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Neutral alkaline earth(-like) atoms have recently been employed in atomicarrays with individual readout, control, and high-fidelity Rydberg-mediatedentanglement. This emerging platform offers a wide range of new quantum scienceapplications that leverage the unique properties of such atoms: ultra-narrowoptical "clock" transitions and isolated nuclear spins. Specifically, theseproperties offer an optical qubit ("o") as well as ground ("g") and metastable("m") nuclear spin qubits, all within a single atom. We consider experimentallyrealistic control of this "omg" architecture and its coupling to Rydberg statesfor entanglement generation, focusing specifically on ytterbium-171($^{171}\text{Yb}$) with nuclear spin $I = 1/2$. We analyze the $S$-seriesRydberg states of $^{171}\text{Yb}$, described by the three spin-$1/2$constituents (two electrons and the nucleus). We confirm that the $F = 3/2$manifold -- a unique spin configuration -- is well suited for entanglingnuclear spin qubits. Further, we analyze the $F = 1/2$ series -- described bytwo overlapping spin configurations -- using a multichannel quantum defecttheory. We study the multilevel dynamics of the nuclear spin states whendriving the clock or Rydberg transition with Rabi frequency $\Omega_\text{c} =2 \pi \times 200$ kHz or $\Omega_\text{R} = 2 \pi \times 6$ MHz, respectively,finding that a modest magnetic field ($\approx200\,\text{G}$) and feasiblelaser polarization intensity purity ($\lesssim0.99$) are sufficient for gatefidelities exceeding 0.99.

Analyzing the Rydberg-based omg architecture for $^{171}$Yb nuclear spins