Anushree Dey

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 two-qubit control phase gate operation with 97\% fidelity by addressing the individual atomic qubits with lasers.

We theoretically show that when two largely separated trapped atoms interact with a trapped ion via Rydberg excitation of the atoms, the ion-mediated interaction between the atoms exceeds the direct atom-atom interaction by several orders of magnitude. Since the motion of the atoms is much slower than the motion of the ion, we resort to Born-Oppenheimer approximation to calculate the ion-mediated adiabatic potential. We also calculate the ion-mediated phonon modes of the atoms that are separated by more than 10 micron. For cylindrical geometry of the system and both the atoms being excited to the same Rydberg state, the stretched and center-of-mass (COM) axial or transverse phonon modes are found to be almost degenerate, while the phonon modes are non-degenerate when one atom is in a Rydberg state and the other in the ground state. We discuss the non-adiabatic effects in the system that give rise to a Gauge structure and associated geometric phase in the system. This study may open a new perspective in quantum computing and exploring molecular physics associated with a conical intersection using an ion-atom hybrid architecture.