Theoretical studies at the interface of atomic physics and precision measurements
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 the results of atomic structure calculations in support of the proposed measurements. The next study investigates the hyperfine-induced effects in a series of experiments related to atomic parity violation (APV). The Stark interference technique, used in APV experiments, requires accurate knowledge of transition polarizability. In Cesium, the $6S_{1/2}\rightarrow{7S_{1/2}}$ APV amplitude, $\mathrm{Im(E_{PNC})}$ is deduced from the measured ratio $\mathrm{Im(E_{PNC})}/\beta$ of the APV amplitude to the vector transition polarizability, $\beta$. %Ideally, the uncertainties in $\beta$ and the above ratio have to be comparable. The ratio was measured with a $0.35\%$ accuracy by the Boulder group [Science {\bf 275}, 1759 (1997)]. Currently, there is tension in different determinations of $\beta$. The most recent value [Phys.\ Rev.\ Lett.\ {\bf 123}, 073002 (2019)] of $\beta$, $27.139\,(42)$ $a_0^{3}$ was deduced from the semi-empirical determination of the scalar transition polarizability $\alpha$ and the measured ratio between the scalar and vector polarizability $\alpha/\beta$ . %To address an issue that the reported value is comparable in $\sim\,$ $0.2\%$ This value, however, differs by $\sim 0.7\%$ from a previous determination of $\beta$ [Phys.\ Rev. \ A. \ {\bf{62}}, 052101 (2000)] based on the measured ratio of magnetic-dipole $6S_{1/2}\rightarrow{7S_{1/2}}$ matrix element to $\beta$. Here, we recompute the E1-dipole matrix elements associated with $\alpha^{[2]}$ using the state-of-art coupled-cluster technique and $\alpha^{[2]}$ evaluates to $-262.26\,(48)\,a_0^3$. The resulting determination for $\beta$ is $27.083\,(57)\,a_0^3$ based on the reported ratio $\alpha/\beta$ of $9.905(11)$ [Phys.\ Rev. \ A. {\bf{55}}, 2 (1997)]. We also quantitatively evaluate the effect of additional third-order hyperfine-induced corrections to the $6S_{1/2}\rightarrow{7S_{1/2}}$ transition polarizability. We show that a new ''tensor'' contribution to transition polarizability appears in the analysis and investigate nuclear spin-dependent-polarizability effects on the nuclear anapole moment and the ratio between the scalar and vector polarizabilities.
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