Abstract

Nonlinear systems in optical cavities and two-photon Optical Bistability in particular, have been shown to provide a convenient framework for the generation of squeezed states of light. Many theoretical studies were done on nonlinear two-photon processes in three-level atoms using a two-level effective Hamiltonian^1,2 with a suitable coupling constant for the two-photon interaction, which substitutes the more complicated three level Hamiltonian in the case of large one-photon atomic detuning. Such an approximation, when permitted, highly reduces the complexity of the system, still maintaining its essential features. Here we investigate the limits of the validity of such an approach by a close comparison with a full three-level model,^3,4 especially in the quantum domain. We consider a ladder-three-level atomic medium interacting with two laser fields injected in the cavity, in the general non-resonant and non-degenerate case. The effective two-level model is first derived in a semiclassical framework, starting from the three-level model, and carrying out a constant elimination of the intermediate-level probability amplitude under the assumption of large detuning of the lower transition. The semiclassical equations thus obtained are suitable to an immediate generalization in the form of a quantum mechanical Master Equation. The identification of the atomic relaxation terms is suggested by the special case of adiabatic elimination of the polarizations and population involving the intermediate level. The comparison with the three-level model is performed numerically both in the semiclassical and in the quantum regime. The predictions of the two models are also compared with some recent experimental results that have been obtained using sodium atoms as a three-level nonlinear medium.⁵

© 1994 IEEE