Degenerate Squeezing in Waveguides: A Unified Theoretical Approach

TL;DR

This paper presents a comprehensive theoretical framework for modeling degenerate squeezing in waveguides, incorporating various nonlinear effects and losses, and provides analytical and benchmark results relevant for quantum sampling applications.

Contribution

It introduces a unified Hamiltonian approach for pulsed SPDC and four-wave mixing in waveguides, including higher-order dispersion and loss effects, with explicit expressions for state evolution.

Findings

Analytical expression for joint spectral amplitude of degenerate squeezing.

Benchmarking against known results in low dispersion limit.

Assessment of source suitability for quantum sampling.

Abstract

We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in $k$-space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the perturbative limit, benchmark our theory against well-known results in the limit of negligible group velocity dispersion, and study the suitability of recently proposed sources for quantum sampling experiments.