Short coherent control pulse with small random errors in its direction

TL;DR

This paper analyzes finite-amplitude short control pulses with small random directional errors, deriving conditions for them to approximate ideal delta pulses, and compares symmetric and asymmetric pulse shapes in meeting these conditions.

Contribution

It provides new conditions under which short control pulses with small random errors can effectively approximate ideal delta pulses, including analysis of symmetric and asymmetric shapes.

Findings

Symmetric pulse shapes can fulfill the approximation conditions.

Not all asymmetric pulse shapes satisfy the conditions.

Conditions derived are valid up to second order in pulse duration.

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 delta-shaped pulse up to an error in the second order of pulse duration. Whether the symmetric and asymmetric pulse shapes would fulfill these conditions is also analyzed. The result shows that, under one of these conditions, all symmetric pulse shapes can fulfill this condition but not for all asymmetric ones..