Multimode Spontaneous Parametric Down-Conversion in the Lossy Medium

TL;DR

This paper analyzes multimode spontaneous parametric down-conversion in lossy waveguides using correlation functions, revealing that losses stabilize rather than destroy quantum properties and providing a comprehensive analytical and numerical framework.

Contribution

It introduces a correlation function approach for multimode SPDC in lossy media, with analytical solutions in the single-mode case and a detailed numerical analysis for multimode scenarios.

Findings

Losses do not destroy quantum properties of SPDC.

The evolution can be divided into three stages.

Losses stabilize the final quantum state.

Abstract

We study the process of multimode Spontaneous Parametric Down--Conversion (SPDC) in the lossy, one dimensional waveguide. We propose a description using first order Correlation Functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with a complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three wave mixing with ultrashort pump, linear propagation and attenuation, and we are able to divide the evolution into three stages and predict it qualitatively. We find that losses do not destroy the quantum properties of SPDC but stabilize the final state.