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

Abstract

Van der Waals (vdW) materials enable nonlinear-optical engineering with unprecedented resolution: their strong second-order susceptibilities ($χ^{(2)}$) and twist-tunable interlayer symmetry allow the effective nonlinearity to be shaped continuously, rather than through binary $\pmχ^{(2)}$ 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 $χ^{(2)}$ 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.

Figures (9)

• Figure 1: (a) Schematic of the core concept behind conventional domain-engineering techniques for spectral shaping of SPDC single-photon wave-packets. The relative nonlinear coefficient $\chi^{(2)}_0/|\chi^{(2)}_0|$ is restricted to alternate between +1 and –1 across crystal domains in a non-trivial pattern. (b) Example of a reconstructed normalized nonlinearity profile $g_{\mathrm{reconst}}(z)$ enabled by the non-trivial poling concept depicted in (a), which approximates a target Gaussian function $g_{\mathrm{target}}(z)$. (c) Calculated tracking $\phi_{\mathrm{track}}(z)$ and effective $\phi_{\mathrm{eff}}(z)$ PMFs corresponding to the $g(z)$ functions shown in (b). (d) Schematic of the proposed twist-angle nonlinearity engineering method that enables the design of nonlinear QPM crystals in which $\chi^{(2)}_0/|\chi^{(2)}_0|$ at each crystal domain can be chosen from a discrete set of values between -1 and +1 due to the twist-angle degree of freedom. (e) Example of a reconstructed normalized nonlinearity profile $g_{\mathrm{reconst}}(z)$ enabled by the twist-angle engineering concept depicted in (d), which allows a better approximation to a target Gaussian function $g_{\mathrm{target}}(z)$ than shown in (b). (f) Calculated tracking and effective PMFs corresponding to the $g(z)$ functions shown in (e).
• Figure 2: (a) Calculated single-photon purities for twisted nonlinear crystals designed using our twist-angle algorithm, plotted as a function of the step size of the twist angle for a fixed crystal length of 50$\ell_c$. (b) Calculated single-photon purities for twisted nonlinear crystals of total length 50$\ell_c$, designed according to the twist angle algorithm, with different plots representing differing twist-angle step sizes, plotted as a function of the domain width $w$.
• Figure 3: Calculated single-photon purity as a function of total crystal length $L$ for crystals engineered using different nonlinearity-shaping algorithms. Red dots correspond to crystals designed using the twist-angle domain-engineering algorithm with a fixed twist-angle step size of $1^\circ$ and a fixed domain width of $w=\ell_c$. Green and blue dots show results for the sub-$\ell_c$ domains algorithm with fixed domain widths of $w=0.1\ell_c$ and $w=\ell_c$, respectively.
• Figure 4: Calculated joint-spectral quantities used to evaluate SPDC photon purity for a non-degenerate wavelength configuration in rBN. (a) Calculated momentum mismatch $\Delta k(\lambda_s,\lambda_i)$; the inset highlights the approximately linear behavior of momentum mismatch contours over a narrow wavelength range. (b) PMF obtained via twist-angle domain engineering for the configuration considered. (c) Corresponding pump envelope function (PEF), which together with the PMF determines the spectral purity of the generated photon pairs. (d) Resulting JSA, exhibiting a near-factorable structure and yielding a calculated single-photon purity of $99.67\%$ without spectral filtering.
• Figure S1: (a) Normalised target PMF $\phi_{\mathrm{target}}(\Delta k)$, plotted with the x-axis centred at a chosen momentum mismatch value. (b) Normalised target nonlinearity profile $g_{\mathrm{target}}(z)$, obtained as the Fourier transform of (a), plotted as a function of the normalised crystal length $L$ (with $L = 0$ at the crystal centre). (c) Normalised PMF for $\Delta k = \Delta k_0$$\phi_{\mathrm{track}}(z)$, plotted as a function of position inside the crystal, corresponding to the nonlinearity profile in (b). (d) Reconstructed PMF $\phi_{\mathrm{reconst}}(\Delta k)$, calculated by applying a domain-engineering algorithm to approximate $\phi_{\mathrm{track}}(z)$. Note that $\phi_{\mathrm{reconst}}(\Delta k)$ in (d) is less smooth than $\phi_{\mathrm{target}}(\Delta k)$ in (a), since the chosen algorithm input parameters limit the approximation quality.