We demonstrate single qubit operations on a trapped atom hyperfine qubitusing a single ultrafast pulse from a mode-locked laser. We shape the pulsefrom the laser and perform a pi rotation of the qubit in less than 50 ps with apopulation transfer exceeding 99% and negligible effects from spontaneousemission or ac Stark shifts. The gate time is significantly shorter than theperiod of atomic motion in the trap (Rabi frequency / trap frequency > 10000),demonstrating that this interaction takes place deep within the strongexcitation regime.
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