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

Abstract

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: ultra-narrow 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 (${}^{171}\text{Yb}$) with nuclear spin $I=1/2$. We analyze the $S$-series Rydberg 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 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 ${\Omega }_{\text{c}}=2\pi \times 200$ kHz or ${\Omega }_{\text{R}}=2\pi \times 6$ MHz, respectively, finding that a modest magnetic field ($\approx 200\text{G}$) and feasible laser polarization intensity purity ($\lesssim 0.99$) are sufficient for gate fidelities exceeding 0.99.

N.C., L.L., and W.H. contributed equally

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