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
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
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.
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$>95^{2}fortypicalvaluesoflengthandpumpbandwidth.Thewavelengthoftheseheraldedsinglephotonscanbetunedintherangeof1266–1363nm(\sim$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.
The field of quantum optics offers the intriguing possibility of developing new, potentially ground-breaking technologies based on the laws of quantum physics. Single quanta of light, called photons, are at the heart of many such quantum optical technologies. They can serve, for example, as information carriers in quantum cryptography and in quantum-information processing. If such applications are to fulfill their enormous potential, it is essential to have sources available that provide photons in the required quantum states. An established way of generating states of single photons is based on photon-pair sources. In this approach, the detection of one photon of a pair heralds the presence of the partner photon, which can then be further processed. However, to generate heralded photons in pure quantum states, specific conditions have to be met, making the design and implementation of such sources challenging. This thesis presents two new photon-pair sources that allow the heralded generation of single photons with high purity. Both sources are based on optical fiber, which allows high collection efficiencies for the generated states and opens the possibility of easy integration into modern-day fiber networks. Chapter 1 provides an introduction to quantum optical technologies and gives a short overview of current approaches to generate pure single photons. Chapter 2 presents the basic theory on which the experimental work presented in Chapters 3 and 4 is based. It explains the concept of a spectrally broad single photon and how photon purity can be tested using Hong-Ou-Mandel (HOM) interference. Subsequently, the properties of photon-pair states and the heralded generation of single photons from such states are discussed. It is shown that for a heralded photon to be pure, the original photon pair has to be in a factorable state, that is, free of any correlations. The introduced theory is then applied to spontaneous four-wave mixing (SFWM) in optical fibers, a nonlinear process that allows the generation of photon pairs. It is shown how the factorability of the created pairs depends on the fiber's dispersion properties, and the necessary conditions for the generation of factorable states are derived. The chapter concludes with an analysis of the photon statistics of the four-wave mixing process, explaining how statistics and the g(2) correlation function can be used to evaluate the factorability of the SFWM output state. Chapters 3 and 4 contain the main results of this thesis. Chapter 3 presents the first spectrally decorrelated photon-pair source bridging the visible and telecommunication wavelength ranges. The photon pairs are generated by SFWM in a photonic crystal fiber (PCF). The chapter documents the procedure of how the PCF source was designed and fabricated, as well as its characterization based on spectral measurements and photon statistics. One photon of the pair state is generated in the visible at 513.5 nm, where it can be efficiently detected with silicon-based single-photon detectors. It serves as a herald for its broadband partner photon, which is emitted in the telecom wavelength range at 1547 nm. A spectral coincidence measurement shows that the heralded photon exhibits a purity of up to 0.82. At increased pump powers, even the heralded generation of higher photon-number states in the telecom band becomes feasible. In Chapter 4, we use commercial birefringent fiber to herald high-purity photons of picosecond duration at 848 nm. The presented two-source HOM interference experiment shows that the heralded unfiltered state has a purity of at least 0.73. This value is increased to 0.84 with the application of wavelength filters suppressing low-intensity side peaks in the spectrum. The heralded photons are coupled into a single-mode fiber with an efficiency of 85%, the highest reported value to date for factorable sources. It is also shown that a commercial polarization controller can be used to fine-tune the generated wavelengths. This facilitates matching photons from multiple sources, as required for optical quantum computing schemes. Chapter 5 summarizes all results and provides an outlook toward potential future projects.