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Register a new userNuclear magnetic octupole moment and the hyperfine structure of the $5D_{3/2,5/2}$ states of the Ba$^+$ ion
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The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of Ba$^+$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $Omega$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $Omega$ without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in Ba$^+$ experiments.
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Hyperfine structure (HFS) of atomic energy levels arises due to interactions of atomic electrons with a hierarchy of nuclear multipole moments, including magnetic dipole, electric quadrupole and higher rank moments. Recently, a determination of the magnetic octupole moment of the $^{173}mathrm{Yb}$ nucleus was reported from HFS measurements in neutral ${}^{173}mathrm{Yb}$ [PRA 87, 012512 (2013)], and is four orders of magnitude larger than the nuclear theory prediction. Considering this substantial discrepancy between the spectroscopically extracted value and nuclear theory, here we propose to use an alternative system to resolve this tension, a singly charged ion of the same $^{173}mathrm{Yb}$ isotope. Utilizing the substantial suite of tools developed around $mathrm{Yb}^+$ for quantum information applications, we propose to extract nuclear octupole and hexadecapole moments from measuring hyperfine splittings in the extremely long lived first excited state ($4f^{13}(^2!F^{o})6s^2$, $J=7/2$) of $^{173}mathrm{Yb}^+$. We present results of atomic structure calculations in support of the proposed measurements.
We measure the hyperfine structure of the $5p^65d$ ${}^2D_{3/2}$, $5p^65d$ ${}^2D_{5/2}$, $5p^64f$ ${}^2F^o_{5/2}$, and $5p^64f$ ${}^2F^o_{7/2}$ levels in doubly-ionized lanthanum (La III; La$^{2+}$) in a hollow cathode lamp using optogalvanic spectroscopy. Analysis of the observed spectra allows us to determine the hyperfine $A$ coefficients for these levels to be $A_{D3/2}=412(4)$ MHz, $A_{D5/2}=20(5)$ MHz, $A_{F5/2}=319(2)$ MHz, and $A_{F7/2}=155(4)$ MHz; and provide estimates for the hyperfine $B$ coefficients as $B_{D3/2}=105(29)$ MHz, $B_{D5/2}=157(40)$ MHz, $B_{F5/2}=-2(53)$ MHz, and $B_{F7/2}=171(51)$ MHz.
We present a measurement of the branching fractions for decay from the long-lived $5D_{5/2}$ level in Ba. The branching fraction for decay into the $6S_{1/2}$ ground state was found to be $0.846(25)_{mathrm{stat}}(4)_{mathrm{sys}}$. We also report an improved measurement of the $5D_{5/2}$ lifetime, $tau_{5D_{5/2}}=31.2(0.9)$~s. Together these measurements provide the first experimental determination of transition rates for decay out of the $5D_{5/2}$ level. The low ($<7 times 10^{-12}$~Torr) pressure in the ion trap in which these measurements were made simplified data acquisition and analysis. Comparison of the experimental results with theoretical predictions of the transition rates shows good agreement.
In this paper, we have calculated parity nonconserving electric dipole transition amplitudes of the hyperfine components for the transitions between the ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin dependent amplitudes from experimental measurements. The wavefunctions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.
The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known clock transitions between m=0 levels at zero magnetic field.
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