  Neutral atom qubits with Rydberg-mediated interactions are a leading platform
for developing large-scale coherent quantum systems. In the majority of
experiments to date, the Rydberg states are not trapped by the same potential
that confines ground state atoms, resulting in atom loss and constraints on the
achievable interaction time. In this work, we demonstrate that the Rydberg
states of an alkaline earth atom, ytterbium, can be stably trapped by the same
red-detuned optical tweezer that also confines the ground state, by leveraging
the polarizability of the Yb$^+$ ion core. Using the previously unobserved
\tripletS series, we demonstrate trapped Rydberg atom lifetimes exceeding
$100\,\mu$s, and observe no evidence of auto- or photo-ionization from the trap
light for these states. We measure a coherence time of $T_2 = 59$ $\mu$s
between two Rydberg levels, exceeding the 28 $\mu$s lifetime of untrapped
Rydberg atoms under the same conditions. These results are promising for
extending the interaction time of Rydberg atom arrays for quantum simulation
and computing, and are vital to capitalize on the extended Rydberg lifetimes in
circular states or cryogenic environments.
