Entanglement certification in bulk nonlinear crystals for degenerate and non-degenerate SPDC: spectral filter effects on transverse spatial correlations

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 non-degenerate configurations. In the far field, the degenerate conditional momentum width is pump-limited and filter-invariant, while non-degenerate configurations exhibit monotonic growth in both marginal and conditional momentum widths -- with the walk-off axis $\approx 100$ 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 $\approx 10\%$ at an optimal bandwidth ${\Delta }_{\mathrm{dip}}\approx 1.35\Delta {\lambda }_{\mathrm{SPDC}}$ before rising due to geometric displacement. When the filter is placed on the idler arm, the dip shifts by the exact factor $({\lambda }_i/{\lambda }_s{)}^2$. Both results are universal for any non-degenerate SPDC source, requiring only a finite crystal length, $d\theta /d\lambda \ne 0$, and incoherent spectral averaging. The Reid EPR uncertainty product is consistently smaller on the walk-off axis -- a structural advantage of bulk birefringent geometry absent in quasi-phase-matched sources. The optimal filter bandwidth ${\Delta }_F={\Delta }_{\mathrm{dip}}$ 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.

16 pages including references, 8 figures, 4 in main sections and 4 in appendices

References in corpus (25)

• Experimental quantum teleportation
• Advances in Photonic Quantum Sensing
• Quantum Imaging with Undetected Photons
• Experimental realization of sub-shot-noise quantum imaging
• Imaging with a small number of photons
• Spatial correlations in parametric down-conversion
• Imaging high-dimensional spatial entanglement with a camera
• Simultaneous near-field and far field spatial quantum correlations in spontaneous parametric down-conversion
• EPR-based ghost imaging using a single-photon-sensitive camera
• Advances in quantum imaging
• Introduction to the Transverse Spatial Correlations in Spontaneous Parametric Down-Conversion through the Biphoton Birth Zone
• Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology
• Transverse Entanglement Migration in Hilbert Space
• Theory of Quantum Imaging with Undetected Photons
• High-sensitivity imaging with multi-mode twin beams
• Anisotropically high entanglement of biphotons generated in spontaneous parametric down conversion
• Quantum imaging of biological organisms through spatial and polarization entanglement
• Heisenberg Scaling Quantum Microscopy: Experiment and Theory
• Compressive Object Tracking using Entangled Photons
• Pixel super-resolution using spatially-entangled photon pairs
• Effects of crystal length on the angular spectrum of spontaneous parametric downconversion photon pairs
• Quantum Imaging for Semiconductor Industry
• Propagation-induced entanglement revival
• Anisotropic Spatial Entanglement
• Certifying spatial entanglement between non-degenerate photon pairs with a camera