Two quantum oscillators coupled with a planar radio frequency ion trap

In this scheme, two quantum oscillators in a planar radio frequency ion trap are coupled by the trap electrodes. The ions motional states encode the quantum bits (qubits), and a swap gate could be achieved. Under different conditions of the experiments, the intensity of the coupling between two quantum oscillators and the dissipation of the system are calculated. We compute fidelities for a quantum swap gate and discuss experimental issues.