Distance between density operators in multiphoton processes

In this paper we investigate the distance between density operators in multiphoton processes. We study the distances between the time-evolved states of the atom, of the field, and of the total system and their respective reference states, compare them with the atomic inversion as well as the purity of the field, disclose their corresponding relations in various multiphoton processes. The physical interpretations are given by using a fully quantized Bloch equation in the two-photon process.