Mid-Infrared Single-Photon Detection via Enhanced Cross-Phase Modulation in Topology-Optimized Epsilon-Near-Zero Dual-Wavelength Nanocavities

Abstract

We use the Green's tensor quantization theory for open resonant nanostructures with absorption losses to study cross-phase modulation (XPM) at the single-photon level in nanoscale Kerr-type epsilon-near-zero (ENZ) materials with an effective nonlinear susceptibility integrated inside dual-wavelength nanocavities. We obtain analytical formulas for the XPM frequency shifts in hybrid nanocavities that simultaneously trap a classical probe beam at 1.5 $\mu$m and single-photon pump at 3 $\mu$m wavelengths. We present a comprehensive analysis of the fundamental limits for mid-infrared single-photon detection in the quantum nondemolition modality for nanostructured cadmium oxide (CdO) regions with ENZ-enhanced nonlinearity embedded in a silicon (Si) environment inversely designed by free-form topology optimization. We numerically implement our theoretical results using finite element simulations within the rigorous framework of quasi-normal modes, demonstrating a single-photon XPM frequency shift $\Delta f_s\approx 55.6\text{ GHz}$ with fractional shift (i.e., frequency pulling) $\Delta f_s/f_s\approx 2.78\times 10^{-4}$ and addressing the feasibility of detection in the hybrid Si-CdO dual-wavelength nanocavity, either with a classical probe beam or a squeezed probe state, including the contributions of traditional limitations from self-phase modulation noise, thermorefractive noise, shot noise, and free-carrier absorption effects. Finally, we present a comparative size scaling analysis of the XPM phase shift and phase noise contributions for dual-wavelength nanocavities based on CdO and indium tin oxide (ITO) nonlinear ENZ materials. This work establishes a robust benchmark for the engineering of mid-infrared single-photon nonlinear devices such as nondemolition quantum detectors, sensors, and all-optical gates on a solid state photonic platform.