On the consistency of Rabi frequency calculations

Abstract

Three methods of calculating the on-resonance Rabi frequency for an atomic transition are described in detail. These methods are the use of standard angular momentum coupling formula for state expansion the application of the reduction formula for composite systems; and the application of reduction equations for vector operators from Condon and Shortley. It is shown that all three methods are equivalent, in contrast with previously reported difficulties in obtaining consistency in the phase. Each method is illustrated by calculating the Rabi frequencies for each hyperfine transition in a n2S 1/2-n'2q3/2 manifold. The importance of consistency in the ordering of the quantum numbers in matrix elements of operator components is discussed.