  This paper deals with different ways to extract the effective two-dimensional
lower level dynamics of a lambda system excited by off-resonant laser beams. We
present a commonly used procedure for elimination of the upper level, and we
show that it may lead to ambiguous results. To overcome this problem and better
understand the applicability conditions of this scheme, we review two rigorous
methods which allow us both to derive an unambiguous effective two-level
Hamiltonian of the system and to quantify the accuracy of the approximation
achieved: the first one relies on the exact solution of the Schrodinger
equation, while the second one resorts to the Green's function formalism and
the Feshbach projection operator technique.
