extended coupled-cluster theory. Numerical experiments show that for single-reference systems the coupled-cluster weights are in excellent agreement with those obtained from the full configuration-interaction wave function. Moreover, the well-known insensitivity of the total energy obtained from truncated coupled-cluster models to the choice of orbital basis is clearly exposed by weights computed in the $\hat{T}_1$-transformed determinant basis. We demonstrate that the inseparability of the conventional linear parameterization of the bra (left state) for systems composed of noninteracting subsystems may lead to ill-behaved (negative or greater than unity) weights, an issue that can only be fully remedied by switching to extended coupled-cluster theory. The latter is corroborated by results obtained with quadratic coupled-cluster theory, which is shown numerically to yield a significant improvement., Comment: 35 pages, 4 figures

Real-time propagation methods for chemistry and physics are invariably formulated using variational techniques. The time-dependent bivariational principle (TD-BIVP) is known to be the proper framework for coupled-cluster type methods, and is here studied from a differential geometric point of view. It is demonstrated how two distinct classical Hamilton's equations of motion arise from considering the real and imaginary parts of the action integral. The latter is new, and can in principle be used to develop novel propagation methods. Conservation laws and Poisson brackets are introduced, completing the analogy with classical mechanics. An overview of established real-time propagation methods is given in the context of our formulation of the TD-BIVP, namely time-dependent traditional coupled-cluster theory, orbital-adaptive coupled-cluster theory, time-dependent orthogonal optimized coupled-cluster theory, and equation-of-motion coupled cluster theory.

The formalism of real-time (RT) methods has been well-established during recent years, while no inclusion beyond the double excitation has been discussed. In this article, we introduce an implementation of real-time coupled cluster singles, doubles and approximate triples (CC3) method to explore the potential of a high excitation level. The CC3 method is well-known for its advantages in calculating dynamic properties and combining with the response theory. It is a well-qualified candidate for handling the interaction between the system and the applied field, and therefore suitable for a RT implementation. The derivation and implementation are first demonstrated following applications on calculating frequency-dependent properties. Terms with triples are calculated and added upon the existing CCSD equations, giving the method a formally $N^{7}$ scaling. The Graphics Processing Unit (GPU) accelerated implementation is utilized to reduce the computational cost. It is been verified that the GPU implementation can speed up the calculation by up to a factor of 17 for water cluster test cases. Additionally, the single-precision arithmetic is used and compared to the conventional double-precision arithmetic. No significant difference is found in the polarizabilities and $G'$ tensor results, but a higher percentage error for the first hyperpolarizabilities is observed. Compared to the linear response (LR) CC3 results, the percentage errors of RT-CC3 polarizabilities and RT-CC3 first hyperpolarizabilities are under 0.1% and 1%, respectively for the $H_2O$/cc-pVDZ test case. Furthermore, a discussion on the calculation of polarizabilities is included, which compares RT-CC3 with RT-CCSD and time-dependent nonorthogonal orbital-optimized coupled cluster doubles (TDNOCCD), in order to examine the performance of RT-CC3 and the orbital-optimization effect using a group of ten-electron systems., Comment: 56 pages, 5 figures, 10 tables

Juvenile idiopathic arthritis (JIA) is the most common rheumatic disease during childhood and adolescence. The temporomandibular joints (TMJ) are among the most frequently affected joints in patients with JIA, and mandibular growth is especially vulnerable to arthritic changes of the TMJ in children. A clinical examination is the most cost-effective method to diagnose TMJ involvement, but clinicians find it difficult to interpret and inaccurate when used only on clinical examinations. This study implemented an explainable artificial intelligence (AI) model that can help clinicians assess TMJ involvement. The classification model was trained using Random Forest on 6154 clinical examinations of 1035 pediatric patients (67% female, 33% male) and evaluated on its ability to correctly classify TMJ involvement or not on a separate test set. Most notably, the results show that the model can classify patients within two years of their first examination as having TMJ involvement with a precision of 0.86 and a sensitivity of 0.7. The results show promise for an AI model in the assessment of TMJ involvement in children and as a decision support tool., Comment: Accepted at EMBC 2024

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 {\aa}ngstr\"om. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schr\"odinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that 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 $5\times 10^{14}$W/cm$^2$. 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., Comment: 20 pages, 10 figures

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wavepackets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this paper, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

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.

Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge invariant formulation of transient absorption spectroscopy is presented within the semi-classical approximation. Avoiding multipole expansions, a computationally viable expression for the spectral response function is derived from the minimal-coupling Hamiltonian of an electronic system interacting with one or more laser pulses described by a source-free, enveloped electromagnetic vector potential. With a fixed-basis expansion of the electronic wave function, the computational cost of simulations of laser-driven electron dynamics beyond the dipole approximation is the same as simulations adopting the dipole approximation. We illustrate the theory by time-dependent configuration interaction and coupled-cluster simulations of core-level absorption and circular dichroism spectra.

We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e. the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.

High-$\langle \beta \rangle$ operations require a fast and robust inference of plasma parameters with a self-consistent MHD equilibrium. Precalculated MHD equilibria are usually employed at W7-X due to the high computational cost. To address this, we couple a physics-regularized NN model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the VMEC, and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots., Comment: 18 pages, 6 figures

We have set up a diagnostic magnet (D-Mag) laboratory for a wide range of applications in plasma physics. It consists of a superconducting magnet for field strengths of up to 5.9 T. The main purpose is to provide an experimental environment for the development of plasma diagnostics for nuclear fusion studies and the investigation of dusty plasmas in strong magnetic fields. We describe in the article the setup and operation of the D-Mag. Some applications are presented for the development of plasma diagnostics, such as neutral pressure gauges and Langmuir probes that have to be operated in strong magnetic fields. Among the examples is the test of the long-pulse capability and stability of the diagnostic pressure gauge (DPG) for the ITER device., Comment: Superconducting Magnet - laboratory for diagnostic development and tests in strong and variable magnetic fields of up to 6 Tesla

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability.

We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the $S$-diagnostic. We provide a derivation of the $S$-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the $S$-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$. Throughout the numerical investigations, the $S$-diagnostic is compared to other SRCC diagnostic procedures, that is, the $T_1$, $D_1$, and $D_2$ diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the $S$-diagnostic outperforms the $T_1$, $D_1$, and $D_2$ diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the $S$-diagnostic for geometry optimizations using SRCC reveal that the $S$-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the $S$-diagnostic for electronic correlation simulations show that the $S$-diagnostic correctly predicts strong multi-reference regimes. The $S$-diagnostic moreover correctly detects the successful SRCC computations for [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$, which have been known to be misdiagnosed by $T_1$ and $D_1$ diagnostics in the past. This shows that the $S$-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is discovered, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of (0.64 $\pm$ 0.03) eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The presented methodology outlines a new approach for band structure engineering guided by directly viewing structurally- and electrically-tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale., Comment: 37 pages, 12 figures (includes supporting information). A revised version has been published in ACS Nano

The computational cost of constructing 3D magnetohydrodynamic (MHD) equilibria is one of the limiting factors in stellarator research and design. Although data-driven approaches have been proposed to provide fast 3D MHD equilibria, the accuracy with which equilibrium properties are reconstructed is unknown. In this work, we describe an artificial neural network (NN) that quickly approximates the ideal-MHD solution operator in Wendelstein 7-X (W7-X) configurations. This model fulfils equilibrium symmetries by construction. The MHD force residual regularizes the solution of the NN to satisfy the ideal-MHD equations. The model predicts the equilibrium solution with high accuracy, and it faithfully reconstructs global equilibrium quantities and proxy functions used in stellarator optimization. We also optimize W7-X magnetic configurations, where desiderable configurations can be found in terms of fast particle confinement. This work demonstrates with which accuracy NN models can approximate the 3D ideal-MHD solution operator and reconstruct equilibrium properties of interest, and it suggests how they might be used to optimize stellarator magnetic configurations., Comment: 47 pages, 28 figures, published in Nuclear Fusion

Linear combinations of complex gaussian functions, where the linear and nonlinear parameters are allowed to vary, are shown to provide an extremely flexible and effective approach for solving the time-dependent Schr\"odinger equation in one spatial dimension. The use of flexible basis sets has been proven notoriously hard within the systematics of the Dirac--Frenkel variational principle. In this work we present an alternative time-propagation scheme that de-emphasizes optimal parameter evolution but directly targets residual minimization via the method of Rothe's method, also called the method of vertical time layers. We test the scheme using a simple model system mimicking an atom subjected to an extreme laser pulse. Such a pulse produces complicated ionization dynamics of the system. The scheme is shown to perform very well on this model and notably does not rely on a computational grid. Only a handful of gaussian functions are needed to achieve an accuracy on par with a high-resolution, grid-based solver. This paves the way for accurate and affordable solution of the time-dependent Schr\"odinger equation for atoms and molecules within and beyond the Born--Oppenheimer approximation., Comment: 8 pages, 6 figures

Laser-induced molecular alignment is well understood within the framework of the Born-Oppenheimer (BO) approximation Without the BO approximation, however, the concept of molecular structure is lost, making alignment hard to define precisely. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter-field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low whilst capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential., Comment: 8 pages, 6 figures

Colored Petri nets offer a compact and user friendly representation of the traditional P/T nets and colored nets with finite color ranges can be unfolded into the underlying P/T nets, however, at the expense of an exponential explosion in size. We present two novel techniques based on static analysis in order to reduce the size of unfolded colored nets. The first method identifies colors that behave equivalently and groups them into equivalence classes, potentially reducing the number of used colors. The second method overapproximates the sets of colors that can appear in places and excludes colors that can never be present in a given place. Both methods are complementary and the combined approach allows us to significantly reduce the size of multiple colored Petri nets from the Model Checking Contest benchmark. We compare the performance of our unfolder with state-of-the-art techniques implemented in the tools MCC, Spike and ITS-Tools, and while our approach is competitive w.r.t. unfolding time, it also outperforms the existing approaches both in the size of unfolded nets as well as in the number of answered model checking queries from the 2021 Model Checking Contest.

In this work we present a derivation of the real-time time-dependent orbital-optimized M{\o}ller-Plesser TDOMP2 and its biorthogonal companion, time-dependent non-orthogonal OMP2 (TDNOMP2), theory starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in time-independent molecular electronic-structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from real-time simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation TDCC2. We also compare with results from CCSD and CC2 linear and quadratic response theory. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, frequency-dependent polarizabilities and hyperpolarizabilties from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

Biased bilayer graphene (BBG) is a variable band gap semiconductor, with a strongly field-dependent band gap of up to $300 \, \text{meV}$, making it of particular interest for graphene-based nano-electronic and -photonic devices. The optical properties of BBG are dominated by strongly bound excitons. We perform ab initio density-functional-theory+Bethe-Salpeter-equation modelling of excitons in BBG and calculate the exciton band structures and optical matrix elements for field strengths in the range $30-300 \, \text{mV}/{\unicode{x212B}}$. The exciton properties prove to have a strong field dependence, with both energy ordering and dipole alignment varying significantly between the low and high field regions. Namely, at low fields we find a mostly dark ground state exciton, as opposed to high fields, where the lowest exciton is bright. Also, excitons preferentially align with a dipole moment opposite the field, due to the field-induced charge transfer in the ground state of BBG. However, in stronger fields, this alignment becomes energetically less favorable. Additionally, the bright excitons show particle- and light-like bands similar to monolayer transition metal dichalchogenides. Finally, we model the radiative lifetimes and emission properties of BBG, which prove to be strongly dependent on temperature in addition to field strength.

Excitons in low-dimensional materials behave mathematically as confined hydrogen atoms. An appealing unified description of confinement in quantum wells or wires, etc., is found by restricting space to a fractional dimension 1 < D <= 3 serving as an adjustable parameter. We compute the dynamic polarizability of D-dimensional excitons in terms of discrete and continuum oscillator strengths. Analyzing exact sum rules, we show that continuum contributions are increasingly important in low dimensions. The dynamical responses of excitons in various dimensions are compared. Finally, an exact and compact closed-form expression for the dynamic polarizability is found. This completely general formula takes D as input and provides exact results for arbitrary frequency.

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number $N$ of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large $N$ for successful key generation. Here we report the first Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with $N \lesssim 3.5\times10^8$ coherent states. With this advance, possible due to novel improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security., Comment: 8 pages (including 3 figures and references) + 12 pages supplement

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations serve as input for the assessment of a number of important physics questions. The VMEC code is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications. Access to fast MHD equilbria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of W7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume averaged normalized plasma pressure $\langle \beta \rangle$ ($\beta$ = $\frac{2 \mu_0 p}{B^2}$) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional neural networks are found to outperform feed-forward fully-connected neural networks. The achieved normalized root-mean-squared error ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales., Comment: 24 pages, 16 figures. Accepted for publication to Nuclear Fusion

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ITG turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

External electric fields are highly attractive for dynamical manipulation of excitons in two-dimensional materials. Here, we theoretically study the ionization of excitons in monolayer transition metal dichalcogenides (TMDs) by intense pulsed electric fields in the terahertz (THz) regime. We find that THz pulses with realistic field strengths are capable of ionizing a significant fraction of photogenerated excitons in TMDs into free charge carriers. Short THz pulses are therefore an efficient, non-invasive method of dynamically controlling the free carrier concentration in monolayer TMDs, which is useful for applications such as THz modulators. We further demonstrate that exciton ionization probabilities should be experimentally measurable by comparing free carrier absorption before and after the THz pulse. Detailed results are provided for different TMDs in various dielectric environments.

In this paper, we study the third-order nonlinear optical response due to transitions between excitonic levels in two-dimensional transition metal dichalcogeniedes. To accomplish this, we use methods not applied to the description of excitons in two-dimensional materials so far and combined with a variational approach to describe the $1s$ excitonic state. The aforementioned transitions allow to probe dark states which are not revealed in absorption experiments. We present general formulas capable of describing any third-order process. The specific case of two-photon absorption in WSe2 is studied. The case of the circular well is also studied as a benchmark of the theory., Comment: 11 pages, 5 figures

Several monolayer transition metal dichalcogenides (TMDs) are direct band gap semiconductors and potentially efficient emitters in light emitting devices. Photons are emitted when strongly bound excitons decay radiatively, and accurate models of such excitons are important for a full understanding of the emission. Importantly, photons are emitted in directions uniquely determined by the exciton center of mass momentum and with lifetimes determined by the exciton transition matrix element. The exciton band structures of two-dimensional hexagonal materials, including TMDs, are highly unusual with coexisting particle- and light-like bands. The latter is non-analytic with emission selection rules essentially opposite to the particle-like states, but has been ignored in analyses of TMD light emission so far. In the present work, we analyse the temperature and angular dependence of light emission from both exciton species and point out several important consequences of the unique exciton band structure. Within a first-principles Density-Functional-Theory+Bethe-Salpeter-Equation framework, we compute exciton band structures and optical matrix elements for the important TMDs MoS2, MoSe2, WS2, and WSe2. At low temperature, only the particle-like band is populated and our results agree with previous work. However, at slightly elevated temperatures, a significant population of the light-like band leads to modified angular emission patterns and lifetimes. Clear experimental fingerprints are predicted and explained by a simple four-state model incorporating spin-orbit as well as intervalley exchange coupling.

We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.

Nonlinear optical (NLO) phenomena such as harmonic generation, Kerr, and Pockels effects are of great technological importance for lasers, frequency converters, modulators, switches, etc. Recently, two-dimensional (2D) materials have drawn significant attention due to their strong and unique NLO properties. Here, we describe an efficient first-principles workflow for calculating the quadratic optical response and apply it to 375 non-centrosymmetric semiconductor monolayers from the Computational 2D Materials Database (C2DB). Sorting the non-resonant nonlinearities with respect to bandgap $E_g$ reveals an upper limit proportional to $E_g^{-4}$, which is neatly explained by two distinct generic models. We identify multiple promising candidates with giant nonlinearities and bandgaps ranging from 0.4 to 5 eV, some of which approach the theoretical upper limit and greatly outperform known materials. Our comprehensive library of ab initio NLO spectra for all 375 monolayers is freely available via the C2DB website. We expect this work to pave the way for highly efficient and compact opto-electronic devices based on 2D materials., Comment: 18 pages, 5 Figures