Effect of Atomic Coherence on Absorption in Four-level Systems: an   Analytical study
  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 upto all orders are presented. The absorption features is studied in two regimes, i) the weak middle transition coupling, i.e.   $\Omega_2 << \Omega_{1,3}$ and ii) the strong middle transition coupling   $\Omega_2 >>\Omega_{1,3}$. 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 $\Omega_1 = \Omega_3$. 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 this 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 upper most 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. 
S N Sandhya