A Quantum Extension of the Semiclassical Theory of Electrical Susceptibility

It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities. The expressions derived allow to determine a set of conditions for the validity of the semiclassical approximation and predict interesting new phenomena such as photon number dependent susceptibility.