Ion-mediated interaction and controlled-phase-gate operation between two atomic qubits

We propose a toy model of ion-atom hybrid quantum system for quantum computing. We show that when two atomic qubits in two largely separated optical tweezers interact with a single trapped ion through Rydberg excitation of the atoms, there exists an ion-mediated atom-atom interaction which exceeds the direct interatomic interaction at large separation. We employ this mediated interaction to demonstrate a two-qubit control phase-gate operation with 97% fidelity by addressing the individual atomic qubits with lasers.