In order to understand the effect of the electric field on this simplified atom we are going to choose the electric field linearly polarized with the polarization axis to be parallel with the axis of the | g ⟩ ⟩ to | e ⟩ ⟩ transition, we call this axis the z ^ ^ axis. This assumption has no real loss of generality. In fact if we were to choose another axis, then we would be able to find another state that would be a linear combination of the previous states which would be parallel to the electric field bringing us back to this assumption of a linearly polarized electric field parallel with the transition axis.