Electric-dipole matrix elements for ns-n'p, nd-n'p, and 6d-4f transitions in Rb are calculated using a relativistic all-order method. A third-order calculation is also carried out for these matrix elements to evaluate the importance of the high-order many-body perturbation theory contributions. The all-order matrix elements are used to evaluate lifetimes of ns and np levels with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and to provide benchmark values for these lifetimes. The dynamic polarizabilities are calculated for ns states of rubidium. The resulting lifetime and polarizability values are compared with available theory and experiment.
Experimental and theoretical study of dynamic polarizabilities in the $5S_{1/2}$-$5D_{5/2}$ clock transition in rubidium-87 and determination of E1 matrix elements
Measurements of rubidium lifetime in a dark magneto-optical trap (DMOT) was performed at various populations of the bright and dark hyperfine states of the trapped atoms. The rubidium lifetime in the trap appeared to be shorter if the atom spent more time in the bright state. A simple explanation of this effect is based on the increase of the cross-section of rubidium collisions with the surrounding warm atoms upon rubidium electronic excitation.
The results of ab initio calculation of E1 amplitudes, lifetimes,and polarizabilities for several low-lying levels of ytterbium are reported. The effective Hamiltonian for the valence electrons has been constructed in the frame of CI+MBPT method and solutions of many electron equation are found.
We present a lifetime measurements of the 6s level of rubidium. We use a time-correlated single-photon counting technique on two different samples of rubidium atoms. A vapor cell with variable rubidium density and a sample of atoms confined and cooled in a magneto-optical trap. The 5P_{1/2} level serves as the resonant intermediate step for the two step excitation to the 6s level. We detect the decay of the 6s level through the cascade fluorescence of the 5P_{3/2} level at 780 nm. The two samples have different systematic effects, but we obtain consistent results that averaged give a lifetime …
The 6s-np_j (n=6-9) electric-dipole matrix elements and 6s-nd_j (n=5-7) electric-quadrupole matrix elements in Ba+ are calculated using the relativistic all-order method. The resulting values are used to evaluate ground state dipole and quadrupole polarizabilities. In addition, the electric-dipole 6p_j-5d_j' matrix elements and magnetic-dipole 5d_{5/2}-5d_{3/2} matrix element are calculated using the same method in order to determine the lifetimes of the 6p_{1/2}, 6p_{3/2}, 5d_{3/2}, and 5d_{5/2} levels. The accuracy of the 6s-5d_j matrix elements is investigated in detail in order to estimate…
Electric-dipole matrix elements for 6p-nd, n=5, 6, 7 transitions in cesium are calculated using a relativistic all-order method. The resulting matrix elements are used to evaluate 5d lifetimes and 6p polarizabilities. The data are compared with experimental lifetime and polarizability measurements made by different groups. Domination of the 6p scalar polarizabilities by 5d-6p dipole matrix elements facilitates an exacting consistency check of 5d lifetime and 6p polarizability data. Values of 5d-6p matrix elements obtained from experimental 5d lifetime data are found to be inconsistent with tho…
We present lifetime measurements of the $5D_{3/2}$ and $5D_{5/2}$ states of rubidium using the time correlated single photon counting method. We perform the experiment in a magneto-optical trap of $^{87}$Rb atoms using a two-step excitation with the trap laser at 780 nm as the first step. We record the 761.9 nm fluorescence from the decay of the $5D_{3/2}$ state to the $5P_{1/2}$ state, and measure the lifetime of the $5D_{3/2}$ state $τ=246.3(1.6)$ ns. We record the 420.2 nm fluorescence from the cascade decay of the $5D_{5/2}$ state to the $5S_{1/2}$ state through the $6P_{3/2}$ state, and e…
Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for stati…
Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7s, 7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for 7s - 7p, 7p - 6d, and 6d - 5f electric-dipole transitions; and 7s - 6d, 7s - 5f, and 5f_5/2 - 5f_7/2 multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions Z = 87 - 92 calculati…
Excitation energies of the ns_{1/2} (n=7-10), np_j (n=7-9), nd_j (n=6-8), nf_{j} (n=5-7), and ng_{j} (n=5-6) states in Th IV are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 96 possible nl_j-n'l'_j' electric-dipole transitions. Multipole matrix elements (7s_{1/2}-6d_j, 7s_{1/2}-5f_j, and 5f_{5/2}-5f_{7/2}) are evaluated to obtain the lifetimes of the $5f_{7/2}$ and 7s_{1/2}$ states. Matrix elements are cal…
We present lifetime measurements of the 7S1/2 level and the 6p manifold of rubidium. We use a timecorrelated single-photon counting technique on a sample of 85Rb atoms confined and cooled in a magneto-optic trap. The upper state of the 5P1/2 repumping transition serves as the resonant intermediate level for twophoton excitation of the 7s level. A probe laser provides the second step of the excitation, and we detect the decay of atomic fluorescence to the 5P3/2 level at 741 nm. The decay process feeds the 6p manifold that decays to the 5s ground state emitting UV photons. We measure lifetimes o…
Using the relativistic coupled-cluster method, we have calculated ionization potentials, E1 matrix elements and dipole polarizabilities of many low-lying states of Ca$^+$. Contributions from the Breit interaction are given explicitly for these properties. Polarizabilities of the ground and the first excited d-states are determined by evaluating the wave functions that are perturbed to first order by the electric dipole operator and the black-body radiation shifts are estimated from these results. We also report the results of branching ratios and lifetimes of the first excited p-states using b…
We have employed the relativistic coupled-cluster theory to calculate the electric dipole matrix elements in the singly ionized barium (Ba$^+$) and radium (Ra$^+$). Matrix elements of Ba$^+$ are used to determine the light-shift ratios for two different wavelengths on which recent experiments are carried out. By combining the measured light-shift ratios and our calculations, we are able to estimate possible errors associate with the used matrix elements in Ba$^+$. Static polarizabilities of the low-lying states and lifetimes of the first excited P-states are also determined using these matrix …
Two different theoretical methods have been used to complete a new calculation of polarizability in the thallium 6p_{1/2}, 7s, and 7p_{1/2} states. The predictions of the two methods agree to within 1% for the 6p_{1/2} and 7s states and 2% for 7p_{1/2} state. We find that the theoretical expression for the 6p_{1/2} - 7s transition polarizability difference is dominated (greater than 90% contribution) by mixing of the 7s state with the 7p_{1/2} and 7p_{3/2} states. By comparing the theoretical expression to an existing Stark shift measurement [Doret et al., Phys. Rev. A 66, 052504 (2002)], new,…
We have measured the radiative lifetimes of ns, np and nd Rydberg states of rubidium in the range 28 < n < 45. To enable long-lived states to be measured, our experiment uses slow-moving Rb atoms in a magneto-optical trap (MOT). Two experimental techniques have been adopted to reduce random and systematic errors. First, a narrow-bandwidth pulsed laser is used to excite the target Rydberg state, resulting in minimal shot-to-shot variation in the initial state population. Second, we monitor the target state population as a function of time delay from the laser pulse using a short-duration, milli…
We have investigated energies, magnetic dipole hyperfine structure constants ($A_{hyf}$) and electric dipole (E1) matrix elements of a number of low-lying states of the triply ionized tin (Sn$^{3+}$) by employing relativistic coupled-cluster theory. Contributions from the Breit interaction and lower-order quantum electrodynamics (QED) effects in determination of above quantities are also given explicitly. These higher-order relativistic effects are found to be important for accurate evaluation of energies, while QED contributions are seen to be contributing significantly to the determination o…
Atomic properties of the 24 low-lying ns, np, nd, nf, and ng states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5f_j, 6d_j, 7p_j, and 7s), and tensor polarizabilities of the 5f_j, 6d_j, 7p_{3/2} states of Th IV are e…
We evaluate the polarizabilities of the 5p_{1/2}, 6s, 6p_{1/2}, and 6p_{3/2} states of In using two different high-precision relativistic methods: linearized coupled-cluster approach where single, double and partial triple excitations of the Dirac-Fock wave function are included to all orders of perturbation theory and an approach that combines the configuration interaction and the coupled-cluster method. Extensive comparison of the accuracy of these methods is carried out. The uncertainties of all recommended values are evaluated. Our result for the 6s-5p_{1/2} Stark shift is in excellent agr…
Motivated by recent interest in their applications, we report a systematic study of Cs atomic properties calculated by a high-precision relativistic all-order method. Excitation energies, reduced matrix elements, transition rates, and lifetimes are determined for levels with principal quantum numbers $n \leq 12$ and orbital angular momentum quantum numbers $l \leq 3$. Recommended values and estimates of uncertainties are provided for a number of electric-dipole transitions and the electric dipole polarizabilities of the $ns$, $np$, and $nd$ states. We also report a calculation of the electric …
A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polari…
Experiments involving ultracold molecules require sufficiently long lifetimes, which can be very short for excited rovibrational states in the molecular potentials. For alkali atoms such as rubidium, a lowest rovibrational molecular state can both be found in the electronic singlet and triplet configurations. The molecular singlet ground state is absolutely stable. However, the lowest triplet state can decay to a deeper bound singlet molecule due to a radiative decay mechanism that involves the interatomic spin-orbit interaction. We investigate this mechanism, and find the lifetime of rubidium…
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths $f_{ik}$, Einstein coefficients $A_{ik}$, state lifetimes $τ_{k}$, transition dipole…
We study the cancellation of differential ac Stark shifts in the 5s and 5p states of rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single, double and important valence triple excitations approximation including all possible non-linear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. "Magic wavelengths" are determi…
We report here oscillator strengths, transition rates, branching ratios and lifetimes due to allowed transitions in potassium (K) atom. We evaluate electric dipole (E1) amplitudes using an all order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the E1 matrix elements mentioned above and estimated from the lifetimes of the 4P states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the g…
The exquisite properties of Rydberg levels make them particularly appealing for emerging quantum technologies. The lifetime of low-angular-momentum laser-accessible levels is however limited to a few $100\,μ\mathrm{s}$ by optical transitions and microwave blackbody radiation (BBR) induced transfers at room temperature. A considerable improvement would be obtained with the few $10\,\mathrm{ms}$ lifetime of circular Rydberg levels in a cryogenic environment reducing the BBR temperature. We demonstrate the preparation of long-lived circular Rydberg levels of laser-cooled Rubidium atoms in a cryos…
The ^1Σ^+ electronic ground states of MgLi^+ and CaLi^+ molecular ions are investigated for their spectroscopic constants and properties such as the dipole- and quadrupole moments, and static dipole polarizabilities. The quadrupole moments and the static dipole polarizabilities for these ions have been calculated and reported here, for the first time. The maximum possible error bars, arising due to the finite basis set and the exclusion of higher correlation effects beyond partial triples, are quoted for reliability. Further, the adiabatic effects such as diagonal Born-Oppenheimer corrections …
We report on spiking dynamics of frequency up-converted emission at 420 nm generated on the 6P3/2-5S1/2 transition in Rb vapour two-photon excited to the 5D5/2 level with laser light at 780 and 776 nm. The spike duration is less than the natural lifetime of any excited level involved in the interaction with both continuous and pulsed pump radiation. The spikes at 420 nm are attributed to temporal properties of the directional emission at 5.23 μm generated on the population inverted 5D5/2-6P3/2 transition. A link between the spiking regime and cooperative effects is discussed. We suggest that t…
In continuation to our earlier reported data on the electric dipole (E1) matrix elements and lifetimes of the metastable states of the alkaline earth ions in [Atomic Data and Nuc. Data Tables {\bf 137} (2021) 101381], we present here the tune-out and magic wavelengths of the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions by determining dynamic E1 polarizabilities. Furthermore, we have evaluated the electric quadrupole (E2) matrix elements of a large number of forbidden transitions using an all-order relativistic many-body method and compare them with the previously reported values…
We have calculated parity nonconserving 7s - 6d_{3/2} amplitude E_PNC in 223Ra+ using high-precision relativistic all-order method where all single and double excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Detailed study of the uncertainty of the parity nonconserving (PNC) amplitude is carried out; additional calculations are performed to estimate some of the missing correlation corrections. A systematic study of the parity conserving atomic properties, including the calculation of the energies, transition matrix elements, lifetimes, hyperfine c…
Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j' transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2 transitions contribute on the order of 90% to the respective polarizabilities of the np_1/2 states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the co…
The blackbody radiation (BBR) shift of the 5s - 4d_{5/2} clock transition in 88Sr+ is calculated to be 0.250(9) Hz at room temperature, T=300K, using the relativistic all-order method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. The BBR shift is a major component in the uncertainty budget of the optical frequency standard based on the 88Sr+ trapped ion. The scalar polarizabilities of the 5s and 4d_{5/2} levels, as well as the tensor polarizability of the 4d_{5/2} level, are presented together with the evaluation of t…
Long ground-Rydberg coherence lifetime is interesting for implementing high-fidelity quantum logic gates, many-body physics, and other quantum information protocols. However, the potential formed by a conventional far-off-resonance red-detuned optical-dipole trap (ODT) is usually repulsive for Rydberg atoms, which will result in fast atom loss and low repetition rate of the experimental sequence. These issues can be addressed by a magic ODT. We performed the calculation of ODT's magic detuning for confinement of cesium ground state and Rydberg state with the same potential well. We used a sum-…
Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a m…
Relativistic configuration-interaction and coupled-cluster calculations of Ir$^{17+}$ transition energies and properties for optical clock applications
We report \textit{ab initio} calculations of the X $^2 Σ_{u}^+$, A $^2Π_u$ and B $^2 Σ_{g}^+$ states of the Ca$_{2}^+$ dimer. All electron CAS+MRCI calculations are performed for the X $^2 Σ_{u}^+$ and B $^2 Σ_{g}^+$ states, while valence CAS+MRCI calculations using an effective core potential are used to describe the A $^2Π_u$ state. A double well is found in the B $^2 Σ_{g}^+$ state. Spectroscopic constants, vibrational levels, transition moments and radiative lifetimes are calculated for the most abundant isotope of calcium ($^{40}$Ca). The static dipole and quadrupole polarizabilities, and…
We demonstrate that several metastable excited states in Hf$~$II, Hf$~$IV and W$~$VI ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. Cooling E1 transitions are available. Energy levels, Landé $g$-factors, transition amplitudes for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions, lifetimes, and electric quadrupole moments for Hf$~$II, Hf$~$IV, and W$~$VI ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (…
Magic wavelengthsfor the $7S_{1/2}-7P_{1/2,3/2}$ transitions in Fr were reported by Dammalapati \textit{et al.} in [Phys. Rev. A 93, 043407 (2016)]. These $λ_{\rm{magic}}$ were determined by plotting dynamic polarizabilities ($α$) of the involved states with the above transitions against a desired range of wavelength. Electric dipole (E1) matrix elements listed in [J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7P_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine…
