Precision Measurement of Lifetime and Branching Ratios of the $4f^{13}5d6s{}^1[5\mathrm{/}2{]}_{5\mathrm{/}2}$ state in Yb${}^{+}$ ions

We report spectroscopic and time-resolved experimental observations to characterize the $[\mathrm{X}\mathrm{e}]4f^{13}{(}^2{F}_{5\mathrm{/}2}^o)5d6s({}^1\text{\hspace{0.17em}⁣}D){}^1[5\mathrm{/}2{]}_{5\mathrm{/}2}^o$ state in ${}^{172}$Yb${}^{+}$ ions. We access this state from the metastable $4f^{14}5d{(}^2{D}_{3\mathrm{/}2,5\mathrm{/}2})$ manifold and observe an unexpectedly long lifetime of $\tau =37.9(9)\mu$s that allows visible Rabi oscillations and resolved-sideband spectroscopy. Using a combination of coherent population dynamics, high-fidelity detection and heralded state preparation, and optical pumping methods, we measure the branching ratios to the ${}^2{D}_{3\mathrm{/}2}$, ${}^2{D}_{5\mathrm{/}2}$, ${}^2{S}_{1\mathrm{/}2}$ states to be 0.359(2), 0.639(2), 0.0023(16), respectively. The branching ratio to the $4f^{13}6s^2({{}^{2}F}_{7\mathrm{/}2})$ is compatible with zero within our experimental resolution. We also report measurements of its Landé g-factor and the branching ratio of the ${}^2{D}_{5\mathrm{/}2}$ to ${}^2{S}_{1\mathrm{/}2}$ decay in ${}^{172}$Yb${}^{+}$ to be 0.188(3), improving its relative uncertainty by an order of magnitude. Our measurements pave the way to a better understanding of the atomic structure of Yb${}^{+}$ ions, which still lacks accurate numerical descriptions, and the use of high-lying excited states for partial detection and qubit manipulation in the omg architecture.