Quantum extension to the semiclassical theory of electrical susceptibility

Abstract

The semiclassical expressions for susceptibilities are inadequate when quantum aspects of light become prominent. A more appropriate formulation of the electrical susceptibility theory requires the quantization of the electromagnetic field. We show here a way to do this up to the second order, within a low-dimensional system. The generalized expressions reveal that susceptibilities depend on the quantum state of light. As experimentally verifiable consequences of this, we predict new phenomena such as photon number-dependent refractive index, even in the linear regime, and non-quadratic second harmonic generation, which should be appreciable when very low-intensity coherent light is involved. We also deduce when the semiclassical expressions, which happen to be particular cases of those derived here, can be used confidently.