Theory of Multimode Squeezed Light Generation in Lossy Media

TL;DR

This paper develops a comprehensive theoretical framework for understanding multimode squeezed light in lossy media, including new methods to identify broadband modes with maximal squeezing.

Contribution

It introduces a unified approach for modeling multimode squeezed light in lossy environments, including a novel broadband basis that maximizes squeezing.

Findings

No broadband basis without quadrature correlations exists in lossy media.

Mercer and Williamson-Euler decompositions do not maximize squeezing.

A new broadband basis is constructed to optimize squeezing measurement.

Abstract

A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson-Euler decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it.