Coherent Control of Trapped Ion Qubits with Localized Electric Fields

We present a new method for parallel coherent control of trapped ion qubits in separate interaction zones by simultaneously applying an electric field and a spin-dependent gradient. The phase and amplitude of the effective single-qubit rotation both depend on the electric field, which can be localised to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic field gradients in a surface-electrode ion trap, and measure the localisation of the electric field.