Consideration of electromanetically induced transparency of four level atoms in quantum cavity with fully quantum approach

In this paper, an M type four level system in full quantum approach was considered. To investigate of the Electromagnetically Induced Transparency (EIT) in this system under radiation of one quantized probe field and two quantized control field, the relation between polarization and electric field, and the time evaluation equations of the density matrix were used. And finally the real and imaginary parts of susceptibility coefficients χ for an M type four level system in full quantum approach were obtained. Then, by plotting Reχ and Imχ, the effect of parameters of system such as the amplitude of the control field, number of photon, detuning and decay rate on EIT in full quantum approach were investigated.