Detuned Electromagnetically Induced Transparency in an $N$-type Atom

The electromagnetically induced transparency (EIT) in an $N$ configuration is studied under both resonant and off-resonant conditions. In a certain off-resonant condition the dark state of the four level system, which is almost the same as the resonant dark state in $\Lambda$ configuration, is rebuilt. The actual system with damping is examined using optical Bloch equation, both numerically and analytically. Based on this detuned dark state, some new applications with frequency shifts can be realized.