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arXiv:1307.3261 · Physical Review A

Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source

María Corona, Karina Garay-Palmett, Alfred B. U’Ren

Published Sep 15, 2011• 62 citations

Abstract

We study the third-order spontaneous parametric down-conversion (TOSPDC) process, as a means to generate entangled photon triplets. Specifically, we consider thin optical fibers as the nonlinear medium to be used as the basis for TOSPDC in configurations where phase matching is attained through the use of more than one fiber transverse modes. Our analysis in this paper, which follows from our earlier paper [Opt. Lett. 36, 190--192 (2011)], aims to supply experimentalists with the details required in order to design a TOSPDC photon-triplet source. Specifically, our analysis focuses on the photon triplet state, on the rate of emission, and on the TOSPDC phase-matching characteristics for the cases of frequency-degenerate and frequency nondegenerate TOSPDC.

DOI: 10.1103/physreva.84.033823

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We study the third-order spontaneous parametric down-conversion (TOSPDC) process, as a means to generate entangled photon triplets. Specifically, we consider thin optical fibers as the nonlinear medium to be used as the basis for TOSPDC in configurations where phase matching is attained through the use of more than one fiber transverse modes. Our analysis in this paper, which follows from our earlier paper [Opt. Lett. 36, 190--192 (2011)], aims to supply experimentalists with the details required in order to design a TOSPDC photon-triplet source. Specifically, our analysis focuses on the photon triplet state, on the rate of emission, and on the TOSPDC phase-matching characteristics for the cases of frequency-degenerate and frequency nondegenerate TOSPDC.

We propose a general scheme to investigate photon triplet generation (PTG) via third-order spontaneous parametric downconversion (TOSPDC) in χ (3) nonlinear structures. Our approach leverages the quantum-classical correspondence between TOSPDC and its reverse classical process, three-wave sum-frequency generation (TSFG), to efficiently estimate the PTG rate. We apply this framework to nonlinear metasurfaces supporting quasi-bound states in the continuum (qBICs) in the optical range. From numerical analysis of noncollinear TSFG with degenerate input waves at qBIC wavelengths, we predict wavelength-tunable three-photon emission with spatio-angular correlations. These findings establish a novel method for modeling TOSPDC and also highlight the potential of nonlinear resonant metasurfaces as compact free-space photon triplet sources with quantum state control.

This paper presents a study of the phasematching properties of the third-order parametric down-conversion process in multimode optical fibers with a step-index profile. Through this process, entangled photon triplets can be generated in the spontaneous regime. We show that phasematching is achieved in a wide range of fiber geometries, provided that the pump field propagates in a higher-order mode. Furthermore, we show the nonlinear coefficient and the absolute emitted flux for each source configuration, evaluated from expressions derived by us in previous theoretical studies concerning the spontaneous and stimulated emission regimes.

We study the processes of spontaneous four wave mixing and of third-order spontaneous parametric downconversion in optical fibers, as the basis for the implementation of photon-pair and photon-triplet sources. We present a comparative analysis of the two processes including expressions for the respective quantum states and plots of the joint spectral intensity, a discussion of phasematching characteristics, and expressions for the conversion efficiency. We have also included a comparative study based on numerical results for the conversion efficiency for the two sources, as a function of several key experimental parameters.

We study the process of seeded or stimulated third-order parametric down-conversion as an extension of our previous work on spontaneous parametric down-conversion (TOSPDC). We present general expressions for the spectra and throughputs expected for the cases where the seed field or fields overlap either only one or two of the TOSPDC modes and allow for both pump and seed to be either monochromatic or pulsed. We present a numerical study for a particular source design, showing that doubly overlapped seeding can lead to a considerably greater generated flux as compared with singly overlapped seeding. We, furthermore, show that doubly overlapped seeding permits stimulated emission tomography for the reconstruction of the three-photon TOSPDC joint spectral intensity. We hope that our paper will guide future experimental efforts based on the process of third-order parametric down-conversion.