Progress toward a polarization rotation measurement of the $6S_{1/2} \leftrightarrow 5D_{3/2}$ magnetic dipole transition amplitude in Ba$^{+}$

We report our progress on the measurement of the magnetic dipole transition moment (\textit{M1}) in Ba$^{+}$ for the $6S_{1/2} (m)\leftrightarrow 5D_{3/2} (m^{'})$ transition with a linearly polarized 2051 nm laser. The motivation behind this study is to make a precise measurement of \textit{M1}, which is the leading source of systematic error in our planned parity nonconservation measurement. To date there are only two theory calculations that have been reported for \textit{M1} in Ba$^{+}$ which are $80\times 10^{-5}\mu_{B}$ [1] and $20 \times 10^{-5}\mu_{B}$ [2]. In our technique, the Rabi frequency was measured for the $6S_{1/2} \leftrightarrow 5D_{3/2} $ transition with $\Delta m=0$ and $\Delta m=2$ as a function of the linear polarization angle of the 2051 nm beam. We used the $\Delta m=2$ transition (that has no \textit{M1} contribution) as a check for systematics in the polarization of the beam. By measuring the polarization dependence of the $\Delta m=0$ transition Rabi frequency we can extract the ratio of the \textit{M1} to the much larger and well known electric quadrupole amplitude, from which we can extract \textit{M1}.\\[4pt] [1] PRA \textbf{74}, 062504\\[0pt] [2], PRA \textbf{88}, 034501.