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New Journal of Physics

Design of bright, fiber-coupled and fully factorable photon pair sources

Luis Edgar Vicent, Alfred B. U’Ren, Radhika Rangarajan, Clara I. Osorio, Juan P. Torres, Lijian Zhang, Ian A. Walmsley

Published Sep 15, 2010• 46 citations
Publisher

Abstract

From quantum computation to quantum key distribution, many quantum-enhanced applications rely on the ability to generate pure single photons. Even though the process of spontaneous parametric downconversion (SPDC) is widely used as the basis for photon-pair sources, the conditions for pure heralded single-photon generation, taking into account both spectral and spatial degrees of freedom, have not been fully described. We present an analysis of the spatio-temporal correlations present in photon pairs produced by type-I, non-collinear SPDC. We derive a set of conditions for full factorability in all degrees of freedom—required for the heralding of pure single photons—between the signal and idler modes. In this paper, we consider several possible approaches for the design of bright, fiber-coupled and factorable photon-pair sources. We show through numerical simulations of the exact equations that sources based on: (i) the suppression of spatio-temporal entanglement according to our derived conditions and (ii) a tightly focused pump beam together with optimized fiber-collection modes and spectral filtering of the signal and idler photon pairs, lead to a source brightness of the same order of magnitude. Likewise, we find that both of these sources lead to a drastically higher factorable photon-pair flux, compared to an unengineered source.

DOI
10.1088/1367-2630/12/9/093027

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From quantum computation to quantum key distribution, many quantum-enhanced applications rely on the ability to generate pure single photons. Even though the process of spontaneous parametric downconversion (SPDC) is widely used as the basis for photon-pair sources, the conditions for pure heralded single-photon generation, taking into account both spectral and spatial degrees of freedom, have not been fully described. We present an analysis of the spatio-temporal correlations present in photon pairs produced by type-I, non-collinear SPDC. We derive a set of conditions for full factorability in all degrees of freedom—required for the heralding of pure single photons—between the signal and idler modes. In this paper, we consider several possible approaches for the design of bright, fiber-coupled and factorable photon-pair sources. We show through numerical simulations of the exact equations that sources based on: (i) the suppression of spatio-temporal entanglement according to our derived conditions and (ii) a tightly focused pump beam together with optimized fiber-collection modes and spectral filtering of the signal and idler photon pairs, lead to a source brightness of the same order of magnitude. Likewise, we find that both of these sources lead to a drastically higher factorable photon-pair flux, compared to an unengineered source.
We present a source of near-infrared photon pairs based on the process of spontaneous parametric downconversion (SPDC), for which the joint signal-idler quantum state is designed to be factorable in the frequency-time and in the transverse position-momentum degrees of freedom. Our technique is based on the use of a broadband pump and vector group velocity matching between the pump, signal, and idler waves. We show experimentally that a source based on this technique can be configured for the generation of: i) pure heralded single photons, and ii) polarization-entangled photon pairs which are free from spectral correlations, in both cases without resorting to spectral filtering. While critical for many applications in optical quantum information processing, such a source has not previously been demonstrated.
Spontaneous parametric down-conversion (SPDC) is a reliable and robust source of photons for quantum information applications. For applications that involve operations such as entanglement swapping or single-photon heralding, two-photon states are required to be factorable (uncorrelated) in their spectral and spatial degrees of freedom. We report the design and experimental characterization of an SPDC source that has been optimized for high spectral and spatial purity. The source is pumped by the 776 nm output of a mode-locked Ti:Sapphire laser and consists of a periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal phase-matched for collinear type-II SPDC. The dispersive properties of PPKTP at these wavelengths is such that it is possible to minimize the spectral entanglement by matching the widths of the pump to the spectral phase-matching function. The spatial entanglement is minimized through careful control of the pump focus, yielding nearly single-mode emission. An advantage of this approach is that the emission rate into the collection modes is very high, resulting in a very bright SPDC source. We also report a scheme that employs the output of collinear sources such as these to produce polarization-entangled photon pairs. The scheme, which requires only simple polarization elements, can be scaled to N-photon GHZ states.
The interference of single heralded photons from multiple parametric downconversion sources requires photon pairs in factorable states. Typically, these are selected from an ensemble of pairs by narrow filters that remove any exhibiting correlations. In order to eliminate these lossy filters, factorable photon pairs free from any spatio-temporal correlations must be created directly at each source. This requires careful engineering of the group velocity dispersion of the nonlinear crystal in which pair generation takes place. Several schemes have been proposed to do this in the plane-wave regime, but in a realistic experiment one must also take into account the effects of focusing on the two-photon state. Focusing leads to space–time coupling between the pump structure and the downconverted pairs that has the potential to reduce their factorability, but if carefully managed can actually increase it. In this paper, we consider some of the effects of focusing and their consequences for pure single photon generation.
Entangled photon pairs play a crucial role in emerging quantum technologies, acting as tamper-proof padlocks in secure quantum communication, ultra-precise probes in quantum metrology and high-fidelity information carriers in photonic quantum computing. Amongst the many technological possibilities for generating photon pairs, sources based on spontaneous parametric down-conversion (SPDC) in second-order nonlinear crystals are still the workhorse tool in quantum optics laboratories, and more recently even in long-distance quantum communication with satellites. SPDC is a widely used method to create entangled photon pairs. The number of photon pairs that can be detected in a particular choice of collection modes, typically being optical single-mode fibers, depends critically on the spatial characteristics of the multi-mode SPDC emission as well as the particular beam waist of the collection modes. While several studies have already addressed the issue of optimal fiber coupling of SPDC photons in theory and experiment, the results of these studies arrive at different conclusions. Here, we present the results of a comprehensive experimental study on the optimal collection of photon pairs into single-mode optical fibers. Our approach is based on quasi-phase-matched type II SPDC from a periodically poled KTiOPO4 (ppKTP) crystal. We discuss the influence of pump and collection focal parameters on the spectral brightness and heralding efficiency, as well as practical issues of alignment tolerances into an optical single mode fiber. Further, Using two-photon interference (Hong-Ou-Mandel interference), we assess the spectral bandwidth of the photon pairs for variable crystal lengths. The results are in good agreement with our theoretical model, thus providing the recipe of building ultra bright and stable entangled photon sources.
In an experiment reported recently (Mosley et al 2008 Phys. Rev. Lett. 100 133601), we demonstrated that, through group velocity matched parametric downconversion, heralded single photons can be generated in pure quantum states without spectral filtering. The technique relies on factorable photon pair production, initially developed theoretically in the strict collinear regime; focusing—required in any experimental implementation—can ruin this factorability. Here, we present the numerical model used to design our single photon sources and minimize spectral correlations in the light of such experimental considerations. Furthermore, we show that the results of our model are in good agreement with measurements made on the photon pairs and give a detailed description of the exact requirements for constructing this type of source.