Faraday rotation in a resonant five-level system via electromagnetically induced transparency

We study the Faraday rotation of polarization of a probe field in a cold, coherently driven five-level system with an M-type configuration. By means of a method of multiple scales we derive two coupled nonlinear envelope equations, which govern the evolution of two circularly polarized components of the probe field. It is shown that due to the quantum interference effect induced by two control fields, one can obtain a large rotation angle with a very low absorption of the probe field. In addition, an efficient control over the polarization state of the probe field in the system can also be easily realized.