With this in mind, we can limit ourselves to just the transition from | g ⟩ ⟩ to | e ⟩ ⟩ . We are going to use an electric field which can be written as E → → ( r → → , t ) = z ^ ^ E ( r → → ) cos ⁡ ⁡ ( w t − − ϕ ϕ ( r → → ) ) where z ^ ^ is the transition axis, w is the angular frequency of the light incoming into the atom (think of it as a laser being shone into the atom), ϕ ϕ is the light phase which can depend on the position, and E is the amplitude of the laser light.