Comparative study on quasi-phase-matching of Type-0, Type-I, and Type-II configurations for SPDC in PPLN crystals

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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.