Progress toward measuring the 6S$_{1/2}$ $\leftrightarrow$ 5D$_{3/2}$ magnetic-dipole transition moment in Ba$^{+}$*

We report the latest results from our effort to measure the magnetic-dipole transition moment (M1) between the $6S_{1/2}$ and $5D_{3/2}$ manifolds in Ba$^{+}$. We describe a new technique for calibrating view-port birefringence and how we will use it to enhance the M1 signal. To access the transition moment we use a variation of a previously proposed technique\footnote {S.R. Williams, \emph{ et. al.} Phys. Rev. A 88, 012515 (2013).} that allows us to isolate the magnetic-dipole coupling from the much larger electric-quadrupole coupling in the transition rates between particular Zeeman sub-levels. Knowledge of M1 is crucial for a parity-nonconservation experiment in the ion where M1 will be a leading source of systematic errors. No measurement of this M1 has been made in Ba$^{+}$, however, there are three calculations that predict it to be 80$\times 10^{-5} \mu_{B}$,\footnote{B.K. Sahoo, \emph{ et. al.} Phys. Rev. A 74, 062504 (2006). } 22$\times 10^{-5} \mu_{B}$,\footnote{G.H. Gossel, \emph{ et. al.} Phys. Rev. A 88, 034501 (2013). } and 17$\times 10^{-5} \mu_{B}$.\footnote{M. Safronova, Private communication} A precise measurement may help resolve this theoretical discrepancy which originates from their different estimations of many-body effects.