Simplification of the electromagnetically induced transparency system with degenerate Zeeman states

We propose a transformation method that simplifies quantitative analysis in the Lambda-type electromagnetically induced transparency (EIT) system containing degenerate Zeeman states. This transformation maps several coupled three-state systems into a simple three-state system. Moreover, we demonstrate that the transformation is an excellent approximation under adiabatic conditions and the calculation results from several coupled systems are in good agreement with those from the simple system. The transformation method is a powerful tool for relevant studies of EIT, slow light, and storage of light.