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 (Yb-171) with nuclear spin I = 1/2. We analyze the S-series Rydberg states of Yb-171, 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 entangling nuclear spin qubits. Further, we analyze the F = 1/2 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 Omega(c) = 2 pi x 200 kHz or Omega(R) = 2 pi x 6 MHz, respectively, finding that a modest magnetic field (approximate to 200 G) and feasible laser polarization intensity purity (less than or similar to 0.99) are sufficient for gate fidelities exceeding 0.99. We also study singlebeam Raman rotations of the nuclear spin qubits and identify a "magic" linear polarization angle with respect to the magnetic field at which purely ax rotations are possible.