Suppose the atom experiences an external classical electric field of frequency ω ω L , given by E → → ( t ) = E → → 0 e − − i ω ω L t + E → → 0 ∗ ∗ e i ω ω L t ; e.g., a plane wave propagating in space. Then under the dipole approximation the interaction Hamiltonian between the atom and the electric field can be expressed as