On-chip high-order parametric downconversion in the excitonic Mott insulator Nb$_3$Cl$_8$ for programmable multiphoton entangled states

TL;DR

This work tackles the challenge of generating high-order multiphoton entangled states by leveraging giant high-order nonlinearities in a 2D excitonic Mott insulator Nb$_3$Cl$_8$. Via $GW$-BSE and TD-BSE simulations, it shows $χ^{(n)}$ up to $n=7$ are enormous, driven by flat bands and ferroelectric Frenkel excitons with out-of-plane dipoles, leading to substantial $n$-photon generation rates. It then develops a quantum-optical framework for on-chip $n$-th order SPDC in a 2D sheet and couples this to a 1$\times$N splitter architecture with graphene gates to programmably realize GHZ, $W$, and cluster states. The predicted performance surpasses silica and MoS$_2$-based platforms by several orders of magnitude, enabling scalable, electrically tunable, on-chip multiphoton entangled sources for quantum information processing.

Abstract

Spontaneous parametric downconversion (SPDC) 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 $n$-th order parametric downconversion remains extremely challenging because conventional materials exhibit tiny high-order nonlinearities. Here we show that single-layer Nb$_3$Cl$_8$, an excitonic Mott insulator on a breathing Kagome lattice, supports exceptionally large nonlinear susceptibilities up to seventh order. Many-body GW--Bethe--Salpeter and time-dependent BSE / Kadanoff--Baym simulations yield resonant $χ^{(2)}$--$χ^{(7)}$ for monolayer Nb$_3$Cl$_8$, with $|χ^{(4)}|$ and $|χ^{(5)}|$ surpassing values in prototypical transition metal dichalcogenides by 5--9 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$\times N$ integrated beam splitters with arbitrary power ratios, we propose an on-chip architecture where each output arm hosts an Nb$_3$Cl$_8$ patch, optionally gated by graphene to tune the complex $n$-photon amplitudes. Using the ab-initio $χ^{(3)}$ and $χ^{(4)}$ values, we predict that three-photon GHZ$_3$ and four-photon cluster-state sources in this platform can achieve $n$-photon generation rates up to $\sim 10^8$ and $\sim 10^6$ times larger, respectively, than silica-fiber- and MoS$_2$-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.

Figures (6)

• Figure 1: Schematic of a 1$\times$5 Nb$_3$Cl$_8$--graphene high-order parametric downconversion device. A pump beam at frequency $\omega_p$ propagates in a single-mode input waveguide and is distributed by a 1$\times$5 beam splitter into five output waveguides. Each output arm contains a monolayer Nb$_3$Cl$_8$ patch acting as the high-order nonlinear medium, capped by a graphene gate biased at voltages $V_{g1},\dots,V_{g5}$. By tuning the gate voltages, the complex high-order susceptibility $\chi^{(n)}_{\mathrm{eff}}$ and local phase matching in each arm are modified, providing independent control over the complex $n$-photon downconversion amplitudes $\kappa_1,\dots,\kappa_5$ used to engineer multiphoton entangled states.
• Figure 2: Top view of 2D Nb$_3$Cl$_8$ monolayer. Nb atoms are green and Cl atoms are grey balls.
• Figure 3: The absorption spectra of ML Nb$_3$Cl$_8$, imaginary part of the dielectric function Im($\epsilon^{(1)}_{xx(yy)}$) (blue solid line), and refractive index n (dotted line). The insert: the oscillator strength as a function of energy.
• Figure 4: The absorption spectra of ML Nb$_3$Cl$_8$, imaginary part of the dielectric function Im($\epsilon^{(1)}_{zz}$) (red solid line), and refractive index n (dotted line). The inset shows the oscillator strength as a function of energy.
• Figure 5: Spatial distributions of (a) a localized dark Frenkel exciton at -0.51 eV and (b) a distributed bright exciton at 2.04 eV.