Generation of photon pairs by spontaneous four-wave mixing in linearly uncoupled resonators

TL;DR

This paper investigates photon pair generation through spontaneous four-wave mixing in two uncoupled resonators with independent tuning, analyzing different coupling schemes and deriving formulas for pair generation rates.

Contribution

It introduces a novel structure of two linearly uncoupled resonators with nonlinear interaction, providing analytic expressions for photon pair generation rates in this setup.

Findings

Derivation of pair generation rate formulas for uncoupled resonator structures.

Comparison of two coupling schemes: directional coupler and Mach-Zehnder interferometer.

Demonstration of the potential advantages over single resonator systems.

Abstract

We present a detailed study of the generation of photon pairs by spontaneous four-wave mixing in a structure composed of two linearly uncoupled resonators, where energy can be transferred from one resonator to another only through a nonlinear interaction. Specifically, we consider the case of two racetrack-shaped resonators connected by a coupler designed to guarantee that the resonance comb of each resonator can be tuned independently, and to allow the nonlinear interaction between modes that belong to different combs. We show that such a coupler can be realized in at least two ways: a directional coupler or a Mach-Zehnder interferometer. For these two scenarios, we derive analytic expressions for the pair generation rate via single-pump spontaneous four-wave mixing, and compare these results with that achievable in a single ring resonator.