Now, the main question we want to solve is what is the average force felt by the atom under this kind of light? We are interested by f = ⟨ ⟨ F ^ ^ ⟩ ⟩ ¯ ¯ = ⟨ ⟨ − − ∇ ∇ V ^ ^ e . d . ( r ^ ^ , t ) ⟩ ⟩ ¯ ¯ which represents the average force felt by the atom. In here the brackets represent an average over all the internal states of the atom (in a quantum fashion), and the bar represent a temporal average in the classical fashion. V ^ ^ e . d . represents the potential due to the electric dipole of the atom.