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    Entanglement certification in bulk nonlinear crystals for degenerate and nondegenerate spontaneous parametric down conversion: Spectral filter effects on transverse spatial correlations

    Hashir Kuniyil*, Asad Ali, and Saif Al-Kuwari

    • *Contact author: hkuniyil@hbku.edu.qa

    Phys. Rev. A 113, 052607 – Published 11 May, 2026

    DOI: https://doi.org/10.1103/drvp-dv4b

    Abstract

    Spatial correlations of photon pairs from spontaneous parametric down-conversion (SPDC) underpin quantum imaging and entanglement certification. We present the first systematic study of spectral filter bandwidth effects on transverse spatial correlations in bulk Type-I BBO for degenerate and nondegenerate configurations. In the far field, the degenerate conditional momentum width is pump-limited and filter-invariant, while nondegenerate configurations exhibit monotonic growth in both marginal and conditional momentum widths—with the walk-off axis approximately 100 times more sensitive than the non-walk-off axis. In the near field, we identify a previously unreported flat-dip-rise profile: the conditional position width narrows by approximately 10% at an optimal bandwidth Δdip≈1.35ΔλSPDC before rising due to geometric displacement. When the filter is placed on the idler arm, the dip shifts by the exact factor (λi/λs)2. Both results are universal for any nondegenerate SPDC source, requiring only a finite crystal length, dθ/dλ≠0, and incoherent spectral averaging. The Reid Einstein-Podolsky-Rosen uncertainty product is consistently smaller on the walk-off axis—a structural advantage of bulk birefringent geometry absent in quasiphase-matched sources. The optimal filter bandwidth ΔF=Δdip is determined entirely by the intrinsic phase-matching bandwidth of the crystal and is directly readable from the X-entanglement spectral width of the source.

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