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Physical Review A

Superspontaneous four-wave mixing in a sequence of lossy ring resonators

Amideddin Mataji‐Kojouri, Marco Liscidini

Published Oct 15, 2024• 1 citation
Publisher

Abstract

The authors study photon pair generation by superspontaneous four-wave mixing in single-channel and double-channel sequences of ring resonators in the presence of loss. They show that, in the presence of loss, superradiant photon-pair generation in single-channel sequences is achievable only when the resonators are either deeply over- or undercoupled.

DOI
10.1103/physreva.110.043509

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The authors study photon pair generation by superspontaneous four-wave mixing in single-channel and double-channel sequences of ring resonators in the presence of loss. They show that, in the presence of loss, superradiant photon-pair generation in single-channel sequences is achievable only when the resonators are either deeply over- or undercoupled.
Cooperative photon pair generation by Spontaneous Four-Wave Mixing (SFWM) process in singlechannel and dual-channel side-coupled ring resonator sequences is investigated. Our analysis shows that superlinear growth of generation rate with respect to the number of rings is possible even in presence of loss. Experimental evidence of super-SFWM is provided by comparing individual and collective generation rates obtained from a dual-channel ring resonator sequence. The results are in good agreement with theory and suggest that high photon pair generation rates can be achieved from integrated silicon ring resonator sequences without initiating nonlinear absorption processes.
Composite optical systems can show compelling collective dynamics. For instance, the cooperative decay of quantum emitters into a common radiation mode can lead to super-radiance, where the emission rate of the ensemble is larger than the sum of the rates of the individual emitters. Here, we report experimental evidence of super spontaneous four-wave mixing, an analogous effect for the generation of photon pairs in a parametric nonlinear process on an integrated photonic device. We study this phenomenon in an array of microring resonators on a silicon photonic chip coupled to bus waveguides. We measure a cooperative pair-generation rate that always exceeds the incoherent sum of the rates of the individual resonators. We investigate the physical mechanisms underlying this collective behavior, clarify the impact of loss, and address the aspects of fundamental and technological relevance of our results.
We develop a general Hamiltonian treatment of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.
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.