An ionic clock qubit inside a circular Rydberg atom
Neutral atoms trapped in optical tweezers and excited to Rydberg states, together with trapped ions, are among the most advanced platforms for quantum simulation and quantum computing. Current experiments often rely on additional atoms in neighboring traps to encode ancilla qubits for local manipulation and readout. Here, we demonstrate a dual ion-Rydberg system comprising two qubits encoded in two individually controlled electrons of the same alkaline-earth atom. The first, a microwave qubit, is encoded in a pair of circular Rydberg states, while the second, an optical qubit, is encoded on a narrow quadrupole transition of the Rydberg atom's ionic core. We demonstrate coherent control of the optical qubit and achieve coherence times of several hundred microseconds under dynamical decoupling. Furthermore, we realize coherent coupling between the two electrons via electrostatic quadrupole interactions over the large separation between the Rydberg electron and the ionic core, and map out its angular tunability. Finally, we demonstrate a two-qubit operation, reminiscent of a M{\o}lmer-S{\o}rensen gate, that evolves through an entangled state of the two qubits driven by the quadrupole coupling. Our work opens a pathway to exploit a pair of individually controlled electronic qubits with tunable coupling for quantum simulation and quantum metrology.