The effect of atomic coherence on absorption in four-level atomic systems: an analytical study

Abstract

The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω2 ≪ Ω1,3 and (ii) the strong middle transition coupling Ω2 ≫ Ω1,3. In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω1 = Ω3. While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.