Precise pulse shaping for quantum control of strong optical transitions

Advances of quantum control technology have led to nearly perfect single-qubit control of nuclear spins and atomic hyperfine ground states. In contrast, quantum control of strong optical transitions, even for free atoms, are far from being perfect. Developments of such quantum control appears to be bottlenecked by available laser technology for generating isolated, sub-nanosecond optical waveforms with sub-THz programming bandwidth. Here we propose a simple and robust method for the desired pulse shaping, based on precisely stacking multiple delayed picosecond pulses. Our proof-of-principal demonstration leads to arbitrarily shapeable optical waveforms with 30~GHz bandwidth and $100~$ps duration. We confirm the stability of the waveforms by interfacing the pulses with laser-cooled atoms, resulting in ``super-resolved'' spectroscopic signals. This pulse shaping method may open exciting perspectives in quantum optics, and for fast laser cooling and atom interferometry with mode-locked lasers.