 This is akin to assuming that the operators are uncorrelated, and is a good approximation in the classical limit.It turns out that the resulting equations give the correct qualitative behavior even in the single excitation regime.Additionally, to simplify the equations we make the following replacements

And the Maxwell–Bloch equations can be written in their final form

Within the dipole approximation and rotating-wave approximation, the dynamics of the atomic density matrix, when interacting with laser field, is described by optical Bloch equation, whose effect can be divided into two parts