Why you should not use the electric field to quantize in nonlinear optics

TL;DR

Using the electric field as a quantization variable in nonlinear optics results in incorrect predictions for squeezing and conversion rates, due to fundamental incompatibility with Maxwell's equations in nonlinear dielectrics.

Contribution

The paper demonstrates that electric field quantization is invalid in nonlinear optics, highlighting the need for alternative approaches for accurate quantum descriptions.

Findings

Electric field quantization yields incorrect squeezing parameters.

Conversion rates are inaccurately predicted when using electric field quantization.

Maxwell's equations cannot be satisfied with electric field as a linear combination of bosonic operators in nonlinear media.

Abstract

We show that using the electric field as a quantization variable in nonlinear optics leads to incorrect expressions for the squeezing parameters in spontaneous parametric down-conversion and conversion rates in frequency conversion. This observation is related to the fact that if the electric field is written as a linear combination of bosonic creation and annihilation operators one cannot satisfy Maxwell's equations in a nonlinear dielectric.