Precision Characterization of the ${}^2$D${}_{5\mathrm{/}2}$ State and Quadratic Zeeman Coefficient in ${}^{171}$Yb${}^{+}$

We report measurements of the branching fraction, hyperfine constant, and second-order Zeeman coefficient of the D${}_{5\mathrm{/}2}$ level in ${}^{171}$Yb${}^{+}$ with up to two orders-of-magnitude improvement in precision compared to previously reported values. We estimate the electric quadrupole reduced matrix element of the S${}_{1\mathrm{/}2}$ $\leftrightarrow$ D${}_{5\mathrm{/}2}$ transition to be 12.5(4) $e{a}_0^2$. Furthermore, we determine the transition frequency of the F${}_{7\mathrm{/}2}$ $\leftrightarrow$ ${}^1$D$[3\mathrm{/}2{]}_{3\mathrm{/}2}$ at 760 nm with a $\sim$25-fold improvement in precision. These measurements provide benchmarks for quantum-many-body atomic-physics calculations and provide valuable data for efforts to improve quantum information processors based on Yb${}^{+}$.