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Physical Review A

Optimizing the coupling efficiency of spontaneous parametric down-conversion photon pairs into single-mode fibers

Nicolas Schwaller, Geobae Park, Ryo Okamoto, Shigeki Takeuchi

Published Oct 28, 2022• 8 citations
Publisher

Abstract

Both correlated-mode coupling efficiency and photon pair flux (brightness) of spontaneous parametric down-conversion (SPDC) coupled into single-mode fibers are key parameters for various quantum information science applications. We present an experimental investigation on the optimization of the correlated-mode coupling efficiency and the brightness of frequency-degenerated SPDC photon pairs into single-mode optical fibers. Using photon pairs generated from a type-I phase-matched bulk $\ensuremath{\beta}$-barium borate crystal pumped by a continuous-wave laser, we carefully evaluated both the correlated-mode coupling efficiency and the brightness of SPDC light coupled to a single-mode optical fiber, while continuously changing the focusing of the pump and collection modes, experimenting with Rayleigh lengths from 3 to 280 (for the pump) and 0.2 to 20 (for the collection) times the crystal length. The measured data suggest that the correlated-mode coupling efficiency can be close to unity for any pump focus, however, the optimal Rayleigh length of the collection mode depends on the pump focus parameter, and the brightness can be increased by tightening the pump focus, provided that the Rayleigh length of the collection mode is precisely adjusted. A maximal correlated-mode coupling efficiency of $99.0\ifmmode\pm\else\textpm\fi{}1.3%$ was experimentally achieved. These results will be useful for photonic quantum science and technology using SPDC sources with high heralding efficiencies.

DOI
10.1103/physreva.106.043719

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Both correlated-mode coupling efficiency and photon pair flux (brightness) of spontaneous parametric down-conversion (SPDC) coupled into single-mode fibers are key parameters for various quantum information science applications. We present an experimental investigation on the optimization of the correlated-mode coupling efficiency and the brightness of frequency-degenerated SPDC photon pairs into single-mode optical fibers. Using photon pairs generated from a type-I phase-matched bulk \ensuremathβ\ensuremath{\beta}\ensuremathβ-barium borate crystal pumped by a continuous-wave laser, we carefully evaluated both the correlated-mode coupling efficiency and the brightness of SPDC light coupled to a single-mode optical fiber, while continuously changing the focusing of the pump and collection modes, experimenting with Rayleigh lengths from 3 to 280 (for the pump) and 0.2 to 20 (for the collection) times the crystal length. The measured data suggest that the correlated-mode coupling efficiency can be close to unity for any pump focus, however, the optimal Rayleigh length of the collection mode depends on the pump focus parameter, and the brightness can be increased by tightening the pump focus, provided that the Rayleigh length of the collection mode is precisely adjusted. A maximal correlated-mode coupling efficiency of 99.0\ifmmode±\else\textpm\fi1.399.0\ifmmode\pm\else\textpm\fi{}1.3%99.0\ifmmode±\else\textpm\fi1.3 was experimentally achieved. These results will be useful for photonic quantum science and technology using SPDC sources with high heralding efficiencies.
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.
We investigate the methods to obtain maximum correlated photon pairs generated in Type I spontaneous parametric down conversion (SPDC) with focused pump beam. We study the effect of pump focusing on the photon collection efficiency of signal and idler modes. The correlated photon pair collection efficiency decreases asymptotically with input pump beam focusing parameter [1]. The results obtained here are expected to be useful in designing appropriate optical fibers for generating efficient entangled photon sources for quantum information applications.
Optimizing the brightness of a spontaneous parametric down-conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wave function, generalizing previous known results, by considering collinear and noncollinear emission. We present analytical expressions for our results in the thin-crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is 1/21/\sqrt{2}1/2​ for collinear degenerate emission and approaches 1/21/21/2 for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\ensuremath{\beta}$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin-crystal regime.
We present an ultrabright polarization-entangled photon source that is optimally coupled into single-mode fibers (SMFs). This study theoretically and experimentally examines the characteristics of spontaneous parametric down-conversion (SPDC) photons, including their spectrum, bandwidth, emission angle, and intensity, as functions of crystal length, temperature and beam waist condition. Notably, we measure the collinear spatial modes of photon-pairs and collection optics under various beam waist conditions and analyze them using a collinear Gaussian approximation model. By employing a simple mode-matching optical setup, we optimize the SMF coupling and heralding efficiencies of the photon-pairs. Consequently, we achieve a spectral brightness exceeding 2.0 MHz/mW/nm from a fiber-coupled entangled photon source, utilizing a 30-mm ppKTP crystal inside a polarization Sagnac interferometer. This represents the highest spectral brightness of SPDC photons generated using a CW laser pumped bulk crystal to date. Polarization entanglement was verified by a quantum state tomography and a polarization-correlation measurement. The fidelity of the entangled state is measured to be 97.8 % and the Bell-CHSH value S = 2.782 +- 0.04. The results obtained here provide practical insights for designing high-performance SPDC sources for satellite-based communication and long-distance optical links with extremely high-photon loss.
Photon sources based on spontaneous parametric down-conversion (SPDC) are central to experimental quantum optics and quantum technologies. Their performance is commonly quantified by three metrics: pair-collection probability, heralding efficiency, and spectral purity. In bulk-crystal SPDC, these metrics are known to be mutually constrained, yet the physical origin of the resulting trade-offs is often obscured. We show that these trade-offs originate from the frequency-dependent population of discrete spatial modes in the SPDC emission. By performing a Laguerre-Gauss mode decomposition at each frequency component, we show how spectral-spatial non-separability impacts collection probability, heralding efficiency, and purity. We apply this framework to two widely used quasi-phase-matching configurations: collinear degenerate type-0 and type-II SPDC in periodically poled bulk crystals, and quantify how different phase-matching functions shape the spectral-spatial mode structure. In particular, for type-II SPDC we compare standard periodically poled and aperiodically poled Gaussian phase matching. We experimentally validate some of our theoretical results using spatial- and spectral-projection measurements. This spectral-spatial mode analysis provides a quantitative and predictive framework for understanding and engineering bulk-crystal photon sources, enabling systematic multi-parameter optimization beyond qualitative design guidelines.
There are several problems that must be solved in order to increase the distance of quantum communication protocols based on photons as an information carriers. One of them is the dispersion, whose effects can be minimized by engineering spectral properties of transmitted photons. In particular, it is expected that positively correlated photon pairs can be very useful. We present the full characterization of a source of single photon pairs at a telecom wavelength based on type II spontaneous parametric down conversion (SPDC) process in a beta-barium borate (BBO) crystal. In the type II process, a pump photon, which is polarized extraordinarily, splits in a nonlinear medium into signal and idler photons, which are polarized perpendicularly to each other. In order for the process to be efficient a phase matching condition must be fulfilled. These conditions originate from momentum and energy conservation rules and put severe restrictions on source parameters. Seemingly, these conditions force the photon pair to be negatively correlated in their spectral domain. However, it is possible to achieve positive correlation for pulsed pumping. The experimentally available degrees of freedom of a source are the width of the pumping beam, the collected modes’ widths, the length of the nonlinear crystal and the duration of the pumping pulse. In our numerical model we use the following figures of merit: the pair production rate, the efficiency of photon coupling into a single mode fiber, the spectral correlation of the coupled photon pair. The last one is defined as the Pearson correlation parameter for a joint spectral distribution. The aim here is to find the largest positive spectral correlation and the highest coupling efficiency. By resorting to the numerical model Ref. [1] we showed in Ref. [2], that by careful adjustment of the pump’s and the collected modes’ characteristics, one can optimize any of the source's parameters. Our numerical outcomes conform to the experimental results presented in Refs [3,4]. Here we investigate typical, experimentally available source parameters: the widths of the pump beam and collected modes ranging from 20μm to 500m, the crystal length ranging from 1mm to 7.5mm while the pulse duration is set to 50fs, 100fs or 150fs. We achieve the correlation coefficient value as high as approximately 0.8, or – for different values of parameters – coupling efficiency equal to 0.76.