Moment Matrix Elements Research Articles

A Spectroscopic Investigation of the Lowest Electronic States of the I+ 2 Cation as a Candidate for Detecting the Time Variation of Fundamental Constants

The four lowest Ω substates (X2Π3/2,g, X2Π1/2,g, A2Π3/2,u and A2Π1/2,u) of the I+ 2 cation have been studied by high-precision ab initio calculations in comparison with experimental high-resolution absorption spectra. The potential energy curves were calculated using the multi-reference configuration interaction (MRCI) method and Dirac method, respectively. Rovibrational levels of these electronic states were derived by solving the radial Schrödinger rovibrational equation. Molecular constants were obtained in fitting energy levels to a spectroscopic model. Using the fit spectroscopic constants and newly calculated transition dipole moment matrix elements, line strengths of vibronic bands in the A2Π3/2,u- X2Π3/2,g system, as well as Einstein A coefficients for 45 of these bands with ν′ = 11−19 and ν′′ = 1−5, have been derived. The Einstein A coefficients were used to compute radiative lifetimes of the ν′ = 11−19 vibrational levels of the A2Π3/2,u state. Enhancement factors for detecting the variation of the fine-structure constant (α) and the proton-to-electron mass ratio(µ) using transitions between nearly degenerate rovibronic levels of these low-lying states have been calculated.

High harmonic generations triggered by the intense laser field in GaAs/AlxGa1-xAs honeycomb quantum well wires

Under constant electric and magnetic fields, the potential profile of the honeycomb quantum well wire (HQWW) is studied for varying intense laser fields to trigger and optimize high harmonics (nonlinear optical rectification, second and third harmonic generation coefficients). The finite element method has been used to simulate wavefunctions and their corresponding energy levels under effective mass approximation. We have shown that an intense laser field reshapes the potential profile of the HQWW, and this results in maximum and minimum for dipole moment matrix elements and energy differences. The increase and decrease of energy differences create blue and red shifts in the optical spectrum. In the end, we have calculated nonlinear optical rectification as 11.1x10−5 m/V. The second harmonic generation coefficient is found as 18.4x10−7 m/V which is three times and a lot bigger than bulk GaAs and GaAs/AlGaAs superlattice. The third harmonic generation coefficient is calculated as 6.2x10−15 m2/V2. As a conclusion, we have shown that HQWW can be used in harmonic generation-based optical devices.

The effect of structure parameters and static electric field on the nonlinear optical properties of triple InGaAs/GaAs quantum well

Optical properties of InxGa1-xAs/GaAs triple QW are studied for different quantum well thicknesses and external electric fields. The effective mass approximation is used to calculate the band alignment of the structure. The finite difference method (FDM) is applied to solve the 1D- Schrödinger equation. Intersubband energies and the total optical absorption coefficients (TOACs) and total relative refractive index changes (RRICs) are numerically calculated under the applied external electric field. The structure parameters and applied electric field cause the separation of the energy levels and variation of the dipole moment matrix elements. These separations are responsible for the resonant peak shifts. It is shown that the varied structure parameters and external electric field cause red or blue shifts in the resonant peak position of TOAC and RRIC coefficients.

Intense terahertz laser field induced electro-magneto-donor impurity associated photoionization cross-section in Gaussian quantum wires

Using expressions derived within the compact density matrix approach, the peaks of optical absorption and the changes of refractive index of a hydrogenic impurity in a GaAs/GaAlAs Gaussian quantum well wire are calculated taking into account the influence of static electric, magnetic and intense laser fields. The photoionization cross section, with normalized photon energy, is computed for different values of static electric field, magnetic field, and laser dressing parameter. The dipole moment matrix elements and the transition energy between ground and first excited state energy levels are computed as functions of quantum wire width and confinement potential depth, with and without external perturbations. Donor impurity binding energy is investigated in presence of the aforementioned electromagnetic probes, using parabolic band and effective mass approximations. The results show that the absorption coefficients depend on the transition energy difference between initial and final states involved as well as on the corresponding polarization response via dipole matrix elements. Discussed optical properties are field-sensitive and they can be tuned within the desired energy ranges using these external perturbations. • Peaks of optical absorption and changes of refractive index of a hydrogenic impurity in a GaAs/GaAlAs Gaussian quantum well wire are calculated. • They have been computed taking into account the influence of static electric, magnetic and intense laser fields. • Photoionization cross section, with normalized photon energy, is computed. • Donor impurity binding energy is investigated in the presence of aforementioned electromagnetic-probes, using parabolic band and effective mass approximations. • Discussed optical properties are field-sensitive and they can be tuned within the desired energy ranges using these external perturbations.

Linear and nonlinear optical properties of semi-elliptical InAs quantum dots: Effects of wetting layer thickness and electric field

In this paper, we have studied the optical properties of semi-elliptical InAs quantum dots (QDs) embedded in GaAs. Under effective mass approximation, the finite element method has been used to obtain wavefunctions and corresponding energy eigenvalues in three-dimension. It has been shown that the wetting layer (WL) thickness has a small effect on the (1-2) transition, but is more effective on the dipole moment matrix element (DMME) of the (2-3) and (1-3) transitions. It is seen that the linear absorption coefficients of the (2-3) and (1-3) transition reach the maximum at 4 A WL thickness. After that, we set the WL thickness to 4 A and we studied the effect of the electric field applied through the axial direction. The same as the WL effect, the electric field has caused a minor change in DMME of the (1-2) transition but it makes DMME of the (2-3) and (1-3) transitions stronger which results in very high linear absorption coefficients. For 20kV/cm electric field intensity, the linear absorption coefficient reaches the maximum for the (2-3) and (1-3) transition.

Intense laser field effect on the nonlinear optical properties of triple quantum wells consisting of parabolic and inverse-parabolic quantum wells

The nonlinear optical rectification, the second harmonic generation coefficient, and the third harmonic generation coefficient in parabolic-inverse parabolic-parabolic quantum wells (PIPPQWs) and inverse parabolic-parabolic-inverse parabolic quantum wells (IPPIPQWs) are calculated varying the intense laser field (ILF) parameter (). The modifications of the dipole moment matrix elements and the energy levels are depending on the potential shape. The results show that the ILF intensity exerts an active influence on the profile, height, and width of the confinement potential of both PIPPQW and IPPIPQW. The potential profile of IPPIPQW has been affected otherwise than PIPPQW for different ILF intensities. The nonlinear optical rectification, the second harmonic generation, and the third harmonic generation coefficients of PIPPQW and IPPIPQW could be altered in the energy range and the size of the resonance peak by rising the ILF intensity. By changing the parameter, it is conceivable to organize red or blue shift at the resonance peak positions of the nonlinear optical rectification, the second harmonic generation, and the third harmonic generation coefficients. The shift of the nonlinear optical rectification coefficient occurs when the difference between the ground and the second energy levels changes. According to the parameters used here, while for PIPPQW the spectrum of the resonance peak of the nonlinear optical rectification displays a blue shift with increasing ILF, this spectrum displays a red shift for IPPIPQW. The consequences can be valued in investigating new ways of changing the optical and electronic properties of semiconductor quantum wells.

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Hydrostatic pressure, temperature and Al-concentration effects on optical rectification of spherical quantum dots under inversely quadratic Hellmann potential

Effects of hydrostatic pressure, temperature and Al-concentration on optical rectification (OR) of GaAs/Ga1−xAlxAs spherical quantum dots (QDs) under an inverse of a quadratic Hellmann potential are discussed in detail. The solution of Schrödinger equation is adopting Nikiforov–Uvarov (NU) method. Using the compact density-matrix approach and iterative method, an analytical expression of the OR coefficient can be obtained. The result of the calculation illuminates that hydrostatic pressure, temperature, Al-concentration and the radius of the QDs can make an impact on the energy level interval, dipole moment matrix elements, effective mass and other factors, so that the peak value of OR coefficient and resonance peak changing under the action of these factors. Furthermore, the potential height have a bearing on the OR coefficient.

Riemannian geometry of resonant optical responses

The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has been challenging to relate quantum geometry to resonant optical responses. The main obstacle is that optical transitions involve a pair of states, while existing geometrical properties are defined for a single state. As a result, a concrete geometric understanding of optical responses has so far been limited to two-level systems, where the Hilbert space is completely determined by a single state and its orthogonal complement. Here, we construct a general theory of Riemannian geometry for resonant optical processes by identifying transition dipole moment matrix elements as tangent vectors. This theory applies to arbitrarily high-order responses, suggesting that optical responses can generally be thought of as manifestations of the Riemannian geometry of quantum states. We use our theory to show that third-order photovoltaic Hall effects are related to the Riemann curvature tensor and demonstrate an experimentally accessible regime where they dominate the response.

Line lists for the b1Σ+-X3Σ− and a1Δ-X3Σ− transitions of SO

SO is found in many astronomical sources such as the atmospheres of Io and Venus. In order to create more complete line lists, we fit spectroscopic data on SO from the literature using PGOPHER. The fits covered v = 0 to v = 6 for the X3Σ−state, v = 0–5 for the a1Δ state and v = 0–2 for b1Σ+ state. LeRoy's RKR program was used to produce pointwise potential energy curves. High level ab initio calculations, including spin-orbit coupling, were carried out to obtain the electric transition dipole moment functions for the nominally forbidden b1Σ+-X3Σ−and a1Δ-X3Σ−transitions. The RKR potentials and transition dipole moment points were input into LeRoy's LEVEL program to calculate the transition dipole matrix elements for all possible b-X and a-X bands. For the b1Σ+-X3Σ−transition, the electric and magnetic transition dipole matrix elements were scaled using the experimental values obtained by Setzer et al. [J Mol Spectrosc 1999;198:163–174] for the 0–0 band. The transition dipole moment matrix elements were used in PGOPHER to produce our line lists for all possible bands of the b1Σ+-X3Σ−and a1Δ-X3Σ−transitions.

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Estimations of FH···X hydrogen bond energies from IR intensities: Iogansen's rule revisited.

In this work the possibility of using the IR intensity of the stretching vibration νs of proton donor group for estimation of hydrogen bond strength was investigated. For a set of complexes with FH···X (X = F, N, O) hydrogen bonds in the wide range of energies (0.1-49.2 kcal/mol) vibrational frequencies νs and their intensities A were calculated (CCSD at complete basis set limit). The validity of the previously proposed linear proportionality between the intensification of the stretching vibration νs in IR spectra and hydrogen bond enthalpy -ΔH = 12.2 (A. V. Iogansen, Spectrochimica Acta A 1999) was examined. It is shown that for a range of similar hydrogen bond types with complexation energies ∆E <15 kcal/mol the ∆E( ) function remains similar to that proposed in the Iogansen's work, while upon strengthening this dependency becomes significantly nonlinear. We examined two other parameters ( and ) related to IR intensity as descriptors of hydrogen bond strength which are proportional to transition dipole moment matrix element and mass-independent dipole moment derivative. It was found that the dependency ∆E( ) stays linear in the whole studied range of complexation energies and it can be used for evaluation of ∆E from infrared spectral data with the accuracy about 2 kcal/mol. The mass-independent product is an appropriate descriptor for sets of complexes with various hydrogen bond types. Simple equations proposed in this work can be used for estimations of hydrogen bond strength in various systems, where experimental thermodynamic methods or direct calculations are difficult or even impossible.

Pyramidal core-shell quantum dot under applied electric and magnetic fields

We have theoretically investigated the electronic states in a core/shell pyramidal quantum dot with GaAs core embedded in AlGaAs matrix. This system has a quite similar recent experimental realization through a cone/shell structure [Phys. Status Solidi-RRL 13, 1800245 (2018)]. The research has been performed within the effective mass approximation taking into account position-dependent effective masses and the presence of external electric and magnetic fields. For the numerical solution of the resulting three-dimensional partial differential equation we have used a finite element method. A detailed study of the conduction band states wave functions and their associated energy levels is presented, with the analysis of the effect of the geometry and the external probes. The calculation of the non-permanent electric polarization via the off-diagonal intraband dipole moment matrix elements allows to consider the related optical response by evaluating the coefficients of light absorption and relative refractive index changes, under different applied magnetic field configurations.

The effect of intense laser field on the nonlinear optical features in asymmetric multiple step and inverse V-shaped multiple step quantum wells

For asymmetric multiple step quantum wells (AMS QWs) and asymmetric inverse V-shaped multiple step quantum wells (AIVSMS QWs), the nonlinear optical features, such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) coefficients are analyzed as according on the intense laser field (ILF). The found consequences indicate that the ILF parameter confirms a vital influence on the shape and height of the confined potential profile of both AMS QWs and AIVSMS QWs, and the alterations of the dipole moment matrix elements and the energy levels are adhered on the profile of the confined potential. According to the results, the potential profile and height of the AIVSMS QWs compared to AMS QWs were affected differently from ILF intensity. These results indicate that NOR, SHG, and THG coefficient of AMS QWs and AIVSMS QWs may be regulated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. By varying the ILF parameter, it is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients. Our results can be valuable in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.Highlights•The electro-optical properties of AMS QWs and AIVSMS QWs vary by increasing ILF.•The change of AIVSMS QWs compared to AMS QWs is more affected by ILF.•NOR, SHG, and THG coefficients change with rising ILF.•RP spectrums show blue or red shifts as according to ILF.

Depending on the intense laser field of the nonlinear optical rectification, second and third harmonic generation in asymmetric parabolic-step and inverse parabolic-step quantum wells

The nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) coefficients in asymmetric parabolic-step quantum wells (APSQW) and asymmetric inverse parabolic-step quantum wells (AIPSQW) are considered as depending on the intense laser field (ILF). The found consequences indicate that ILF parameter approves a dynamic influence on the shape, width and height of the confined potential profile of both APSQW and AIPSQW, and the alterations of the dipole moment matrix elements and the energy levels (ELs) are followed on the profile of the confined potential. The potential profile and height of the AIPSQW compared to APSQW were affected differently from ILF intensity. With and without the ILF, the ELs in the APSQW are smaller than in the AIPSQW. These results designate that NOR, SHG, and THG coefficient of APSQW and AIPSQW may be controlled in a chosen energy range and the magnitude of the resonance peak (RP) by increasing ILF value. By modifying the ILF parameter, it is possible to classify red or blue shifts at the RP positions of the NOR, SHG and THG coefficients. We hope that our results will offer significant development of optical devices in many potential device applications for the appropriate selection of ILF values.

Sub-Doppler Resonances Caused by Rabi Oscillations on Atomic Transitions in Thin Gas Cells

Excitation of atoms from the ground quantum level to a metastable state by traveling monochromatic radiation in a thin gas cell, the internal thickness of which is much smaller than its radius, is studied theoretically. Sub-Doppler resonances are detected and analyzed that arise in the population of a metastable atomic level due to light-induced Rabi oscillations on a given optical transition and specific features of transit-time relaxation of atoms in a considered cell with a rarified gas upon scanning the radiation frequency. Such nontrivial resonances can be recorded in fluorescence of atoms with the help of an additional probe light beam. A method is proposed for a direct measurement of the Rabi frequency from spectral intervals between detected sub-Doppler resonances. The results obtained can be applied in atomic spectroscopy for the precision determination of components of dipole moment matrix elements, as well as for the Einstein coefficients and oscillator strengths related to these components, for quantum transitions between the ground and metastable levels of atoms.

Nonlinear Optical Rectification, Second and Third Harmonic Generations in Square-Step and Graded-Step Quantum Wells under Intense Laser Field

For square-step quantum wells (SSQWs) and graded-step quantum wells (GSQWs), the nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG) coefficients under an intense laser field (ILF) are analyzed. The found results indicate that ILF can ensure a vital influence on the shape and height of the confined potential profile of both SSQWs and GSQWs, and alterations of the dipole moment matrix elements and the energy levels are adhered on the profile of the confined potential. According to the results, the potential profile and height of the GSQWs are affected more significantly by ILF intensity compared to SSQWs. These results indicate that NOR, SHG and THG coefficients of SSQWs and GSQWs may be calibrated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. It is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients by varying the ILF parameter. Our results can be useful in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.

Linear and nonlinear optical properties of asymmetric triple quantum wells under intense laser field

For asymmetric triple quantum wells (ATQW) the linear and nonlinear optical absorption coefficient (OAC) and the optical refractive index change (ORIC) are analyzed according to the intense laser field (ILF). The obtained results show that the ILF parameter () has an important effect on the shape and height of the confined potential profile of the ATQW, and alterations in the energy levels and the dipole moment matrix elements depend on the shape of the confinement potential. For = 10 nm (according to the parameters used in this study), ATQW turns into an asymmetric wider double confinement potential. As a consequence of the energy difference between the energy states, the absorption spectrum of (1–2) and (1–3) optical transitions initially shows a redshift (up to = 6 nm and = 4 nm, respectively) and then indicates a blueshift by increasing the ILF. For the (2–3) transition, the optical absorption spectrum continuously shows a blueshift and displays an oncoming shift toward the higher energies. Thus, the linear and nonlinear OAC and ORIC may be adjusted by modifying the ILF parameter. Our results are of use in the investigation into new ways of manipulating the optoelectronic properties of triple quantum well devices.Highlights• The electronic and optical properties of ATQW vary with increasing ILF value.• The effect of ILF on the quantum well (QW) differs depending on the shape of the QW.• OAC and ORIC change with rising ILF.• The absorption spectrum shows blueshifts or redshifts depending on the ILF.

Sin2 θW estimate and neutrino electromagnetic properties from low-energy solar data

We report new values of weak-mixing angle (), neutrino effective magnetic moment () and the charge radii using the lowest energy (to-date) solar neutrino data of pp, 7Be and pep spectra from phase I and phase II runs of Borexino experiment. The best-fit values obtained are at 1σ with a precision comparable to that of the combined reactor and accelerator very short-baseline experiments and at 90% C.L. with a factor of 3 improvement over the previous bounds. This leads to the improvement of constraints on all the related magnetic moment matrix elements for the Majorana-type and Dirac-type neutrinos in mass basis and also stronger bounds on the magnetic moment flavor states. The bounds on the neutrino charge radii obtained are cm2 cm2 and cm2 cm2 at 90% C.L.

Zero-Field Splitting Parameters from Four-Component Relativistic Methods.

We report an approach for determination of zero-field splitting parameters from four-component relativistic calculations. Our approach involves neither perturbative treatment of spin-orbit interaction nor truncation of the spin-orbit coupled states. We make use of a multi-state implementation of relativistic complete active space perturbation theory (CASPT2), partially contracted N-electron valence perturbation theory (NEVPT2), and multi-reference configuration interaction theory (MRCI), all with the fully internally contracted ansatz. A mapping is performed from the Dirac Hamiltonian to the pseudospin Hamiltonian, using correlated energies and the magnetic moment matrix elements of the reference wave functions. Direct spin-spin coupling is naturally included through the full 2-electron Breit interaction. Benchmark calculations on chalcogen diatomics and pseudotetrahedral cobalt(II) complexes show accuracy comparable to the commonly used state-interaction with spin-orbit (SI-SO) approach, while tests on a uranium(III) single-ion magnet suggest that for actinide complexes the strengths of our approach through the more robust treatment of spin-orbit effects and the avoidance of state truncation are of greater importance.