Azimuthal eigenmodes at strongly non-degenerate parametric down-conversion

TL;DR

This paper explores the angular structure of radiation in non-degenerate parametric down-conversion in the terahertz range, revealing azimuthal eigenmodes and a scattering matrix that describe biphoton production and macroscopic quantum states.

Contribution

It introduces azimuthal eigenmodes for the nonlinear interaction operator in non-degenerate parametric down-conversion, enabling analysis of optical-terahertz biphoton generation.

Findings

Azimuthal eigenmodes can be obtained under certain approximations.

A Bogolyubov transformation describes the evolution of field operators.

A scattering matrix for arbitrary parametric gain is derived.

Abstract

Quantum-optical technologies based on parametric light down-conversion are not yet applied in the terahertz frequency range. This is owing to the complexity of detecting single photons in the terahertz frequency range and the strong entanglement of modes of optical-terahertz biphotons. This study investigates the angular structure of scattered radiation generated by strongly non-degenerate parametric down-conversion when the frequency of the idler radiation does not exceed several terahertz. We demonstrate that under certain approximations, it is possible to obtain azimuthal eigenmodes for the nonlinear-interaction operator. The solution of the evolution equations for the field operators in these eigenmodes has the form of the Bogolyubov transformation, which allows a scattering matrix to be obtained for arbitrary values of the parametric gain. This scattering matrix describes both the production of biphoton pairs and the generation of intense fluxes of correlated optical-terahertz fields that form a macroscopic quantum state of radiation in two spectral ranges.