Qubit leakage suppression by ultrafast composite pulses

The leakage suppression problem is considered for a three-level ladder-type quantum system, in which the first two levels are the qubit system and the third is the leakage state weakly coupled to the qubit system. We show that two (three) phase- and amplitude-controlled pulses are sufficient for arbitrary qubit controls from the ground (an arbitrary) initial state, with leakage suppressed up to the first order of perturbation without additional pulse-area cost. A proof-of-principle experiment was performed with shaped ultrafast optical pulses and cold rubidium atoms, and the result shows a good agreement with the theory.