Dipole Transition Matrix Elements Research Articles

Dipole-dipole broadening of Rbns−npmicrowave transitions

The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$, a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Photoelectron angular distributions from autoionizing 4s14p66p1 states in atomic krypton probed with femtosecond time resolution

Photoelectron angular distributions (PADs) are obtained for a pair of 4s(1)4p(6)6p(1) (a singlet and a triplet) autoionizing states in atomic krypton. A high-order harmonic pulse is used to excite the pair of states and a time-delayed 801 nm ionization pulse probes the PADs to the final 4s(1)4p(6) continuum with femtosecond time resolution. The ejected electrons are detected with velocity map imaging to retrieve the time-resolved photoelectron spectrum and PADs. The PAD for the triplet state is inherently separable by virtue of its longer autoionization lifetime. Measuring the total signal over time allows for the PADs to be extracted for both the singlet state and the triplet state. Anisotropy parameters for the triplet state are measured to be β(2)=0.55 ± 0.17 and β(4)=-0.01 ± 0.10, while the singlet state yields β(2)=2.19 ± 0.18 and β(4)=1.84 ± 0.14. For the singlet state, the ratio of radial transition dipole matrix elements, X, of outgoing S to D partial waves and total phase shift difference between these waves, Δ, are determined to be X=0.56 ± 0.08 and Δ=2.19 ± 0.11 rad. The continuum quantum defect difference between the S and D electron partial waves is determined to be -0.15 ± 0.03 for the singlet state. Based on previous analyses, the triplet state is expected to have anisotropy parameters independent of electron kinetic energy and equal to β(2)=5∕7 and β(4)=-12∕7. Deviations from the predicted values are thought to be a result of state mixing by spin-orbit and configuration interactions in the intermediate and final states; theoretical calculations are required to quantify these effects.

Quantum control by means of Hamiltonian structure manipulation

A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited electromagnetic resources.

The predicted spectrum of the hypermetallic molecule MgOMg

The present study of MgOMg is a continuation of our theoretical work on Group 2 M(2)O hypermetallic oxides. Previous ab initio calculations have shown that MgOMg has a linear (1)Σ(g)+ ground electronic state and a very low lying first excited triplet electronic state that is also linear; the triplet state has (3)Σ(u)+ symmetry. No gas phase spectrum of this molecule has been assigned, and here we simulate the infrared absorption spectrum for both states. We calculate the three-dimensional potential energy surface, and the electric dipole moment surfaces, of each of the two states using a multireference configuration interaction (MRCISD) approach based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions with a cc-pCVQZ basis set. A variational MORBID calculation using our potential energy and dipole moment surfaces is performed to determine rovibrational term values and to simulate the infrared absorption spectrum of the two states. We also calculate the dipole polarizability of both states at their equilibrium geometry in order to assist in the interpretation of future beam deflection experiments. Finally, in order to assist in the analysis of the electronic spectrum, we calculate the vertical excitation energies, and electric dipole transition matrix elements, for six excited singlet states and five excited triplet states using the state-average full valence CASSCF-MRCISD/aug-cc-pCVQZ procedure.

Photoelectron angular distributions from polarized Ne*atoms near threshold

Photoelectron distributions of the polarized $2{p}^{5}3d$ Rydberg states of neon have been studied with a newly built velocity map imaging analyzer. The atoms were polarized by absorption of synchrotron radiation and ionized by an infrared laser. The asymmetry parameters ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$ characterizing two-photon resonant ionization have been extracted from the measured images and compared with the results of a quantum defect treatment. To achieve a good theoretical description of the data, it is necessary to take into account the dependence of the dipole transition matrix elements and phases of the partial waves on the angular momentum quantum numbers pertaining to various continuum channels.

Nonlinear coherent magneto-optical response of a single chiral carbon nanotube

We propose a theoretical framework and dynamical model for the description of the natural optical activity and Faraday rotation in an individual chiral single-wall carbon nanotube (CNT) in the highly nonlinear coherent regime. The model is based on a discrete-level representation of the optically active states near the band edge. Chirality is modelled by a system Hamiltonian in a four-level basis corresponding to energy-level configurations, specific for each handedness, that are mirror reflections of each other. The axial magnetic field is introduced through the Aharonov–Bohm and Zeeman energy-level shifts. The time evolution of the quantum system, describing a single nanotube with defined chirality, under an ultrashort polarized pulse excitation is studied using the coupled coherent vector Maxwell-pseudospin equations (Slavcheva 2008 Phys. Rev. B 77 115347). We provide an estimate for the effective dielectric constant and the optical dipole matrix element for transitions excited by circularly polarized light in a single nanotube and calculate the magnitude of the circular dichroism and the specific rotatory power in the absence and in the presence of an axial magnetic field. Giant natural gyrotropy (polarization rotatory power ∼3000° mm−1 (B=0 T)), superior to that of the crystal birefringent materials, liquid crystals and comparable or exceeding that of the artificially made helical photonic structures, is numerically demonstrated for the specific case of a (5, 4) nanotube. A quantitative estimate of the coherent nonlinear magneto-chiral optical effect in an axial magnetic field is given (∼30 000° mm−1 at B=8 T). The model provides a framework for the investigation of the chirality and magnetic field dependence of the ultrafast nonlinear optical response of a single CNT.

Calculation of Dipole Transition Matrix Elements and Expectation Values by Vibrational Coupled Cluster Method.

An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.

Time-resolved Fourier-transform infrared emission spectroscopy of Ag in the (1300–3600)-cm−1region: Transitions involvingfandgstates and oscillator strengths

We report on a study of the emission spectra of Ag vapor in a vacuum (${10}^{\ensuremath{-}2}$ Torr) formed in ablation of an Ag metal target by a high-repetition rate (1.0 kHz) pulsed nanosecond ArF laser ($\ensuremath{\lambda}=193$ nm, output energy of 15 mJ). The time-resolved infrared emission spectrum of Ag was recorded in the 1300- to 3600-cm${}^{\ensuremath{-}1}$ spectral region using the Fourier transform infrared spectroscopy technique with a resolution of $0.02$ cm${}^{\ensuremath{-}1}$. The time profiles of the measured lines have maxima at 5\char21{}6 $\ensuremath{\mu}$s after a laser shot and display nonexponential decay with a decay time of 3\char21{}7 $\ensuremath{\mu}$s. The lines reported here are given with an uncertainty of 0.0005\char21{}0.016 cm${}^{\ensuremath{-}1}$. The line classification is performed using relative line strengths expressed in terms of transition dipole matrix elements calculated with the help of the Fues model potential; these calculations show agreement with the large experimental and calculated data sets available in the literature. In addition to these data we also calculate transition probabilities and line and oscillator strengths for a number of transitions in the 1300- to 5000-cm${}^{\ensuremath{-}1}$ range between $(4{d}^{10}){\mathit{nl}}_{j}$ states of Ag.

Calculation of gain and luminescence spectra of quantum-cascade laser structures taking into account asymmetric emission line broadening

The energy levels, wave functions, and matrix elements of optical dipole transitions are calculated numerically for superlattice quantum-cascade structures. The effect of spectral broadening on the shape of emission spectra is estimated and semiphenomenological asymmetric profiles of emission line broadening are proposed. It is shown that the electroluminescence spectra well agree with the calculated spontaneous recombination spectra.

Rate equation for intense core-level photoexcitation and relaxation in metals

A dynamical equation for intense core–valence photoexcitation and collisional relaxation in a metal is derived by combining cluster-model electronic-structure calculations and the equation of motion for density matrices. By invoking the Markov approximation, it can be reduced to a generalized rate equation, where the rate coefficients for collisional and radiative transitions are derived from the cluster Hamiltonian in a self-contained fashion; they incorporate energy-level shifts due to electron–hole interactions as well as modification of dipole transition matrix elements due to induced polarization. Numerical examples are shown for K-edge excitation of lithium metal by a laser pulse with the photon energy of 60 eV and the intensity of 1014 W cm−2. It is found that creation of multiple core holes gives rise to a shift of the absorption edge towards the high-energy side, leading to a reduction of the absorption coefficient within 10 fs timescale. Such an ultrafast switching mechanism may have relevance to recently demonstrated nonlinear transmission of soft x-ray and vacuum ultraviolet free-electron laser pulses through metallic targets.

Electronic structure of GaN and Ga investigated by soft x-ray spectroscopy and first-principles methods

The electronic structure and chemical bonding of wurtzite-GaN investigated by $\text{N}\text{ }1s$ soft x-ray absorption spectroscopy and $\text{N}\text{ }K$, $\text{Ga}\text{ }{M}_{1}$, and $\text{Ga}\text{ }{M}_{2,3}$ emission spectroscopy is compared to that of pure Ga. The measurements are interpreted by calculated spectra using first-principles density-functional theory (DFT) including dipole transition matrix elements and additional on-site Coulomb interaction $(\text{WC-GGA}+U)$. The $\text{Ga}\text{ }4p\text{-N}\text{ }2p$ and $\text{Ga}\text{ }4s\text{-N}\text{ }2p$ hybridization and chemical bond regions are identified at the top of the valence band between $\ensuremath{-}1.0$ and $\ensuremath{-}2.0$ and further down between $\ensuremath{-}5.5$ and $\ensuremath{-}6.5\text{ }\text{eV}$, respectively. In addition, $\text{N}\text{ }2s\text{-N}\text{ }2p\text{-Ga}\text{ }4s$ and $\text{N}\text{ }2s\text{-N}\text{ }2p\text{-Ga}\text{ }3d$ hybridization regions occur at the bottom of the valence band between $\ensuremath{-}13$ and $\ensuremath{-}15\text{ }\text{eV}$, and between $\ensuremath{-}17.0$ and $\ensuremath{-}18.0\text{ }\text{eV}$, respectively. A bandlike satellite feature is also found around $\ensuremath{-}10\text{ }\text{eV}$ in the $\text{Ga}\text{ }{M}_{1}$ and $\text{Ga}\text{ }{M}_{2,3}$ emission from GaN, but is absent in pure Ga and the calculated ground-state spectra. The difference between the identified spectroscopic features of GaN and Ga are discussed in relation to the various hybridization regions calculated within band-structure methods.

Radiative charge transfer and radiative association in He++Ne collisions

A fully quantum-mechanical approach is utilized to study the collision process of He${}^{+}$ with neutral neon, and the radiative charge transfer (RCT) and radiative association (RA) cross sections are presented in the energy range from 0.08 meV to 1 eV, while the optical potential and semiclassical methods are adopted to calculate the total radiative decay cross sections for energies from 0.08 meV to 5 keV. The potential energy curves and dipole transition matrix elements are obtained by an ab initio multireference configuration interaction package. For the related three lowest $X$ ${}^{2}{\ensuremath{\Sigma}}^{+}$, $A$ ${}^{2}\ensuremath{\Pi}$, and $B$ ${}^{2}{\ensuremath{\Sigma}}^{+}$ states, the spectroscopic data are in good agreement with other theoretical calculations and experimental measurements. Our results indicate that the RCT cross section is much larger than the nonradiative charge transfer cross section for collision energy $E$ $<$ 20 eV, and when $E$ $>$ 40 eV, the nonradiative process becomes dominant. Especially, we found that in the present collision system the RA process is more important than the RCT process when $E$ $<$ 1 meV. The RCT and RA rate coefficients are also given for temperatures from 1 to 4 $\ifmmode\times\else\texttimes\fi{}{10}^{3}$ K.

Photodetachment of the Positronium Negative Ion with Exponential Cosine-Screened Coulomb Potentials

We have made an investigation to study the photodetachment of positronium negative ion (Ps −) interacting with exponential cosine-screened Coulomb potentials (ECSCP) within the framework of dipole approximation. The dipole transition matrix elements are calculated using the asymptotic form of highly accurate initial wave function of the bound ionic state and plane wave for final electron–positronium state. Results for photodetachment cross section in ECSCP are reported for the screening parameter in the range [0.0,0.35] (in \({a_0^{-1}}\)). Our results for the unscreened case agree nicely with some of the most accurate results available in the literature. Furthermore we make a comparative study of the photodetachment of Ps − in ECSCP with the photodetachment of Ps − in screened Coulomb potential. To the best of our knowledge, such a study on the photodetachment of Ps − in ECSCP is carried out for the first time in the literature.

Ab initio anharmonic vibrational frequency predictions for linear proton-bound complexes OC–H+–CO and N2–H+–N2

Ab initio anharmonic transition frequencies are calculated for strongly coupled (i) asymmetric and (ii) symmetric proton stretching modes in the X-H(+)-X linear ionic hydrogen bonded complexes for OCHCO(+) and N(2)HN(2)(+). The optimized potential surface is calculated in these two coordinates for each molecular ion at CCSD(T)/aug-cc-pVnZ (n = 2-4) levels and extrapolated to the complete-basis-set limit (CBS). Slices through both 2D surfaces reveal a relatively soft potential in the asymmetric proton stretching coordinate at near equilibrium geometries, which rapidly becomes a double minimum potential with increasing symmetric proton acceptor center of mass separation. Eigenvalues are obtained by solution of the 2D Schrödinger equation with potential/kinetic energy coupling explicity taken into account, converged in a distributed Gaussian basis set as a function of grid density. The asymmetric proton stretch fundamental frequency for N(2)HN(2)(+) is predicted at 848 cm(-1), with strong negative anharmonicity in the progression characteristic of a shallow "particle in a box" potential. The corresponding proton stretch fundamental for OCHCO(+) is anomalously low at 386 cm(-1), but with a strong alternation in the vibrational spacing due to the presence of a shallow D(infinityh) transition state barrier (Delta = 398 cm(-1)) between the two equivalent minimum geometries. Calculation of a 2D dipole moment surface and transition matrix elements reveals surprisingly strong combination and difference bands with appreciable intensity throughout the 300-1500 cm(-1) region. Corrected for zero point (DeltaZPE) and thermal vibrational excitation (DeltaE(vib)) at 300 K, the single and double dissociation energies in these complexes are in excellent agreement with thermochemical gas phase ion data.

Electronic structure and chemical bonding anisotropy investigation of wurtzite AlN

The electronic structure and the anisotropy of the Al - N {\pi} and {\sigma} chemical bonding of wurtzite AlN has been investigated by bulk-sensitive total fluorescence yield absorption and soft x-ray emission spectroscopies. The measured N K, Al L1, and Al L2,3 x-ray emission and N 1s x-ray absorption spectra are compared with calculated spectra using first principles density-functional theory including dipole transition matrix elements. The main N 2p - Al 3p hybridization regions are identified at -1.0 to -1.8 eV and -5.0 to -5.5 eV below the top of the valence band. In addition, N 2s - Al 3p and N 2s - Al 3s hybridization regions are found at the bottom of the valence band around -13.5 eV and -15 eV, respectively. A strongly modified spectral shape of Al 3s states in the Al L2,3 emission from AlN in comparison to Al metal is found, which is also reflected in the N 2p - Al 3p hybridization observed in the Al L1 emission. The differences between the electronic structure and chemical bonding of AlN and Al metal are discussed in relation to the position of the hybridization regions and the valence band edge influencing the magnitude of the large band gap.

Analysis of the dipole matrix elements of electronic optical transitions in the P 2 + /Si system

This study is concerned with a singly ionized pair of phosphorus donors in the silicon crystal lattice. The results of numerical calculations of the energy spectrum and dipole matrix elements in such a system are reported. The conditions, in which the P2+/Si system can be used in the implementation of quantum operations with resonance laser pulses, are determined. Estimation of the time of such operations yields ∼10 ps.

Ab initio modeling of molecular IR spectra of astrophysical interest: application to CH4

Aims. We describe an ab initio-based numerical method of obtaining infrared spectroscopic data (line list) of polyatomic molecules that allows calculation of complete sets of lines for temperatures up to several thousand Kelvin. While the main focus is on completeness and consistency, not spectroscopic accuracy, the approach is in principle “exact” for line positions and, although not exact for line strengths, of sufficient accuracy to be of value, especially in wavelength regions where there are gaps in reliable experimental data.Methods. Global potential energy and dipole moment hypersurfaces are fitted to the results of ab initio electronic structure calculations. The MULTIMODE software is then used to obtain rovibrational energy levels and dipole transition matrix elements. This information is used to calculate a complete set of Einstein coefficients of spontaneous emission A ij .Results. The method is applied to obtain a spectroscopic database for methane containing over 1.4 million lines up to an upper state energy of 6200 cm-1 (9000 K). The emission spectrum of CH4 at 1000 K is calculated with the complete set of Einstein coefficients and compared with the one obtained from the HITRAN database. Gaps in the database are realistically filled in by the calculated spectrum.Conclusions. Consistent and complete databases are important for astrophysical applications. Databases obtained by the method described here fulfill this requirement and are sufficiently accurate for astrophysical applications such as model atmosphere calculations and the corresponding synthetic spectra.

Electronic structure investigation of the cubic inverse perovskiteSc3AlN

The electronic structure and chemical bonding of the recently discovered inverse perovskite Sc3AlN, in comparison to ScN and Sc metal have been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Sc L, N K, Al L1, and Al L2,3 emission spectra are compared with calculated spectra using first principle density-functional theory including dipole transition matrix elements. The main Sc 3d - N 2p and Sc 3d - Al 3p chemical bond regions are identified at -4 eV and -1.4 eV below the Fermi level, respectively. A strongly modified spectral shape of 3s states in the Al L2,3 emission from Sc3AlN in comparison to pure Al metal is found, which reflects the Sc 3d - Al 3p hybridization observed in the Al L1 emission. The differences between the electronic structure of Sc3AlN, ScN, and Sc metal are discussed in relation to the change of the conductivity and elastic properties.

Comparison of Autler–Townes splitting based absolute measurements of the L7i2 A Σ1u+−X Σ1g+ electronic transition dipole moment with ab initio theory

We report a comparison between experimental and theoretical electronic transition dipole moment values for the (7)Li(2) A (1)Sigma(u) (+)-X (1)Sigma(g) (+) system. The experimental results are based on measuring the absolute magnitude of the transition dipole matrix elements from Autler-Townes splitting of rovibrational transitions for different R-centroid values. The ab initio theoretical calculations of the transition dipole moment for the (7)Li(2) A (1)Sigma(u) (+)-X (1)Sigma(g) (+) system were performed using two different quantum-mechanical models: an all-electron valence bond self-consistent-field method and a pseudopotential molecular orbital method. As expected for the smallest molecule with core electrons, the agreement between experiment and theory is very good.