Coincident count rates in absorbing dielectric media

TL;DR

This paper investigates how absorption affects parametric down conversion in nonlinear media, showing that while absorption slightly increases coincident count rates, it negligibly impacts entanglement quality.

Contribution

It introduces a quantum electrodynamics framework to analyze absorption effects on biphoton generation and provides explicit expressions for coincident count rates considering noise polarization fields.

Findings

Absorption causes a negligible increase in count rates (~10^{-12}) at 10% per cm.

Maximally entangled states can still be produced despite strong absorption.

Linear absorption dominates the decay effects over nonlinear noise polarization contributions.

Abstract

A study of the effects of absorption on the nonlinear process of parametric down conversion is presented. Absorption within the nonlinear medium is accounted for by employing the framework of macroscopic QED and the Green tensor quantization of the electromagnetic field. An effective interaction Hamiltonian, which describes the nonlinear interaction of the electric field and the linear noise polarization field, is used to derive the quantum state of the light leaving a nonlinear crystal. The signal and idler modes of this quantum state are found to be a superpositions of the electric and noise polarization fields. Using this state, the expression for the coincident count rates for both Type I and Type II conversion are found. The nonlinear interaction with the noise polarization field were shown to cause an increase in the rate on the order of 10^{-12} for absorption of 10% per cm. This astonishingly small effect is found to be negligible compared to the decay caused by linear absorption of the propagating modes. From the expressions for the biphoton amplitude it can be seen the maximally entangled states can still be produced even in the presence of strong absorption.