Short coherent control pulse with small random errors in its direction

Abstract

The finite-amplitude short coherent control pulse with small random errors in its direction is considered. We derive the conditions for it to approximate an ideal δ-shaped pulse up to an error in the second order of pulse duration. Whether the symmetric and asymmetric pulse shapes would fulfil these conditions is also analysed. The result shows that, under one of these conditions, all symmetric pulse shapes can fulfil this condition but not for all of the asymmetric ones.