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