Accurate and agile digital control of optical phase, amplitude and frequency for coherent atomic manipulation of atomic systems

We demonstrate a system for fast and agile digital control oflaser phase, amplitude and frequency for applications in coherent atomicsystems. The full versatility of a direct digital synthesis radiofrequencysource is faithfully transferred to laser radiation via acousto-opticmodulation. Optical beatnotes are used to measure phase steps up to 2π,which are accurately implemented with a resolution of ≤ 10 mrad. By linearizing the optical modulation process, amplitude-shaped pulses of durations ranging from 500 ns to 500 ms, in excellent agreement with the programmed functional form, are demonstrated. Pulse durations are limited only by the 30 ns rise time of the modulation process, and a measured extinction ratio of > 5 × 1011 is achieved. The system presented here was developed specifically for controlling the quantum state of trapped ions with sequences of multiple laser pulses, including composite and bichromatic pulses. The demonstrated techniques are widely applicable to other atomic systems ranging across quantum information processing,frequency metrology, atom interferometry, and single-photon generation.