Gaussian functions are optimal for waveguided nonlinear-quantum-optical processes

TL;DR

This paper proves that Gaussian functions are uniquely optimal for achieving separable joint spectral amplitudes in waveguided nonlinear quantum optics, crucial for quantum light generation and manipulation.

Contribution

It establishes that only Gaussian pump and phase-matching functions produce a separable JSA, solving a key design problem in nonlinear quantum optics.

Findings

Gaussian functions are necessary for JSA separability.

Mapping to quantum information theory reveals the uniqueness of Gaussian states.

Maximizing JSA separability requires one function to be Gaussian.

Abstract

Many nonlinear optical technologies require the two-mode spectral amplitude function that describes them---the \emph{joint spectral amplitude} (JSA)---to be separable. We prove that the JSA factorizes \emph{only} when the incident pump field and phase-matching function are Gaussian functions. We show this by mapping our problem to a known result, in continuous variable quantum information, that only squeezed states remain unentangled when combined on a beam splitter. We then conjecture that only a squeezed state minimizes entanglement when sent through a beam splitter with another pre-specified ket. This implies that to maximize JSA separability when one of the (pump or nonlinear medium) functions is non-Gaussian, the other function \emph{must} be Gaussian. This answers an outstanding question about optimal design of certain nonlinear processes, and is of practical interest to researchers using waveguide nonlinear optics to generate and manipulate quantum light.