Analyzing the Rydberg-based optical-metastable-ground architecture for Yb171 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 ($^{171}\mathrm{Yb}$) with nuclear spin $I=\frac{1}{2}$. We analyze the $S$-series Rydberg states of $^{171}\mathrm{Yb}$, described by the three spin-$\frac{1}{2}$ constituents (two electrons and the nucleus). We confirm that the $F=\frac{3}{2}$ manifold, a unique spin configuration, is well suited for entangling nuclear spin qubits. Further, we analyze the $F=\frac{1}{2}$ 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 ${\mathrm{\ensuremath{\Omega}}}_{c}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}200\phantom{\rule{0.28em}{0ex}}\text{kHz}$ or ${\mathrm{\ensuremath{\Omega}}}_{R}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}6\phantom{\rule{0.28em}{0ex}}\text{MHz}$, respectively, finding that a modest magnetic field ($\ensuremath{\approx}200\phantom{\rule{0.28em}{0ex}}\text{G}$) and feasible laser polarization intensity purity ($\ensuremath{\lesssim}0.99$) 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 ${\ensuremath{\sigma}}_{x}$ rotations are possible.