Twist-Engineered Nonlinearity in Two-Dimensional Crystals for Tailored Quantum Light

Van der Waals (vdW) materials enable nonlinear-optical engineering with unprecedented resolution: their strong second-order susceptibilities ($\chi^{(2)}$) and twist-tunable interlayer symmetry allow the effective nonlinearity to be shaped continuously, rather than through binary $\pm\chi^{(2)}$ domain inversion as in bulk ferroelectrics. Here, we show that twist-angle domain engineering exploits this continuous degree of freedom to reconstruct target longitudinal nonlinearity profiles with high fidelity. Using spontaneous parametric down-conversion (SPDC) as a benchmark, we demonstrate that twist-engineered vdW crystals yield significantly improved approximations of target phase-matching functions and correspondingly higher single-photon purities, particularly in compact devices where fabrication constraints limit conventional approaches. We further show that this framework remains effective in experimentally relevant vdW materials and demanding non-degenerate wavelength regimes involving mid-infrared photons. More broadly, the ability to continuously and locally program $\chi^{(2)}$ establishes a general framework for tailoring a wide range of SPDC properties, including absolute brightness, joint spectral amplitude structure, signal-idler frequency separation, and temporal wavepacket shape beyond what is accessible in conventional nonlinear crystals. These results position vdW heterostructures as a powerful platform for engineered quantum light sources and open new opportunities for nonlinear-optical devices shaped with monolayer thickness scale.