On-chip high-order parametric downconversion in the excitonic Mott insulator Nb3Cl8 for programmable multiphoton entangled states

Spontaneous parametric downconversion and four-wave mixing in χ(2) and χ(3) media underpin most entangled-photon sources, but direct generation of higher-order entangled multiphoton states by nth order parametric downconversion remains extremely challenging because conventional materials exhibit tiny high-order nonlinearities. Here, we show that single-layer Nb3Cl8, an excitonic Mott insulator on a breathing Kagome lattice, supports exceptionally large nonlinear susceptibilities up to the seventh order. Many-body GW–Bethe–Salpeter (BSE) and time-dependent BSE/Kadanoff–Baym simulations yield resonant χ(2)–χ(7) for monolayer Nb3Cl8, with |χ(4)| and |χ(5)| surpassing values in prototypical transition metal dichalcogenides by several orders of magnitude. We trace this enhancement to flat bands and strongly bound Frenkel excitons with ferroelectrically aligned out-of-plane dipoles. Building on experimentally demonstrated 1 × N integrated beam splitters with arbitrary power ratios, we propose an on-chip architecture where each output arm hosts an Nb3Cl8 patch, optionally gated by graphene to tune the complex n-photon amplitudes. Using the ab initioχ(3) and χ(4) values, we predict that three-photon GHZ3 and four-photon cluster-state sources in this platform can achieve n-photon generation rates up to ∼108 and ∼106 times larger, respectively, than silica-fiber- and MoS2-based implementations with comparable geometry. We derive the quantum Hamiltonian and explicit n-photon generation rates for this platform and show how suitable interferometric networks enable electrically and spectrally tunable GHZ, W, and cluster states based on genuine high-order nonlinear processes in a 2D excitonic Mott insulator.