Distance between density operators: Applications to the Jaynes-Cummings model

Abstract
A measure for the distance between two arbitrary density operators, based on the Hilbert-Schmidt norm, is investigated. It is applied to the Jaynes-Cummings model where the question of the extent to which a given state is close to the initial state or to another state of interest has commanded a lot of attention. This problem is studied in detail for the whole system as well as for the field and the atom subsystems. The behavior of the distance for some important particular cases is numerically evaluated. Some interesting aspects of the field and the atom dynamics are discovered.