Dipole Matrix Elements Research Articles

In plane magnetic field and intense laser field effects on second harmonic generation of asymmetric AlGaAs/GaAs double quantum well

The optical properties for nano-structured semiconductor systems are of great importance nowadays, due to its possible implementation for the design of efficient optoelectronic devices. It is also well known that external fields can modify the electronic structure, and induce changes the optical properties as well. In particular the asymmetric double quantum well structures are of paramount importance because its wide range on possible configurations and also because are experimentally feasible and well controlled, particularly AlxGa1-xAs/GaAs heterostructures. In this work we report a systematic study on second harmonic generation (SHG) for an asymmetric AlxGa1-xAs/GaAs double quantum well as a function of non-resonant intense laser field and in-plane magnetic field effect. We analyze the energy level behavior as well as the dipole matrix elements as a function of the above mentioned factors that are important for the SHG. We report a particular configuration that optimize the SHG peak, with and without intense laser field effect, as well as magnetic fields, that also tune the SHG.

Magnetic Sublevel Independent Magic and Tune-Out Wavelengths of the Alkaline-Earth Ions

Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths (λTs). Similarly, differential light shift in a transition vanishes at the magic wavelengths (λmagics). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λmagic. Similarly, the λT values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole (α) values of only one state whereas the λmagic values require evaluation of α values for two states. However, both the λmagic and λT values depend on angular momenta and their magnetic components (M) of states. Here, we report the λmagic and λT values of many S1/2 and D3/2,5/2 states, and transitions among these states of the Mg+, Ca+, Sr+ and Ba+ ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations.

Line lists for X3Σ− and a1Δ vibration-rotation bands of SO

SO is found in several astronomical sources such as the atmospheres of Io and Venus. To complete our work on SO line lists, we used our previous fits for v = 0 to v = 6 for the X3Σ- state and v = 0–5 for the a1Δ state [JQSRT 272, 107772 (2021)] for line positions, and high-level ab initio calculations of electric dipole moments for line strengths for the vibration-rotation bands. LeRoy's RKR program was used to produce pointwise potential energy curves. N- and v-dependent dipole matrix elements were produced with LeRoy's LEVEL program and the final line lists were made with Western's PGOPHER program. All possible vibrational bands were calculated, and the line strengths included the Herman-Wallis effect caused by vibration-rotation interaction.

Erratum to “InGaN Quantum Dot Superlattices as Ratchet Band Solar Cells” [Mar 22 474-482

After publication of the original article [4], we found a unit-conversion error in the calculations of absorption cross sections. None of the equations in the original article are incorrect, but our numerical implementation of the dipole matrix elements of (2) made their calculated values too large by a factor of 25.6. The absorption cross sections $\sigma$ depend on the matrix element squared, so they are all overstated by a factor of 656. The corrected Fig. 4 is changed only in the vertical-axis labels.

Photoionization of helium atom embedded in classical non-ideal plasma at high non-relativistic photon energies

The effects of the non-ideality (NI) of classical plasmas on the photoionization of helium atoms at high non-relativistic photon energies are investigated within the framework of the dipole approximation. Screened interaction in non-ideal plasmas is represented by an effective potential, deduced from a solution of Bogolyubov's hierarchy equations on discarding the effects of quantum degeneracy. A highly correlated wave function consisting of 715 terms for the ground state of helium has been used to evaluate the dipole matrix element. Changes in the asymptotic cross sections of single, double, and total photoionizations due to varying NI of plasmas have been investigated in detail. Particular emphasis is made to study the changes in the asymptotic ratio of the double-to-single photoionization cross section caused by the variation of non-ideality parameter in a wide range. It is found that increasing plasma NI makes the feasibility of occurrence of double photoionization to broaden.

On the importance of electron–electron and electron–phonon scatterings and energy renormalizations during carrier relaxation in monolayer transition-metal dichalcogenides

An ab initio based fully microscopic many-body approach is used to study the carrier relaxation dynamics in monolayer transition-metal dichalcogenides. Bandstructures and wavefunctions as well as phonon energies and coupling matrix elements are calculated using density functional theory. The resulting dipole and Coulomb matrix elements are implemented in the Dirac–Bloch equations to calculate carrier–carrier and carrier–phonon scatterings throughout the whole Brillouin zone (BZ). It is shown that carrier scatterings lead to a relaxation into hot quasi-Fermi distributions on a single femtosecond timescale. Carrier cool down and inter-valley transitions are mediated by phonon scatterings on a picosecond timescale. Strong, density-dependent energy renormalizations are shown to be valley-dependent. For MoTe2, MoSe2 and MoS2 the change of energies with occupation is found to be about 50% stronger in the Σ and Λ side valleys than in the K and K′ valleys. However, for realistic carrier densities, the materials always maintain their direct bandgap at the K points of the BZ.

Interpretation of enhanced electric dipole transitions in Br73 by the reflection-asymmetric triaxial particle rotor model

The recently observed positive and negative parity bands in $^{73}\mathrm{Br}$ are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra as well as the electric transition probabilities $B(E1), B(E2)$, and the ratio $B(E1)/B(E2)$ are well reproduced by the theoretical calculations. It is found that the enhanced interband $E1$ transitions between the opposite-parity bands, a crucial evidence for octupole correlations, are mainly contributed by the intrinsic single-particle electric dipole matrix elements.

Photoelectron spectra of argon in circularly polarized pulses studied by atom-Volkov strong-field approximation

We studied the above-threshold ionization (ATI) spectra of argon in circularly polarized pulse by the atom-Volkov strong-field approximation (SFA). A dip appears in the spectra due to the presence of a zero in the dipole matrix element, corresponding to a transition from the ground state to the L = 2 continuum at electron kinetic energy ∼30.6 eV. No such dip appears when the time-dependent Schrödinger equation (TDSE) is used instead, because the transition amplitude in SFA is the first-order term in the S-matrix series while TDSE contains all orders. In contrast, the effect of Cooper minimum shows up in high-order harmonic generations, which is an inverse process of photoionization where the recombination transition is first-order. We examine several sets of pulse parameters and found that when the SFA validity conditions are satisfied, the atom-Volkov SFA generates better ATI spectra than the simple SFA.

Measurement of the Rb87 D -line vector tune-out wavelength

We report a precision measurement of a tune-out wavelength for 87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using $\sigma_-$ polarized light with an an estimated purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.

Rydberg energies and transition probabilities of Li I for np\u2013ms (m\u2009\u2264\u20095) transitions

BackgroundMathematical modeling provides grounds for understanding scientific systems theoretically. It serves as a guide for experimentalists in determining directions of investigation. Recently, the Covid-19 pandemic has caused disturbances in almost every walk of life. Scientists have played their role and have continued research on the effects of the pandemic. Various mathematical models have been used in different branches of science (Djilali et al. in Phys Scr 96 12 124016, 2021; Math Biosci Eng 18(6):8245–8256, 2021; Zeb et al. in Alex Eng J 61(7):5649–5665). Well-established mathematical models give results close to those obtained by experiments. The Weakest Bound Electron Potential Model is one such model, which explains hydrogen-like atoms and ions. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies.ResultsThis paper presents the energies of the Rydberg series, 2s2ns, and 2s2np of Li I, calculated using WBEPM. The energies are used to calculate transition probabilities from np to 2s, 3s, 4s, and 5s levels. The transition probabilities are compared with corresponding values in published data where available. The agreement with known values is good; most of the transition probabilities calculated in this work are new. A computer program was developed to find the value of the dipole matrix element. The calculations were further verified by calculating the lifetimes of some low-lying levels.ConclusionsFour series of Li I have been studied, and energies of the Rydberg levels in the series were calculated. The energies then are used to calculate transition probabilities from np to ms transitions, where m = 2, 3, 4, & 5 and n = 1–15. The results are compared where available. An excellent agreement with previously published data shows the reliability of calculations. Most of the transition probabilities are new.

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

The aim of this article is to discuss the hydrostatic pressure, temperature and Al-concentration effects on the optical rectification(OR) of GaAs/Ga1−xAlxAs spherical quantum dots(QDs) under a potential model called inversely quadratic Hellmann(IQH) plus inversely quadratic Kratzer(IQK) potential. The solution of Schrödinger equation is adopting the formula method. Using the density matrix theory and iterative method, the analytical expression of the OR coefficient is deduced. The results show that these external factors and structural parameters, such as the radius of the QDs and the depth of potential can affect the dipole matrix elements, energy level interval and effective mass of electrons, so that these parameters will affect the variation trend of the OR coefficient.

Theoretical study of electronic and optical properties in doped quantum structures with Razavy confining potential: effects of external fields

We investigate the energy states of confined electrons in doped quantum structures with Razavy-like confining potentials. The theoretical investigation is performed within the effective mass and parabolic band approximations, including the influence of externally applied electric and magnetic fields. First, we analyze the case of a Razavy quantum well and determine its conduction subband spectrum, focusing on the lowest energy levels and their probability densities. These properties have been numerically determined by self-consistently solving the coupled system of Schrödinger, Poisson, and charge neutrality equations. Doping is introduced via an on-center $$\delta$$ -like layer. In order to evaluate the associated total (linear plus nonlinear) optical absorption coefficient (TOAC), we have calculated the corresponding diagonal and off-diagonal electric dipole matrix elements, the main energy separation, and the occupancy ratio which are the main factors governing the variation in this optical response. A detailed discussion is given about the influence of doping concentration as well as electric and magnetic fields, which can produce shifts in the light absorption signal, toward either lower or higher frequencies. As an extension of the self-consistent method to a two-dimensional problem, the energy states of quantum wire system of circular cross section, with internal doping and Razavy potential, have been calculated. The response of eigenvalues, self-consistent potentials and electron densities is studied with the variation in $$\delta$$ -doping layer width and of the donor density. Finally, the origin of Friedel-like oscillations, that arise in the density profile, generated by the occupation of internal and surface electronic states has been explained.

Giant Optical Oscillator Strengths in Perturbed Hexagonal Germanium

By means of ab initio calculations we demonstrate that perturbed hexagonal germanium is a superior material for active optoelectronic devices in the infrared spectral region. Perfect lonsdaleite germanium is a pseudodirect semiconductor, with a direct fundamental band gap but almost vanishing optical transitions. Perturbing the system by replacing a germanium atom with a silicon atom in the primitive cell increases the oscillator strength at the onset gap by orders of magnitude, with a concurrent blue shift of the transition energies. This effect is mainly due to the increased s character of the lowest conduction band because of the perturbation‐induced wave function mixing. A structural distortion of pure lonsdaleite Ge can enhance as well optical oscillator strengths, but their magnitude significantly depends on the specific details of the resulting atomic geometry. In particular, moderate tensile uniaxial strain can induce an order inversion of the two lowest conduction bands, leading to an extremely efficient enhancement of the dipole matrix elements at the minimum gap. In general, chemical and/or structural perturbations are shown to make lonsdaleite germanium a suitable material for light emitting devices.

Orbital−energy splitting in Ruddlesden−Popper layered halide perovskites for tunable optoelectronic properties

The electronic orbital characteristics at the band edges play an important role in determining the electrical, optical and defect properties of perovskite photovoltaic materials. It is highly desirable to establish the relationship between the underlying atomic orbitals and the optoelectronic properties as a guide to maximize the photovoltaic performance. Here, using first-principles calculations and taking Ruddlesden-Popper (RP) phase layered perovskites Cs n +1 Ge n I n +1 Cl 2n as examples, we demonstrate how to rationally optimize the optoelectronic properties (e.g., band gap, transition dipole matrix elements, carrier effective masses, bandwidth) through a simple band structure parameter. Our results show that reducing the splitting energy |Δ c | between the in-plane p x , y and out-of-plane p z orbitals at the conduction band minimum (CBM) can effectively reduce the band gap and carrier effective masses while greatly improving the optical absorption in the visible region. Thereby, the orbital-property relationship with Δ c is well established through biaxial compressive strain. Finally, it is shown that this approach can be reasonably extended to several other non-cubic halide perovskites with similar p orbitals characteristics at the conduction band edge. Therefore, we believe that our proposed orbital engineering approach will provide atomic-level guidance for understanding the performance limits of layered perovskite solar cells. • Orbital−energy splitting in Ruddlesden−Popper layered halide perovskites. • Optimizing the optoelectronic properties through a simple band structure parameter. • Reducing the splitting energy .|Δ c | can effectively tune the optoelectronic properties.

Microscopic theory for the incoherent resonant and coherent off-resonant optical response of tellurium

An $\mathit{ab}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathit{initio}$-based fully microscopic approach is applied to study the nonlinear optical response of bulk tellurium. The structural and electronic properties are calculated from first principles using the shLDA-1/2 method within density functional theory. The resulting band structure and dipole matrix elements serve as input for the quantum mechanical evaluation of the anisotropic linear optical absorption spectra, yielding results in excellent agreement with published experimental data. Assuming quasiequilibrium carrier distributions in the conduction and valence bands, absorption/gain and spontaneous emission spectra are computed from the semiconductor Bloch and luminescence equations. For ultrafast intense off-resonant excitation, the generation of high harmonics is evaluated and the emission spectra are calculated for samples of different thicknesses.

Reversibly Tuning the Optical Properties of Defective Transition‐Metal Dichalcogenide Monolayers

Potential applications of monolayer of transition metal dichalcogenides (TMDs) in optoelectronic and flexible devices are under heavy investigation. Although TMD monolayers are highly robust to external mechanical fields, their electronic structure is sensitive to compressive and tensile strain. In addition, intrinsic point defects are present in synthesized samples of these 2D materials which leads to the modification of their electronic and optical properties. Presence of vacancy complexes leads to absorption with larger dipole matrix elements in comparison with the case of simple transition metal vacancies. Using first principles calculations, the effect of various strain situations on the absorption spectra of such defective monolayers is scrutinized and also shows that strain engineering allows for reversible tuning of the optical properties.

Phonon-assisted laser-induced third-order optical susceptibility for interband transition in a group II–VI asymmetric quantum well

Exciton–LO phonon interaction of the Fröhlich type is studied in the CdS/CdSe/CdS asymmetric double quantum well under an applied laser field. The intensity of laser effect on the exciton binding energy, oscillator strength, optical transition energies, and third-order harmonic generation are investigated by changing the right well sizes and barrier sizes. The laser-associated confined energies and their corresponding binding energies are brought out with the variation of well sizes. The position-dependent potential is altered by the laser-associated parameter. The laser-field-dependent third-order optical susceptibilities due to interband transitions in the asymmetric well are investigated. The effective Coulomb potential, using the Aldrich and Bajaj polaronic effect, is included in the Hamiltonian. The results show that the laser field considerably affects the confining potential of the quantum well and causes a drastic deformation of the confining potential profile. The obtained optical nonlinearities suffer a redshift in the asymmetric quantum well; also, their peak values are determined by the dipole matrix elements.

Effect of external electric field on photo-responsivity of CdS/ZnSe multiple quantum well photodetector

We show the enhancement of photo-responsivity through applied external electric field F of CdS/ZnSe multiple quantum well (MQW) photo-detector for the detection of mid infrared wavelengths. The subband energy levels E n are calculated using the Schrödinger equation via finite difference method by incorporating exchange-correlation potential and Hartree potential caused by doping in the well layer. We note that by increasing F , E n and the corresponding optical transition energies decreases. It is observed that dipole matrix element M 21 reduces for higher F and we obtain approximately 38 % lower value of M 21 at F = 40 kV/cm. Moreover, absorption coefficient decreases with F due to the strong dependence on M 21 . We obtain current density of 0.03 A/cm 2 and responsivity of 0.012 A/W at wavelength λ = 2.73 μm for M (number of wells) = 20, well width L w = 2 nm at F = 20 kV/cm. We show that the responsivity is enhanced by increasing M, L w as well as doping concentration N D in the well. We also achieved higher photo-responsivity in CdS/ZnSe MQW using our proposed model as compared to the earlier reported results for GaAs/AlGaAs QWIP . • We achieved enhancement of photo-responsivity in CdS/ZnSe QWIP as a function of electric field ( F ). • The Photocurrent ( J ) and Responsivity ( R ) are more significant at higher F . • Enhnacement of J and R with F is due to the reduction in dipole matrix element. • Increasing doping concentrations, number of wells and well widths of QWIP enhances responsivity.

Relaxation of single-electron spin qubits in silicon in the presence of interface steps

We develop a valley-dependent envelope function theory that can describe the effects of arbitrary configurations of interface steps and miscuts on the qubit relaxation time. For a given interface roughness, we show how our theory can be used to find the valley-dependent dipole matrix elements, the valley splitting, and the spin-valley coupling as a function of the electromagnetic fields in a Si/SiGe quantum dot spin qubit. We demonstrate that our theory can quantitatively reproduce and explain the result of experimental measurements for the spin relaxation time with only a minimal set of free parameters. Investigating the sample dependence of spin relaxation, we find that at certain conditions for a disordered quantum dot, the spin-valley coupling vanishes. This, in turn, completely blocks the valley-induced qubit decay. We show that the presence of interface steps can in general give rise to a strongly anisotropic behavior of the spin relaxation time. Remarkably, by properly tuning the gate-induced out-of-plane electric field, it is possible to turn the spin-valley hot spot into a ``cold spot'' at which the relaxation time is significantly prolonged and where the spin relaxation time is additionally first-order insensitive to the fluctuations of the magnetic field. This electrical tunability enables on-demand fast qubit reset and initialization that is critical for many quantum algorithms and error correction schemes. We therefore argue that the valley degree of freedom can be used as an advantage for Si spin qubits.

Light-matter coupling and quantum geometry in moiré materials

Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moir\'e materials. On the other hand, the coupling between light and matter is of key importance across disciplines and especially for Floquet and cavity engineering of solids. Here we present fundamental relations between light-matter coupling and quantum geometry of Bloch wave functions, with a particular focus on flat-band and moir\'e materials, in which the quenching of the electronic kinetic energy could allow one to reach the limit of strong light-matter coupling more easily than in highly dispersive systems. We show that, despite the fact that flat bands have vanishing band velocities and curvatures, light couples to them via geometric contributions. Specifically, the intra-band quantum metric allows diamagnetic coupling inside a flat band; the inter-band Berry connection governs dipole matrix elements between flat and dispersive bands. We illustrate these effects in two representative model systems: (i) a sawtooth quantum chain with a single flat band, and (ii) a tight-binding model for twisted bilayer graphene. For (i) we highlight the importance of quantum geometry by demonstrating a nonvanishing diamagnetic light-matter coupling inside the flat band. For (ii) we explore the twist-angle dependence of various light-matter coupling matrix elements. Furthermore, at the magic angle corresponding to almost flat bands, we show a Floquet-topological gap opening under irradiation with circularly polarized light despite the nearly vanishing Fermi velocity. We discuss how these findings provide fundamental design principles and tools for light-matter-coupling-based control of emergent electronic properties in flat-band and moir\'e materials.