Spectroscopic Stability in Two-Photon Absorption by Atoms

When there exists no external field, physical results should not depend on the choice of quantization axis. This theorem is known as spectroscopic stability and is well established for one photon absorption and emission processes. In two photon absorption by a three level atom one can make the excitation of the top level forbidden if the absorption processes are restricted to one selection rule in ΔM (=+1, 0 or -1). The choice of selection rule assumes relative orientation between the polarization of the radiation field and an external field. If this relative orientation is changed the selection rule would also change and the top level would appear as a final result of two photon absorption . A question is what happens if the external field disappears in the latter case. Would the top level disappear although the selection rule stays unaltered? It is shown that the probability of having the top level disappears when the external field vanishes, confirming the spectroscopic stability and the degree of violation is obtained as a function of the strength of the external field.