We have studied the ionization of Rydberg wave packets by subpicosecond, nearly unipolar electromagnetic field pulses, in the regime where the duration of the electric field is less than the classical Kepler orbit time 2n3 for the wave packet. In contrast to the subpicosecond optical pulses, subpicosecond field pulses can ionize wave packets when the probability density near the inner turning point of the Kepler orbit is low. The transfer of energy from the electromagnetic field to essentially free electrons demonstrates that the pulses are substantially shorter than one field cycle. Such half-cycle pulses can track the wave packet throughout its orbit, in order to study wave packet trajectories or other processes at the quantum-classical boundary
