Effective hamiltonians in two-photon laser theory

Abstract

We show that different equations of motion for the field density matrix of the non-degenerate, two-photon laser are obtained depending upon whether one uses the full or the effective hamiltonian. Although the two models give the same equation for the diagonal elements under certain conditions, we have found no conditions under which they give the same results for the offdiagonal elements. This means that expressions for the linewidths, frequency shifts, etc. obtained using the effective hamiltonian are incorrect. The origin of the discrepancy is the neglect of Stark shifts in the effective hamiltonian approach.