Magnetic Quadrupole Transitions Research Articles

Long-Lived Coherence on a μHz Scale Optical Magnetic Quadrupole Transition.

We report on the coherent excitation of the ultranarrow ^{1}S_{0}-^{3}P_{2} magnetic quadrupole transition in ^{88}Sr. By confining atoms in a state insensitive optical lattice, we achieve excitation fractions of 97(1)% and observe linewidths as narrow as 58(1)Hz. With Ramsey spectroscopy, we find coherence times of 14(1)ms, which can be extended to 266(36)ms using a spin-echo sequence. We determine the lifetime of the ^{3}P_{2} level for spontaneous emission of magnetic quadrupole radiation to be 110(31)min, confirming long-standing theoretical predictions. These results establish an additional clock transition in strontium and pave the way for applications of the metastable ^{3}P_{2} state in quantum computing and quantum simulations.

Relativistic atomic structure calculations of Li-like ions used for plasma diagnostic studies

We have carried out atomic structure calculations using systematically enlarged multiconfiguration Dirac-Fock wavefunctions of Li-like ions of the most prominent plasma impurities (Ar, Ti, Fe, Ni, Kr and W) found in presently working tokamaks. Relativistic Breit interaction and quantum electrodynamic (QED) corrections such as vacuum polarization and self-energy corrections are also included in the calculations prior to the evaluation of low lying energy levels, transition probabilities, oscillator strengths and line strengths. Selective radiative data for electric dipole and magnetic quadrupole transitions are also reported. Special emphasis is given in the computations of fundamental quantities such as oscillator strengths as they are widely used in atomic data and analysis structure (ADAS) databases to evaluate quantities such as effective collision strengths. Present computed values are compared with existing available results on NIST database and few similar earlier computations and a good agreement has been found. We believe that the detailed atomic data with the relativistic and QED corrections will assist in spectroscopic studies such as accurate line identification and plasma modelling work in tokamak plasma, laser induced breakdown spectroscopy (LIBS), highly charged ions clocks and astrophysical observations.

Large-scale relativistic calculations of spectral data in Zr XXVIII, Nb XXIX and Tc XXXI of tokamak interest

Large-scale relativistic multiconfiguration Dirac–Fock calculations of energy levels and lifetimes of the 206 states arising from the 3s23p, 3p3, 3s3p3d, 3p3d2, 3s24p, 3s24f, 3s3p2, 3s23d, 3s3d2, 3s24d, 3s24s, 3s3p4s, 3s3p4d, 3p23d, 3d3, and 3s3p4p configurations of Zr XXVIII, Nb XXIX, and Tc XXXI of tokamak interest are carried out. The active space approximation is employed for the calculations. To obtain accurate and convergent results, the calculations take into account the valence and core-valence correlations within the n= 9 complex, as well as the Breit interaction, self-energy corrections, and vacuum polarization corrections. Detailed information regarding the decay properties of these ions is provided, including the transition wavelengths, line strengths, and radiative transition rates for various types (electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions) of transitions among the levels of the aforementioned configurations. The uncertainties of each dipole transition are evaluated. The present data sets are compared to previous results and a good agreement is observed, which is valuable for emission line identification and fusion modeling, especially in situations where experimental data are scarce.

Fine-Structure Qubit Encoded in Metastable Strontium Trapped in an Optical Lattice.

We demonstrate coherent control of the fine-structure qubit in neutral strontium atoms. This qubit is encoded in the metastable ^{3}P_{2} and ^{3}P_{0} states, coupled by a Raman transition. Using a magnetic quadrupole transition, we demonstrate coherent state initialization of this THz qubit. We show Rabi oscillations with more than 60 coherent cycles and single-qubit rotations on the μs scale. With spin echo, we demonstrate coherence times of tens of ms. Our results pave the way for fast quantum information processors and highly tunable quantum simulators with two-electron atoms.

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z ≲ 30 that are generally of astrophysical interest, and the other one is about the highly charged krypton (Z = 36) and tungsten (Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock (MCDHF) and the relativistic many-body perturbation theory (RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l 3 configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

Theoretical level energies and transition data for 4p[formula omitted]4d[formula omitted], 4p[formula omitted]4d[formula omitted] and 4p[formula omitted]4d[formula omitted]4f configurations of W[formula omitted] ion

The ab initio quasirelativistic approach developed specifically for the calculation of spectral parameters of highly charged ions has been used to determine transition data for the Mo-like tungsten ion W32+. The configuration interaction method is utilized to include electron correlation effects. The relativistic effects are taken into account in the Breit–Pauli approximation. Level energies, radiative lifetimes τ, Landé g-factors are determined for the ground configuration 4p64d6 and two excited configurations 4p54d7 and 4p64d54f. The radiative transition wavelengths λ, emission transition probabilities A, weighted oscillator strengths gf, and transition line strengths S for the electric dipole, electric quadrupole, electric octupole, magnetic dipole, and magnetic quadrupole transitions among the fine-structure levels of these configurations are produced. The uncertainties of computed spectroscopic parameters are evaluated.

Magnetic dipole and quadrupole transitions in the ν2 + ν3 vibrational band of carbon dioxide.

This paper aims at the theoretical study of the CO2 magnetic-dipole ν2 + ν3 rovibrational absorption band that was recently detected in the Martian atmosphere. Specific characteristics of the magnetic dipole operator are carefully examined. Our evaluation of the magnetic-dipole line intensities is based on the variational calculations and the use of molecular properties is determined through specially performed abinitio quantum chemical calculations. The comparison of our simulated magnetic-dipole spectrum with available laboratory taken data also requires the knowledge of line intensities in the quadrupole band, which partially overlaps with that magnetic-dipole. Quadrupole intensities, once reconsidered, are permitted to correct previously reported values of the integrated intensity as well as the intensity of selected branches. The sum of our calculated magnetic-dipole and quadrupole rovibrational lines is shown to be in good agreement with both sets of presently available data from FTIR and OFCEAS laboratory observations.

S01−P23magnetic quadrupole transition in neutral strontium

We present a detailed investigation of the ultranarrow magnetic-quadrupole $^{1}\mathrm{S}_{0}\text{\ensuremath{-}}^{3}\mathrm{P}_{2}$ transition in neutral strontium and show how it can be made accessible for quantum simulation and quantum computation. By engineering the light shift in a one-dimensional optical lattice, we perform high-resolution spectroscopy and observe the characteristic absorption patterns for a magnetic quadrupole transition. We measure an absolute transition frequency of $446,647,242,704(2)$ kHz in $^{88}\mathrm{Sr}$ and an $^{88}\mathrm{Sr}\text{\ensuremath{-}}^{87}\mathrm{Sr}$ isotope shift of $+62.91(4)$ MHz. In a proof-of-principle experiment, we use this transition to demonstrate local addressing in an optical lattice with 532 nm spacing with a Rayleigh-criterion resolution of $494(45)$ nm. Our results pave the way for applications of the magnetic quadrupole transition as an optical qubit and for single-site addressing in optical lattices.

Magnetic quadrupole transitions in the relativistic energy density functional theory

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $$^{16}$$ O, $$^{48}$$ Ca, $$^{208}$$ Pb, open-shell $$^{18} \mathrm O$$ , $$^{42}$$ Ca, $$^{56}$$ Fe, and semi-magic $$^{90}$$ Zr. The evolution of M2 transition properties has been investigated within the $$^{36-64} \mathrm Ca$$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium.

Excitation energies, lifetimes, and transition data for Zr XXIX

The energies and lifetimes of the lowest 303 fine-structure levels belonging to the 3s2, 3s3p, 3s3d, 3p3d, 3d2, 3snl (n = 4 − 6; l = 0 − 5), 3pnl (n = 4 − 5; l = 0 − 4), 3p6s, and 3dnl (n = 4 − 5; l = 0 − 4) configurations of Mg-like zirconium, Zr XXIX, are calculated using the relativistic multiconfiguration Dirac-Hartree-Fack (MCDHF) method employed in the GRASP2018 atomic structure computer package. The MCDHF wavelengths, transition probabilities, weighted oscillator strengths, and line strengths for the electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions between the levels considered are presented. The Breit-interaciton (BI) and quantum electrodynamics (QED) effects are considered in the computations. Comparisons with available experimental and other theoretical data are carried out to evaluate the accuracy of the present results.

Transition energies and transition probabilities for the core-excited state [formula omitted] of Li-like ions with [formula omitted] 6–92

The transition energies and radiative transition probabilities for the transition from the (1s2s2p)3/2 group to the ground state 1s22s involving the electric dipole (E1) and magnetic quadrupole (M2) transitions have been systematically calculated for ions along the Li isoelectronic sequence from Z=6 to Z=92. The calculations are performed by using the full relativistic multi-configuration Dirac–Fock (MCDF) method, in which the leading quantum electrodynamics (QED) shifts and the frequency dependence of the Breit interaction are also considered. The present calculation results are in good agreement with available previous results. It is found that the transition probabilities generally increase along with nuclear number Z; however, the abnormal behavior with the minima transition probabilities at Z=28 and Z=25 emerges in the [(1s2s)02p3/2]3/2→1s22s via E1 transition and the [(1s2s)12p3/2]3/2→1s22s via M2 transition, respectively; the M2 transition probabilities become comparable with that of E1 in mid-Z ions, and particularly for the q line of Z=28 ion, the M2 and E1 transition probabilities would be of the same order of magnitude. In addition, the present results show that the electron correlations impact on the energy levels and transition probabilities mainly work on the low-Z ions, while, the QED and Breit effects mainly work on the high-Z ions. This work should be of particular interest to the analysis of the spectrum and the effects of multipole mixing on the X-ray properties.

Triplet state harvesting and search for forbidden transition intensity in the nitrogen molecule.

Triplet excited states of the N2 molecule play an important role in electric discharges through air or liquid nitrogen accompanied by various afterglows. In the rarefied upper atmosphere, they produce aurora borealis and participate in other energy-transfer processes connected with atmospheric photochemistry and nightglow. In this work, we present spin-orbit coupling calculations of the intensity of various forbidden transitions, including the prediction of the electric dipole transition moment of the new band, which is strongly prohibited by the (+|-) selection rule, the new spin-induced magnetic transition, magnetic and electric quadrupole transitions for the B3Πg Wilkinson band, and the Lyman-Birge-Hopfield a1Πg ← X1Σg transition. Also, two other far-UV singlet-singlet quadrupole transitions are calculated for the first time, namely, the Dressler-Lutz a"1Σg +-X1Σg + and the less studied z1Δg-X1Σg + weak transitions.

Relativistic atomic structure calculations of KIX with plasma parameters

Systematic calculations for energy levels, lifetimes, and radiative data for the KIX are reported, including oscillator strengths, transition wavelengths, line strengths, and radiative rates of electric dipole (E1) transition, electric quadrupole (E2) transition, magnetic dipole (M1) transition, and magnetic quadrupole (M2) transition, using GRASP. Quantum electrodynamics and Breit correction have been considered in our calculations. The importance and effect of valence valence and core valence correlations on the excitation energies have been discussed in graphical and tabular forms. Analogous calculations using flexible atomic code (FAC) and the large-scale configuration interaction technique have also been done to confirm the accuracy of energy levels. The calculated results are in close agreement with NIST compiled data and other available results. The influence of plasma temperature (2 × 106–1 × 1010 K) on the line intensity ratio with the number of electron density has been studied for the hot dense plasma (HDP) graph for KIX. Our reported results will be valuable or beneficial for the characterization of HDP, astrophysical plasmas, and plasma modeling.

Theoretical analysis of atomic parameters of Sm-like and Nd-like W ions in soft x-ray region

We calculated atomic data such as energy levels, transition wavelengths, oscillator strengths and transition rates for Sm-like and Nd-like W ions. We employed flexible atomic code (FAC) in our computations. We computed fine structure levels of configurations 4f125s2, 4f125s5p and 4f135s for Nd-like W and configurations 4f145s2, 4f135s25p and 4f125s25p2 for Sm-like W. We have provided transition data of electric dipole (E1) transitions and magnetic quadrupole (M2) transitions for transition 4f125s2—4f125s5p and magnetic dipole (M1) and electric quadrupole (E2) transition data for transition 4f145s2 − 4f125s25p2. We also found that spectral lines of these transitions in Sm and Nd-like W ion spectra lie in soft x-ray (SXR) region. We compared transition data of Nd-like W and excitation energies of Sm-like W ions with available theoretical and experimental results. We also discussed the effect of configuration interaction on atomic data of Nd-like W and excitation energies of Sm-like W by systematically increasing the number of configurations.

Relativistic excitation energies and transition data for In XL and Sn XLI

Excitation energies, lifetimes, and level designations in jj- and LS-coupling schemes are computed for the lowest 139 fine-structure levels belonging to the 2s22p6, 2s22p5nl (n = 3 − 5, l = 0 − 4), and 2s2p6nl (n = 3 − 4, l = 0 − 3) configurations in Ne-like In XL and Sn XLI. Wavelengths, weighted oscillator strengths, transition probabilities, and line strengths are calculated for allowed and forbidden transitions including electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions. The computations are done with the fully relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method, which incorporates the Breit-interaction (BI) and quantum electrodynamics (QED) effects. The present results are compared to available experimental and other theoretical data in order to determine the accuracy of results.

Theoretical level energies and transition data for 4p64d8, 4p54d9 and 4p64d74f configurations of W[formula omitted] ion

The ab initio quasirelativistic approach developed specifically for the calculation of spectral parameters of highly charged ions was used to derive transition data for the Ru-like tungsten ion W30+. The configuration interaction method was applied to include electron correlation effects. The relativistic effects were taken into account in the Breit–Pauli approximation. The level energies, radiative lifetimes τ, Landé g-factors were determined for the ground configuration 4p64d8 and two excited configurations 4p54d9 and 4p64d74f. The radiative transition wavelengths λ and emission transition probabilities A for the electric dipole, electric quadrupole, electric octupole, magnetic dipole, and magnetic quadrupole transitions among the levels of these configurations were generated.

Fine structure calculations of excitation energies, lifetimes and radiative properties of S-like Kr XXI

Extensive and systematic calculations for energy levels and lifetimes are carried out for the lowest 145 levels arising from the 3s23p4, 3s3p5, 3s23p33d, 3p6, 3s3p43d and 3s23p23 d2 configurations in S-like Kr XXI ion using the multiconfiguration Dirac-Fock (MCDF) method. Additionally, radiative data such as transition wavelengths, absorption oscillator strengths, line strengths and radiative decay rates have also been computed for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground state. The importance of Breit interaction (BI) and quantum electrodynamics (QED) corrections on the energy levels has also been estimated. To assess the credibility and integrity of our MCDF energies, independent calculations using the relativistic configuration interaction (RCI) approach have also been performed. Detailed comparisons are made between our two sets of results, as well as with other existing experimental and theoretical values, and a good agreement is achieved. The present results will be helpful for the modeling and diagnostics of fusion plasmas.

Contribution of doubly and triply excited states in excitation energies with transition data and collisional excitation cross-section of Sn13+ and Sn14+ ions

We have calculated atomic data such as energy levels, transition wavelengths, oscillator strengths, transition rates, lifetimes and Collision cross-section for Sn13+ and Sn14+ ions. We have employed Flexible atomic code (FAC) in our computations. We have computed lowest 50 and 17 fine structure levels for Sn13+ and Sn14+ respectively. We have provided transition data for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) transitions among lowest 17 levels and 50 levels for Kr-like Sn and Rb-like Sn respectively. We have also provided lifetimes of states of Kr-like and Rb-like Sn ions and predicted that magnetic dipole transitions have dominant contribution in lifetimes of states having large lifetime. We have also reported collision cross-section for Kr-like and Rb-like Sn from ground state to lowest 17 levels and 50 levels respectively. We have compared our calculated data with available theoretical and experimental results and discussed difference between them.

Partition function and thermodynamic quantities with atomic data of Ag XLIV

In this work, the atomic parameters of Ag XLIV (Be-like Ag) are examined and evaluated by implementing the GRASP2K package with the multi-configuration Dirac–Hartree–Fock (MCDHF) method for the calculation of wave-functions. We have listed fine structure energy levels of the lowest 170 levels with radiative data for multipole moments, such as electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions, that lie in the region of extreme ultraviolet (EUV) and soft X-ray (SXR) for Ag XLIV from the ground state within the lowest 170 levels. We have compared our GRASP2K and FAC results with theoretical results available in the literature for some levels. Additionally, we have also calculated partition function and thermodynamic quantities for temperature ranges from 104to 107K. We believe that our presented details and data may be beneficial not only in plasma modeling but also in imaging of nanostructure as well as in medicine, semiconductors, and EUV and SXR laser applications.

Relativistic multiconfiguration Dirac-Hartree-Fock calculations for energies, lifetimes, and E1, E2, M1, and M2 line strengths of Y XXXII

Energies, wavelengths, line strengths, transition probabilities, and weighted oscillator strengths for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the levels arising from the n ≤ 3 configurations of oxygen-like yttrium, Y XXXII, are calculated using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method. In the calculations, the valence-valence (VV) and core-valence (CV) correlations, as well as the Breit interaction (BI) and the leading quantum electrodynamics (QED) contributions are considered. Comparisons with the available results are used to determine the uncertainty for energies, wavelengths, and oscillator strengths. For lifetimes, E1, E2, M1, and M2 line strengths, the comparisons are also made between the two sets of the present MCDHF calculations to determine the accuracy of the results.