Analyzing the Rydberg-based optical-metastable-ground architecture for Yb 171 nuclear spins

Neutral alkaline earth(like) atoms have recently been employed in atomic arrays with individual readout, control, and high-fidelity Rydberg-mediated entanglement. This emerging platform offers a wide range of new quantum science applications that leverage the unique properties of such atoms: ultranarrow optical "clock"transitions and isolated nuclear spins. Specifically, these properties offer an optical qubit (o) as well as ground (g) and metastable (m) nuclear spin qubits, all within a single atom. We consider experimentally realistic control of this omg architecture and its coupling to Rydberg states for entanglement generation, focusing specifically on ytterbium-171 (Yb171) with nuclear spin I=12. We analyze the S-series Rydberg states of Yb171, described by the three spin-12 constituents (two electrons and the nucleus). We confirm that the F=32 manifold, a unique spin configuration, is well suited for entangling nuclear spin qubits. Further, we analyze the F=12 series, described by two overlapping spin configurations, using a multichannel quantum defect theory. We study the multilevel dynamics of the nuclear spin states when driving the clock or Rydberg transition with Rabi frequency ωc=2π×200kHz or ωR=2π×6MHz, respectively, finding that a modest magnetic field (≈200G) and feasible laser polarization intensity purity (≲0.99) are sufficient for gate fidelities exceeding 0.99. We also study single-beam Raman rotations of the nuclear spin qubits and identify a "magic"linear polarization angle with respect to the magnetic field at which purely σx rotations are possible.