Analytical wave-packet design scheme: Control of dynamics and creation of exotic wave packets

A general analytical formalism is described for the design of the excitation pulse (in the weak-field limit) that will excite a specified target wave packet. These analytical formulas (accurate to third order in the phase) provide multiple solutions for a class of target wave packets and provide a basis for choosing between these solutions. In addition, the possibility of independent compensation of the second- and third-order phase terms offers flexibility in the creation of exotic wave packets. A concrete design example is given for the generation of a well-localized Rydberg atomic wave packet at a specific target time.