Validity of the effective Hamiltonian in the two-photon atom-field interaction

Abstract

Two-photon processes are usually treated using effective-Hamiltonian approaches. In this paper the question of the validity of the effective Hamiltonian in the interaction of a single atom with a single-mode radiation field is considered, and conditions under which effective and microscopic Hamiltonians lead to identical results for the reduced density matrix for the field are derived. The conditions and limitations for the validity of the effective Hamiltonian are elucidated by considering the population inversion, photon distribution function, and squeezing in the two approaches.