  We demonstrate subpicosecond-time-scale population transfer between the pair
of hyperfine ground states of atomic rubidium using a single laser-pulse. Our
scheme utilizes the geometric and dynamic phases induced during Rabi
oscillation through the fine-structure excited state in order to construct an
$X$ rotation gate for the hyperfine-state qubit system. Experiment performed
with a femtosecond laser and cold rubidium atoms, in a magneto-optical trap,
shows over 98\% maximal population transfer between the clock states.
