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Materials science forum

Influence of Nonlinear Crystal Properties on Entanglement Generation in Spontaneous Parametric Down-Conversion (SPDC) Sources

Hiba Chakir, Farid Abdi, F. M. Abbou

Published Aug 4, 2026• 0 citations
Publisher

Abstract

The generation of entangled photon pairs through spontaneous parametric down conversion (SPDC) is widely used and considered one of the key entanglement generation techniques in quantum optics. The quality of the entanglement produced depends significantly on the physical properties of the nonlinear crystal employed in the SPDC process. In this study, we investigate the influence of the crystal parameters such as phase matching configurations on the degree of entanglement. Our results demonstrate the importance of crystal selection for achieving highly entangled photon sources, which are essential for applications in quantum communication and quantum information.

DOI
10.4028/p-51fnlo

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The generation of entangled photon pairs through spontaneous parametric down conversion (SPDC) is widely used and considered one of the key entanglement generation techniques in quantum optics. The quality of the entanglement produced depends significantly on the physical properties of the nonlinear crystal employed in the SPDC process. In this study, we investigate the influence of the crystal parameters such as phase matching configurations on the degree of entanglement. Our results demonstrate the importance of crystal selection for achieving highly entangled photon sources, which are essential for applications in quantum communication and quantum information.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
The quantum entangled photon-pair source, as an essential component of optical quantum systems, holds great potential for applications such as quantum teleportation, quantum computing, and quantum imaging. The current workhorse technique for preparing photon pairs involves performing spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. However, the current power consumption and cost of preparing entangled photon-pair sources are relatively high, posing challenges to their integration and scalability. In this paper, we propose a low-power system model for the quantum entangled photon-pair source based on SPDC theory and phase matching technology. This model allows us to analyze the performance of each module and the influence of component characteristics on the overall system. In our experimental setup, we utilize a 5 mW laser diode and a typical type-II barium metaborate (BBO) crystal to prepare an entangled photon-pair source. The experimental results are in excellent agreement with the model, indicating a significant step towards achieving the goal of low-power and low-cost entangled photon-pair sources. This achievement not only contributes to the practical application of quantum entanglement lighting, but also paves the way for the widespread adoption of optical quantum systems in the future.
The characteristics of quantum entangled light sources directly influence the application scenarios and overall performance of quantum systems. By modeling the process of generating time-energy entangled photons via spontaneous parametric down-conversion (SPDC) in a periodically poled lithium niobate (PPLN) crystal, with energy entanglement constituting an essential dimension of this source, the properties of energy entanglement have been systematically investigated in Type-I (e→o + o), Type-II (o→o + e), and Type-0 (e→e + e) quasi-phase matching (QPM) configurations. Through establishing a multivariate correlation model, we quantitatively analyzed the effects of pump parameters (pump linewidth and central wavelength deviation) and crystal parameters (crystal length and temperature) on entanglement metrics including single-photon spectral characteristics, Schmidt number K, measurable parameter R, and frequency overlap O for entangled sources generated by three QPM configurations. The results reveal the strong robustness of Type-I crystals to the pump central wavelength variation and Type-0 systems to the temperature variation. The conclusions might provide theoretical foundations and regulation paradigms for designing time-energy entangled sources tailored to different applications.
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.
Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.