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arXiv:1706.03514 · Optics Express

Spectrally pure heralded single photons by spontaneous four-wave mixing in a fiber: reducing impact of dispersion fluctuations

Jacob G. Koefoed, Søren M. M. Friis, Jesper B. Christensen, Karsten Rottwitt

Published Aug 17, 2017• 23 citations
arXivHTMLPDF

Abstract

We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency.

DOI
10.1364/oe.25.020835

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Spectrally pure heralded single photons by spontaneous four-wave mixing in a fiber: reducing impact of dispersion fluctuations

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We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency. (C) 2017 Optical Society of America

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Study of Raman-free photon pair generation using inter-modal four-wave mixing in a few-mode silica fiber

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We present a comprehensive numerical investigation of entangled photon pair generation via spontaneous four-wave mixing (SFWM) in hollow-core photonic crystal fibers (HC-PCFs). By analyzing various fiber geometries, dispersion profiles, and anti-resonant characteristics, we identify optimal configurations that enhance photon-pair generation efficiency. Our study highlights the crucial roles of group velocity dispersion engineering, pump parameters, and phase-matching conditions in shaping the joint spectral amplitude (JSA) of the emitted photons. Utilizing gas-filled or evacuated HC-PCFs significantly reduces Raman noise by minimizing field overlap with the glass, while maintaining strong nonlinear interactions. The results reveal practical regimes for improving spectral purity and heralding efficiency. These findings provide practical design guidelines for scalable, low-noise quantum light sources suitable for quantum communication technologies.

•May 12, 2025•0 citations
We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency.
We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency. (C) 2017 Optical Society of America
Summary form only given. Single-photon sources are key components in applications of photonic quantum technologies such as quantum key distribution (QKD) [1]. One way of realizing single-photon sources is generation of photon pairs (PP) using spontaneous four-wave mixing (FWM): two photons from a pump p annihilate and create two side-band photons at frequencies determined partly by the energy conservation 2ωρ= ω1+ ω2, where ωp,ω1,ω2are the frequencies of the pump and the two side-bands, respectively, and partly by the phase-matching condition. PP generated spontaneously arrive at indeterministic times but even so, they are useful for QKD because one of the photons can be heralded by detecting the other. The heralded photons are then used for transmitting the quantum key.We propose a higher order mode scheme for generating PP in silica fibers; the side-band photons are generated at center wavelength λ1 = 810 nm in the linearly polarized LP02-mode and at λ2 = 1550 nm in the LP01mode, respectively, by pumping in the LP11-mode at λ7, = 1064 nm, where laser sources are readily available. The 810 nm photon is detectable with relatively cheap and efficient silicon-based single-photon detectors, and the heralded 1550 nm photon is mode-matched with transmission fibers in the low-loss spectral window. We design a silica fiber that phase matches these modes and wavelengths while it also reduces the impacts of core radius fluctuations (CRF) caused by fabrication imperfections; the fiber design is inspired by B. P.-P. Kuo et al. [3] and a sketch of the refractive index profile is shown in Fig. 1(a). The scalar wave equation is solved using appropriate Sellmeier data for Germanium-doped silica and the calculated effective indexes for the three modes versus wavelength are shown in Fig. 1(b) together with the core and cladding refractive indexes; the inset shows the wavelength configuration of the pump and two side-bands; phase matching is achieved when the effective indexes of the three modes lie on a straight line [2]. The nonlinear overlap of the waves in this configuration is approximately 18% of the corresponding overlap where all waves are in the LP01-mode.
Summary form only given. Sources of indistinguishable single photons are a key component of many optical quantum systems such as linear optical quantum computers [1] or quantum communication [2]. Spontaneous four-wave mixing is a promising method for in-fiber photon-pair generation with tailored spectral properties. However, a number of parasitic effects can negatively influence the quality of photons heralded from the pair. In this work, we investigate the impact on the quantum purity of heralded photons of arguably the three most important effects: nonlinear phase modulation (NPM), higher-order dispersion (HOD) and dispersion fluctuations (DF) along the fiber leading to variations in phase matching. For the first time, we directly compare two schemes under each of these effects. The first is the asymmetric scheme in which one of the quantum fields is group-velocity matched to the single pump field while the other walks off [3]. The second is the symmetric collision scheme, which uses two pump fields with different group velocities that pass through each other with each of the two quantum fields copropagating with one of the pumps [4]. In all calculations presented here, we use identical Gaussian pumps ∝ exp[-t2/(2T20)] with T0= 1 ps and a group-slowness difference of Δβ1= 1 x 10-11s/m between all non-copropagating fields. For both schemes we include the effect of NPM using analytical time-domain models [4,5] and choose a high generation probability of R= 0.2 to illustrate the impact. The effect of HOD is included with a novel analytical model for the asymmetric scheme and a numerical split-step method [5] for the collision scheme with all fields experiencing group-velocity dispersion of β2= 50 x 10-2652/m. Lastly, the effect of DFs is investigated using a Brownian-motion model for the phase-matching frequency [6] with a standard deviation σω= 0.5/T0and a correlation length in fluctuations of 10 cm.
We demonstrate theoretically the direct (filter-free) generation of spectrally uncorrelated photon pairs, and consequently high-purity heralded single photons at telecommunication wavelengths, in SOI (silicon-on-insulator) nanowaveguides via spontaneous four-wave mixing (SFWM). The inherent strong waveguide dispersion in such high-index contrast structures is employed for discrete-band phase-matching in order to suppress the pair spectral correlations, and to produce photons in the fundamental spatial mode for easy in-out coupling to single-mode optical fibers. Additionally, by optimizing the source parameters like waveguide length, dispersion and pump bandwidth, the group-velocity of generated photons is also engineered to further eliminate spectral correlations. Extensive numerical mode simulations for various waveguide widths are used to design intrinsically pure photon sources via joint spectral amplitude (JSA) engineering. Purity$>9595% is shown to be achievable in a silica-clad SOI waveguide with a cross-section 220 × 600 nm95^{2}fortypicalvaluesoflengthandpumpbandwidth.Thewavelengthoftheseheraldedsinglephotonscanbetunedintherangeof1266–1363nm(for typical values of length and pump bandwidth. The wavelength of these heralded single photons can be tuned in the range of 1266–1363 nm (fortypicalvaluesoflengthandpumpbandwidth.Thewavelengthoftheseheraldedsinglephotonscanbetunedintherangeof1266–1363nm(\sim$O-band) by varying the pump wavelength. Considering the high accuracy provided by silicon nanofabrication techniques, the feasibility of generating single photons across the wavelength range 1333–1425 nm (E-band) and 1437–1510 nm (S-band) for slightly different waveguide widths (625 nm & 650 nm) is also demonstrated. These filter-free integrated photon sources could be important for large-scale linear optical quantum computation (LOQC) and long-distance fiber-optic quantum key distribution (QKD) networks.
Four-wave mixing in optical fibers has been proven to have many applications within processing of classical optical signals. In addition, recent developments in multimode fibers have made it possible to achieve the necessary phase-matching for efficient four-wave mixing over a very wide bandwidth. Thus, the combination of multimode fiber optics and four-wave mixing is very attractive for various applications. This is especially the case for applications in quantum communication, for example in photon-pair generation. This is the subject of this work, where we discuss the impact of fluctuations in core radius on the quality of the heralded single-photon states and demonstrate experimental results of intermodal spontaneous four-wave mixing for photon-pair generation.
We present a comprehensive numerical investigation of entangled photon pair generation via spontaneous four-wave mixing (SFWM) in hollow-core photonic crystal fibers (HC-PCFs). By analyzing various fiber geometries, dispersion profiles, and anti-resonant characteristics, we identify optimal configurations that enhance photon-pair generation efficiency. Our study highlights the crucial roles of group velocity dispersion engineering, pump parameters, and phase-matching conditions in shaping the joint spectral amplitude (JSA) of the emitted photons. Utilizing gas-filled or evacuated HC-PCFs significantly reduces Raman noise by minimizing field overlap with the glass, while maintaining strong nonlinear interactions. The results reveal practical regimes for improving spectral purity and heralding efficiency. These findings provide practical design guidelines for scalable, low-noise quantum light sources suitable for quantum communication technologies.