Various definitions of the coherent states of the angular momentum are shown to be special cases of the oscillator-like coherent states of the groups SU(2) and SO(3) obtained by Mikhailov on the basis of a generalized Schwinger boson realization of the angular momentum algebra. This realization is then generalized to that of the angular momentum algebra of an asymmetric top by means of a transformation from the Euler angles to the Cayley–Klein parameters. The oscillator-like coherent states of an asymmetric top, analogous to those of Mikhailov, are then constructed. It is, then, shown that Janssen's and Mostowski's definitions of the coherent states of a top are special cases of these.
Tailored microwave pulses, to guide asymmetric-top molecules from selected rotational states belonging to the vibronic ground state to generalized angular-momentum coherent states, are designed by using optimal control theory. Characteristics that the molecules have to fulfill in order to achieve the goal with feasible pulses are discussed. Properties of the pulses are discussed as well. The further dephasing among the components of the wave packet which, for the simplest coherent state, is a form of dynamical tunneling, can be locked by exploiting the changes that energy levels and eigenfunctions undergo in the presence of an external static electric field with appropriate intensity. For the special case with
M=0, periodic fields are more flexible in avoiding dephasing. This is shown by examining properties of quasienergies and dressed states resulting from the diagonalization of a truncated Floquet matrix.