Generation of polarization-entangled Bell states in monolithic photonic waveguides by leveraging intrinsic crystal properties

Advanced photonic quantum technologies -- from quantum key distribution to quantum computing -- require on-chip sources of entangled photons that are both efficient and readily scalable. In this theoretical study, we demonstrate the generation of polarization-entangled Bell states in structurally simple waveguides by exploiting the intrinsic properties of nonlinear crystals. We thereby circumvent elaborate phase-matching strategies that commonly involve the spatial modulation of a waveguide's linear or nonlinear optical properties. We derive general criteria for the second-order susceptibility tensor that enable the generation of cross-polarized photon pairs via spontaneous parametric down-conversion in single-material waveguides. Based on these criteria, we systematically categorize all birefringent, non-centrosymmetric crystal classes in terms of their suitability. Using coupled mode theory, we then numerically analyze cuboid waveguides made from two materials that are highly relevant to integrated photonics: lithium niobate, a well-established platform, and barium titanate, an emerging alternative. We find that barium titanate consistently outperforms lithium niobate by providing a higher nonlinear efficiency and high concurrence over a significantly broader spectral range. These findings outline a practical route toward highly efficient, fabrication-friendly, and scalable sources of polarization-entangled photons for integrated quantum photonic circuits.