Long-lived metastable states in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:msup> <mml:mi>f</mml:mi> <mml:mn>13</mml:mn> </mml:msup> <mml:mn>5</mml:mn> <mml:mi>d</mml:mi> <mml:mn>6</mml:mn> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> configuration of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>Yb</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> </mml:math>

We study the occurrence of long-lived metastable states in the 4f$^{13}$5d6s electron configuration of Yb$^+$. By optical pumping of a single trapped ion on the $^2F^\text{o}_{7/2}\rightarrow (7/2,0)_{7/2}$ transition at 377.5 nm, we prepare a wide range of metastable electronic states. We use a co-trapped control ion to sympathetically cool the spectroscopy ion, allowing us to accurately time its subsequent decay. We record a strong decay signal corresponding to a lifetime of 0.92(8) s, a weaker decay signal with lifetime 9.8(+2.9, -2.0) s, and find evidence for a much longer lifetime, $>$ 30 s. We identify the metastable states with these lifetimes qualitatively, and corroborate our results with atomic structure calculations that support the observed lifetimes and decay paths. These long-lived states provide new opportunities in qubit and qudit state detection and optical clocks.