  Coherent-population-trapping resonance is a quantum interference effect that
appears in the two-photon transitions between the ground-state hyperfine levels
of alkali atoms and is often utilized in miniature clock devices. To
quantitatively understand and predict the performance of this phenomenon, it is
necessary to consider the transitions and relaxations between all hyperfine
Zeeman sublevels involved in the different excitation processes of the atom. In
this study, we constructed a computational multi-level atomic model of the
Liouville density-matrix equation for 32 Zeeman sublevels involved in the $D_1$
line of $^{133}$Cs irradiated by two frequencies with circularly polarized
components and then simulated the amplitude and shape of the transmitted light
through a Cs vapor cell. We show that the numerical solutions of the equation
and analytical investigations adequately explain a variety of the
characteristics observed in the experiment.
