to complete the spectroscopy. In all cases, read-out is accomplished by observing whether the $760 \mbox{ nm}$ transition de-shelved the ion back to the ground state manifold.

Precision
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Since the lifetimes of the states in ${}^{173}\mathrm{Yb}^+(^2\!F_{7/2}^o)$ are all expected to on the order of 1 day or longer [@Dzuba2016a], the achievable precision of these measurements is likely to be limited by practical considerations (as opposed to $T_1$). In particular, since a small magnetic field will be used to isolate the $M_F\!=\!0 \! \leftrightarrow \!0$ transitions, second-order Zeeman shifts of the clock states can lead to decoherence. Based on the experimenally determined coherence time of the Zeeman-sensitive hyperfine transitions in the ground state of ${}^{171}\mathrm{Yb}^+$ that we have achieved, we anticipate that $1\mbox{ Hz}$ precision can be obtained by keeping the effective magnetic sensitivity of the “clock transitions” ($M_F\!=\!0 \! \leftrightarrow \!0$) in $\mathrm{Yb}^+({}^2F_{7/2}^o)$ below $10^{-3} \mu_\mathrm{B}$. The offset field required to accomplish this will depend upon how close the zero-field hyperfine states with $\Delta F \! = \! \pm 1$ are to degeneracy. Assuming there is a pair with significantly smaller zero-field splitting $\Delta W$ than the rest, the effective magnetic moment associated with an offset field $B_\mathrm{o}$ scales 