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Register a new userRoles of electron correlation effects for accurate determination of $g_j$ factors of low-lying states of $^{113}$Cd$^+$ and their applications to atomic clock
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We investigate roles of electron correlation effects in the determination of $g_j$ factors of the $ns~^2S_{1/2}$ ($n$=5,6,7), $np~^2P_{1/2,3/2}$ ($n$=5,6), $5d~^2D_{3/2,5/2}$, and $4f~^2F_{5/2,7/2}$ states of the singly ionized cadmium (Cd$^+$) ion. Single and double excited configurations along with important valence triple excited configurations through relativistic coupled-cluster (RCC) theory are taken into account for incorporating electron correlation effects in our calculations. We find significant contributions from the triples to the lower $S$ and $P$ states for attaining high accuracy results. The contributions of Breit interaction and lower-order quantum electrodynamics effects, such as vacuum polarization and self-energy corrections, are also estimated using the RCC theory and are quoted explicitly. In addition, we present energies of the aforementioned states from our calculations and compare them with the experimental results to validate $g_j$ values. Using the $g_j$ factor of the ground state, systematical shift due to the Zeeman effect in the microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 rangle leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 rangle$ transition in $^{113}$Cd$^+$ ion has been estimated.
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The microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 rangle leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 rangle$ transition in the $^{113}$Cd$^+$ ion has been reported as 15199862855.0192(10) Hz [Opt. Lett. {bf 40}, 4249 (2015)]. Fractional systematic due to the black-body radiation (BBR) shift ($beta$) arising from the Stark effect in the above clock transition was used as $-1.1 times 10^{-16}$ from our unpublished preliminary estimation. We present here a precise value as $beta=-1.815(77) times 10^{-16}$ by carrying out rigorous calculations of third-order polarizabilities of the hyperfine levels associated with the clock transition. This is determined by evaluating matrix elements of the magnetic dipole hyperfine interaction Hamiltonian, electric dipole operator and energies between many low-lying states of $^{113}$Cd$^+$. We employ all-order relativistic many-body theories in the frameworks of Fock-space coupled-cluster and relativistic multi-configuration Dirac-Fock methods.
We employ a technique that combines the configuration interaction method with the singles-doubles coupled-cluster method to perform calculation of the energy levels, transition amplitudes, lifetimes, g-factors, and magnetic dipole and electric quadrupole hyperfine structure constants for many low-lying states of neutral actinium. We find very good agreement with existing experimental energy levels and make accurate predictions for missing levels. It has been noted that some of the levels have been previously misidentified; our analysis supports this claim. If spectroscopy is performed with actinium-225, our calculations will lead to values for nuclear structure constants. The accuracy of this can be constrained by comparing with actinium-227.
We experimentally and theoretically determine the magic wavelength of the (5$s^2$)$^{1}S_{0}$$-$(5$s$5$p$)$^{3}P_{0}$ clock transition of $^{111}$Cd to be 419.88(14) nm and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the $^{1}S_{0}$$-$$^{3}P_{1}$ transition to cool the atoms to 6 $mu$K and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate the blackbody shift, including the dynamic correction, to be fractionally 2.83(8)$times$10$^{-16}$ at 300 K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd $^1P_1$ lifetime and the ground state $C_6$ coefficient.
By combining a recent precise measurement of the ionization energy of $^{87}$Rb with previous measurements of electronic and hyperfine structure, an accurate value for the $^{85}textrm{Rb}-^{87}textrm{Rb}$ isotope shift of the 5$^2S_{1/2}$ ground state can be determined. In turn, comparison with additional spectroscopic data makes it possible for the first time to evaluate isotope shifts for the low-lying excited states, accurate in most cases to about 1 MHz. In a few cases, the specific mass shift contribution can be determined in addition to the total shift. This information is particularly useful for spectroscopic analysis of transitions to Rydberg states, and for tests of atomic theory.
We report a measurement of the dynamical polarizability of dysprosium atoms in their electronic ground state at the optical wavelength of 1064 nm, which is of particular interest for laser trapping experiments. Our method is based on collective oscillations in an optical dipole trap, and reaches unprecedented accuracy and precision by comparison with an alkali atom (potassium) as a reference species. We obtain values of 184.4(2.4) a.u. and 1.7(6) a.u. for the scalar and tensor polarizability, respectively. Our experiments have reached a level that permits meaningful tests of current theo- retical descriptions and provides valuable information for future experiments utilizing the intriguing properties of heavy lanthanide atoms.
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