Effects of time ordering in quantum nonlinear optics

TL;DR

This paper investigates how time ordering affects quantum nonlinear optical processes like SPDC, SFWM, and FC, providing analytic approximations and conditions where these effects vanish, enhancing understanding of photon generation.

Contribution

It introduces unitary, Gaussian-preserving analytic approximations for time ordering corrections in quantum nonlinear optics using the Magnus expansion.

Findings

Time ordering corrections vanish with broad phase matching functions.

Analytic approximations are derived for the evolution operator.

Effects on joint spectral amplitude are reduced to quadrature.

Abstract

We study time ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four wave mixing (SFWM) and frequency conversion (FC) using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in spontaneous SPDC and SFWM are reduced to quadrature.