We present the genral and rigorous equation of motion for the reduced density matrix (RDM) describing the time evolution of a system A coupled to a system B for any initial statistical state. We derive the corresponding perturbation expansion up to the second order in the interaction and discuss it for a variety of physical initial conditions. We apply the formalism to the interaction of radiation with matter in terms of a single-mode field coupled to a two-level atomic system through electric-dipole interaction. We solve the equations of motion for the dynamical variables describing the atomic system interacting with i) thermal and ii) coherent incident radiation or coupled to iii) a field produced by classical currents. We show that the «effective» semi-classical Hamiltonian can be established in the case ii), whereas the semi-classical approximation (SCA) is meaningless in the case i). We discuss the range of validity of the SCA in terms of the exactly solvable rotating-wave version of the dipole coupling. We report drastic deviations from the SCA results even in the limit of high intensity of the incident coherent field unless the coupling is very weak or the interaction time elapsed is very short. We analyse the relevance of the initial photon statistics by comparing the SCA with the exact RDM. We discuss the validity of the SCA for various spectroscopic techniques.
ASJC Scopus subject areas
- Physics and Astronomy(all)