Dipole Matrix Elements Research Articles

Effects of intense laser field and position dependent effective mass in Razavy quantum wells and quantum dots

Using the effective mass and parabolic band approximations, we investigated the position-dependent effective mass and non-resonant intense laser field effects on the first and third-order corrections of the absorption and relative changes of the refraction index coefficients for intersubband transition in Razavy-like quantum wells. Calculations have been extended to the spherical Razavy-like quantum dots electronic structure. We have shown that depending on the combinations of the Razavy-like potential parameters, the quantum wells can evolve from parabolic confinement in an isolated quantum well to a configuration of two coupled quantum wells. We have shown that in general the transition energies (dipole matrix elements) between the ground state and the first excited state: i ) are decreasing (increasing) functions of M -parameter, ii ) are increasing (decreasing) functions of A -parameter, iii ) they increase (decrease) when considering the position-dependent effective mass effects, and iv ) are increasing (decreasing) functions of the intense laser field parameter. In the case of the optical absorption and relative changes in the refractive index coefficients, we have shown blueshifts or redshifts by changing the A -, M -, and α 0 -parameters and by considering the effects of the position-dependent effective mass. In spherical quantum dots, we have shown that with an appropriate value of A - and M -parameters the system can evolve from a spherical quantum dot with infinite parabolic potential. • Intense laser field effects in quantum wells and dots. • Position dependent electron effective. • Linear and nonlinear optical absorption and refraction index changes coefficients. • Spatially direct and indirect excitones can be simulated in quantum rings.

Electron-rotation coupling in diatomics under strong-field excitation

The photoexcitation and photodissociation of diatomic molecules by intense pulse lasers has been the subject of extensive investigations over the past decades. However, the usually employed theoretical framework neglects the coupling between the molecular rotational angular momentum ($\mathbf{R}$) and the angular momentum of the electrons projected onto the molecular axis $\mathrm{\ensuremath{\Omega}}=\mathrm{\ensuremath{\Lambda}}+\mathrm{\ensuremath{\Sigma}}$, which results in the known $\mathrm{\ensuremath{\Lambda}}$-doubling phenomenon in high-resolution electronic spectra of diatomic molecules. While neglecting this coupling is an excellent approximation in the weak-field or perturbative regime owing to the large mass difference between the rotating atoms and the electrons, the approximation breaks down for intense laser pulses because of the repeated Rabi cycling of the electronic transitions, which can have a significant effect on the rotational degrees of freedom of the molecule. By correcting the transition dipole matrix elements and introducing angular basis sets based on Wigner D functions, the conventional theoretical treatment is generalized to a universal description valid for both the weak- and strong-field regimes. The theoretical treatment developed here is applied to the $|^{1}\mathrm{\ensuremath{\Sigma}}\ensuremath{\rangle}$ to $|^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\rangle}$ transitions in diatomic systems. Our results reveal that, for field intensities resulting in about one Rabi cycling for extreme ultraviolet or x-ray transitions, the theoretical predictions by the conventional theoretical frame need to be corrected when considering observables such as the molecular alignment and the angular distribution of the photofragments.

Spectra of a Rydberg Atom in Crossed Electric and Magnetic Fields

Contemporary spectroscopic studies of astrophysical and laboratory plasmas frequently deal with extremely large values of principle quantum numbers of atomic systems. These atomic states are very sensitive to electric and magnetic fields of the surrounding medium. While interpreting the spectra of such excited atomic systems, one faces the problem of a huge array of radiative transitions between highly excited atomic levels. Moreover, external electric and magnetic fields significantly complicate the problem because of the absence of standard selection rules typical for the spherical quantization. The analytical expression in the parabolic representation for dipole matrix elements obtained by Gordon contains hyper-geometric series and it has a very complex structure. The matrix elements that involve the presence of electric and magnetic fields are calculated while using a representation closely related to the parabolic quantization on two different axes. This matrix element depends in a complex way on the transition probabilities in the parabolic coordinate system (Gordon’s formulas) and the Wigner d-functions. This circumstance leads to even greater computational difficulties. A method of simplification of these complicated expressions for transition probabilities is demonstrated. The semiclassical approximation for coordinate matrix elements (Gulayev) and recurrence properties of the Wigner d-functions are used. The Hnβ line is under consideration. Specific calculations for the transition 10–8 in the case of parallel and perpendicular fields are presented.

Angle-resolved studies of XUV–IR two-photon ionization in the RABBITT scheme

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is an established technique for studying time-delay in photoionization of atoms and molecules. It has been recently extended to angle-resolved studies, accessing diverse fingerprint observables of the attosecond photoemission dynamics within the bound-continuum and continuum–continuum transitions. In this work, we address the general form of the ISB(θ,τ) two-photon photoelectron angular distributions (PADs) associated to the RABBITT sideband signal, as a function of the emission angle θ, and the delay τ between the XUV attosecond pulse train and the infrared (IR) dressing field at play in the RABBITT scheme. Relying on the expansion in Legendre polynomials, the PAD is synthesized in terms of a reduced set of coefficients which fully describe both its static (τ-independent) and dynamic (τ-dependent) components and enables us to retrieve any observable characterizing the PAD. This unified framework streamlines the comparison between different experimental or theoretical data sets and emphasizes how some observables depend on the experimental conditions. Along with the modelled analysis, we report new results of angle-resolved RABBITT direct ionization of the np valence orbital of Ar(3p6) and Ne(2p6), employing electron-ion coincidence momentum spectroscopy at the new Attolab facility. In this case, the nine coefficients synthesizing the PAD are further linked to the magnitude and phase of the transition dipole matrix elements, providing a fundamental test of theoretical predictions. Similarities and differences are found between Ar and Ne in the explored low energy region, up to 20 eV above the ionization threshold, where the electron dynamics is most sensitive to electronic correlation. Further interpretation of these results would benefit from a comparison with advanced many-body theoretical simulations.

Observation of intravalley phonon scattering of 2s excitons in MoSe2 and WSe2 monolayers

We present a high-resolution resonance Raman study of hBN encapsulated MoSe2 and WSe2 monolayers at 4 K using excitation energies from 1.6 eV to 2.25 eV. We report resonances with the WSe2 A2s and MoSe2 A2s and B2s excited Rydberg states despite their low oscillator strength. When resonant with the 2s states we identify new Raman peaks which are associated with intravalley scattering between different Rydberg states via optical phonons. By calibrating the Raman scattering efficiency and separately constraining the electric dipole matrix elements, we reveal that the scattering rates for k = 0 optical phonons are comparable for both 1s and 2s states despite differences in the envelope functions. We also observe multiple new dispersive Raman peaks including a peak at the WSe2 A2s resonance that demonstrates non-linear dispersion and peak-splitting behavior that suggests the dispersion relations for dark excitonic states at energies near the 2s state are extremely complex.

Calculation of reliable non-resonant Kα X-ray emission spectra of organic molecules and other small molecules

For reliable calculation of vertical ionization energies (VIEs) of both core and valence electrons of gas-phase organic molecules and other small molecules, we developed DFT procedures in 1999 and 2009. The difference between core and valence VIEs give the energies for X-ray emission spectra (XES). The dipole matrix elements between core and valence electrons required for calculation of the XES intensities are now easily available. The simple procedure for calculation of reliable XES is demonstrated by comparison with known XES for H2O(g), NH3(g), CO(g), CO2(g), N2(g), and NNO(g). Consequently, the XES of H2CO(g), formamide(g), 1-nitrosamine(g), N-methylformamide(g), 1-nitrosoaziridine(g), and oxirane(g) are predicted with confidence.

Three-particle states and brightening of intervalley excitons in a doped MoS2 monolayer

Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC) are influenced by complex multi-particle excitonic states. Their theoretical analysis requires solving the many-body problem, which in most cases, is prohibitively complicated. In this work, we calculate the optical spectra by exact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoff approximation where the doping effects are accounted for via the Pauli blocking mechanism, modelled by a discretized mesh in the momentum space. The single-particle basis is extracted from the {\it ab initio} calculations. Obtained three-particle eigenstates and the corresponding transition dipole matrix elements are used to calculate the linear absorption spectra as a function of the doping level. Results for negatively doped MoS$_2$ monolayer (ML) are in an excellent quantitative agreement with the available experimental data, validating our approach. The results predict additional spectral features due to the intervalley exciton that is optically dark in an undoped ML but is brightened by the doping. Our approach can be applied to a plethora of other atomically thin semiconductors, where the doping induced brightening of the many-particle states is also anticipated.

Analysis of an Optical Lattice Methodology for Detection of Atomic Parity Nonconservation

We present an extension and a deepened analysis of a suggested experimental scheme for detecting atomic parity violation, previously published in Phys. Rev. A 2019, 100, 050101. The experimental concept is described in more detail and we compute new ab initio data necessary for assessing the plausibility of the approach. Original theoretical data for transition matrix elements on the electric dipole forbidden transition in caesium 6 s 2 S 1 / 2 – 5 d 2 D 3 / 2 are reported, as are a range of electric dipole matrix elements connected to the ground state 6s. The latter is used for an analysis of the wavelength-dependent light shift in Cs. A range of experimental details is presented, combined with a survey of realistic lasers parameters. These are adopted to project the feasibility of the scheme to eventually be capable of delivering data beyond the standard model of particle physics.

Atomistic analysis of radiative recombination rate, Stokes shift, and density of states in c-plane InGaN/GaN quantum wells

Recent experimental studies have revealed an unusual temperature dependence of the radiative recombination rate in polar InGaN/GaN quantum wells. We show, by direct atomistic evaluation of the radiative recombination rate, that the experimentally observed trend of an increasing rate with increasing temperature results from the population of energetically higher lying electron and hole states with dipole matrix elements larger than those of the band edge states relevant to low temperature studies. Given that the overall evolution of this recombination rate is tightly linked to the energetic distribution of localized states, we investigate the hole density of states and absorption spectra. Based on the calculated absorption spectra, Stokes shift energies are extracted for InGaN quantum wells with In contents ranging from 5% to 25%. Here, good agreement with experimental literature results is found. We provide also hole tail state characteristic energies as a function of the In content, a quantity that indicates the localization character of the ensemble of hole states and which serves often as a key component in modified continuum-based models to capture carrier localization effects in transport or optical gain calculations.

Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes

We have investigated the energies, magnetic dipole hyperfine structure constants (Ahyf) and electric dipole (E1) matrix elements of a number of low-lying states of triply ionized tin (Sn3+) by employing relativistic coupled-cluster theory. Contributions from the Breit interaction and lower-order quantum electrodynamic (QED) effects in the determination of the above quantities are also given explicitly. These higher-order relativistic effects are found to be important for the accurate evaluation of energies, while only QED contributions are seen to contribute significantly to the determination of Ahyf values. Our theoretical results for the energies are in agreement with one of the measurements but show significant differences for some states with another measurement. Reported Ahyf will be useful in guiding the measurements of hyperfine levels in the stable isotopes of Sn3+. The calculated E1 matrix elements are further used to estimate the oscillator strengths, transition probabilities and dipole polarizabilities (α) of many states. Large discrepancies between the present results and previous calculations of oscillator strengths and transition probabilities are observed among a number of states. The estimated α values will be useful for carrying out high precision measurements using the Sn3+ ion in future experiments.

Particle confined in modified ring-shaped potential

The spectrum of a particle confined in Hulthén plus ring-shaped potential is obtained by solving the time-independent Schrödinger equation numerically. The effect of potential parameters on various properties of the particle have been investigated in detail. The energy levels, radial matrix elements, oscillator strengths and polarizabilities of the particle have been found to show strong dependence on the confining potential parameters. The presence of the ring potential is found to appreciably alter the angular part of dipole matrix elements. Also, it is shown that the comparison theorem of Quantum Mechanics for energy eigenvalues for four different potentials, viz., Coulomb, Hulthén, Yukawa and Hulthén2 is independent of the presence of ring potential.

Inter and intra band impurity-related absorption in (In,Ga)N/GaN QW under composition, size and impurity effects

In this paper, we theoretically investigate the impacts of Internal well composition, size and impurity's position on the inter valence-conduction bands and intra conduction band optical absorption in GaN/(In,Ga)N/GaN hetero-structure. Based on the numerically finite element method (FEM), the impurity's related Schrödinger equation is solved for the finite potential barrier considering the dielectric constant and effective-mass mismatches between the well and its surrounding matrix. Our results show that the absorption is strongly governed by the dipole matrix element and initial and final implied states transition energies. For a fixed barrier width, the absorption spectra are found red-shifted (blue-shifted) with increasing the well width (In-concentration). It is also shown that the impurity's absorption phenomenon is more pronounced for the off-center case compared to the on-center one. We conclude that the proper control of these parameters is required to best understanding of the optical absorption for solar cell applications.

Layer and orbital interference effects in photoemission from transition metal dichalcogenides

In this work, we provide an effective model to evaluate the one-electron dipole matrix elements governing optical excitations and the photoemission process of single-layer (SL) and bilayer (BL) transition metal dichalcogenides. By utilizing a $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian, we calculate the photoemission intensity as observed in angle-resolved photoemission from the valence bands around the $\overline{K}$ valley of ${\mathrm{MoS}}_{2}$. In SL ${\mathrm{MoS}}_{2}$, we find a significant masking of intensity outside the first Brillouin zone, which originates from an in-plane interference effect between photoelectrons emitted from the Mo $d$ orbitals. In BL ${\mathrm{MoS}}_{2}$, an additional interlayer interference effect leads to a distinctive modulation of intensity with photon energy. Finally, we use the semiconductor Bloch equations to model the optical excitation in a time- and angle-resolved pump-probe photoemission experiment. We find that the momentum dependence of an optically excited population in the conduction band leads to an observable dichroism in both SL and BL ${\mathrm{MoS}}_{2}$.

Determination of oscillator strengths by using magic wavelengths of the 5s1/2 → 5p1/2,3/2 transitions for Rb

The energy levels and electric dipole matrix elements of Rb atom are calculated using the relativistic configuration interaction with core polarization method. These energy levels and matrix elements are further employed to calculate the electric dipole static and dynamic polarizabilities of the 5s1/2, 5p1/2 and 5p3/2 states. Finally, the magic wavelengths of the 5s1/2 → 5p1/2,3/2 transitions are obtained for linearly and circularly polarized light. We suggest that the accurate measurement on the magic wavelengths for circularly polarized light could be used to determine the high-precise oscillator strengths of the 5p1/2 → 5d3/2, 6d3/2, 7s1/2, 8s1/2 and 5p3/2 → 5d3/2, 5d5/2, 6d5/2, 7s1/2, 8s1/2 transitions.

Simulation of a THz radiation source on AlGaAs/GaAs superlattices

We report on the results of simulations of the carrier transport processes in THz radiation sources. The current-voltage characteristic, dipole matrix elements and LO-phonon relaxation time were obtained using the Ensemble Monte Carlo method, the shooting and effective mass methods. The electron-longitudinal phonon interaction assumed as a dominant mechanism of the carrier scattering for the current-voltage characteristic. The weakly coupled AlGaAs/GaAs superlattices considered for simulations.

Towards a complete next-to-logarithmic description of forward exclusive diffractive dijet electroproduction at HERA: Real corrections

We studied the $ep\rightarrow ep+2jets$ diffractive cross section with ZEUS phase space. Neglecting the $t$-channel momentum in the Born and gluon dipole impact factors, we calculated the corresponding contributions to the cross section differential in $\beta=\frac{Q^{2}}{Q^{2}+M_{2jets}^{2}}$ and the angle $\phi$ between the leptonic and hadronic planes. The gluon dipole contribution was obtained in the exclusive $k_{t}$-algorithm with the exclusive cut $y_{cut}=0.15$ in the small $y_{cut}$ approximation. In the collinear approximation we canceled singularities between real and virtual contributions to the $q\bar{q}$ dipole configuration, keeping the exact $y_{cut}$ dependency. We used the Golec-Biernat - W\"usthoff (GBW) parametrization for the dipole matrix element and linearized the double dipole contributions. The results give roughly $\frac{1}{2}$ of the observed cross section for small $\beta$ and coincides with it for large $\beta.$

Terahertz intersubband transitions in GaAsBi/AlGaAs single quantum well heterostructure

Abstract GaAsBi/AlGaAs single quantum well conduction band structure, energy levels, and their corresponding wavefunctions have been calculated by solving the Schrodinger equation. The influences of the heterostructure parameters on the intersubband transition (ISBT) frequency within the terahertz (THz) domain have been investigated. The results show that the quantum well width has a great impact on the THz ISBT frequency. In particular, an ISBT with a frequency of 2.611 THz (10.80 meV) has been obtained for specifically optimized parameters. The study of the intersubband optical absorption coefficient (OAC) was centered in the frequency band of 2–14 THz (~8–58 meV), therefore the corresponding results are useful for the optimization of THz detectors. Correspondingly, by changing the thickness of the active layer the number of the OAC peaks has been tuned. The dipole matrix element and the Fermi occupation function have been also studied in detail. Furthermore, the influences coming from the incidence angle on the OAC intensity were numerically investigated. The obtained results could be beneficial for the design and the optimization of devices operating in the THz frequency band.

Phase invariance of the semiconductor Bloch equations

We investigate the gauge invariance of the semiconductor Bloch equations (SBEs) in solid high-order harmonic generation (HHG). It is found that the gauge dependence of the SBEs can be attributed to the absence of Berry connection terms in the SBEs in previous studies. When the Berry connection terms are considered, the gauge invariance of the SBEs can be naturally preserved under an arbitrary global phase transformation. To satisfy the demand of the continuity of transition dipole matrix elements in one-dimensional calculations, we propose a gauge that is easy to implement numerically. Finally, the saddle point analysis shows that Berry connections can influence many properties of HHG, such as ellipticity dependence and even harmonic generation. This work uncovers the importance of the Berry connection terms that have been neglected for a long time in simulations of solid HHG. © 2019 American Physical Society.

Oscillator strength and carrier dynamics in type I and inverted type I spherical core/ shell nanostructures under external laser field

Abstract For the first time, the effect of laser on the donor impurity states in spherical nano core/shell systems is examined theoretically by variation technique. In this work, a step like laser dressed confinement potential is employed to evolve the donor dynamics in two different spherical core/shell quantum structures namely (a) Type I GaAs/Al0.3Ga0.7As core shell nanostructure (CSN) and (b) Inverted Type I Al0.3Ga0.7As/GaAs CSN. Donor binding energy (BE) is calculated for various laser dressing parameter ( α 0) for various impurity locations (Ri) by varying the dimensions of the systems. Effect of laser on sub-level energy (E0), oscillator strength (P10), transition energy (E10) and the magnitude of dipole matrix element ( | M 10 | ) of the systems are also determined. The diverse behavior of type I and inverted type I CSNs are analyzed. It is witnessed that in type I the carrier is highly confined whereas inverted type I favors tunneling. This study will help in understanding the influence of laser field on donor impurity in CSNs and its application towards optical devices.

A Wannier orbital based method for resonant inelastic x-ray scattering simulation

We report an algorithm for simulating oxygen K-edge RIXS for weakly correlated systems, using maximally localized Wannier functions as the basis set. The N-electron wavefunctions are formulated using single Slater determinants, and many-body effects are treated explicitly at the dipole matrix element level. The simulated results for oxygen K-edge RIXS from solid state Li2CO3 matches well with the experimental data. Aside from being efficient and reasonably accurate, this algorithm also shows potential to extend to more complex RIXS problems.