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We study phenomenon of electromagnetically induced absorption in the Hanle configuration by solving time-dependent optical Bloch equations for the case of the closed multilevel F(g) = 1 -> F(e) = 2 transition. Our model gives optical Bloch equations as a non-homogeneous system of ordinary linear differential equations. For weak laser fields (Omega << Gamma i.e. Rabi frequency small compared to spontaneous emission rate), a perturbative method to solve linear differential equations can be applied. Perturbative method is realized by solving (in the time-domain) higher-order corrections to the density matrix which in the sum converge to the exact solution of optical Bloch equations. By its form, each successive correction is also system of ordinary linear differential equations which depends on the solution of previous ones. Corrections are partitioned such that odd give corrections to optical coherences, while even give corrections to populations and Zeeman coherences. We present numerical results for the behavior of density matrix elements with successive corrections, and compare them with exact solution of optical Bloch equations. Electromagnetically induced absorption is observed as a 4th and higher (even) correction to populations, when behavior in respect to both time and magnetic field is viewed. Since in our method each correction depends on the solution of previous ones, we can analyze how (through mechanism of transfer of coherences and transfer of populations between Zeeman sublevels) electromagnetically induced absorption is formed. We also discuss qualitative differences in the behavior (with respect to time) of certain density matrix elements for magnetic fields "inside" and "outside" electromagnetically induced absorption resonance.

Perturbative Solution of Optical Bloch Equations for Analysis of Electromagnetically Induced Absorption