Semiclassical and quantum treatments of the interaction between a polychromatic field and a multilevel quantum system coupled to a photon reservoir

Formal expressions are given for the elements of the density matrix of an $n$-level quantum system interacting with a polychromatic electromagnetic field and coupled to the modes of a photon reservoir. The interaction with the polychromatic field is treated in both the semiclassical and quantum approaches, and the expressions obtained for the density matrix in the two cases are compared. It is shown that in most physical situations one can use equivalently the semiclassical or the quantum approach with a simple form of the density matrix of the field at initial time.