Design of an Electrically Tunable Microtoroid for Frequency Selection of Polarization-Entangled Photons

Abstract

Encoding quantum information into discrete optical frequencies, or "frequency bins," uses different colors of light as additional information channels, allowing each photon to carry more information than polarization alone. We present a computational design for an electrically tunable silica microtoroid that selects desired frequency channels after a polarization-entangled photon pair has been generated without disturbing the photons' polarization entanglement. In the proposed architecture, the 750 nm signal photon passes through the microtoroid, while its entangled 880 nm partner bypasses the resonator and serves as a reference for the selected frequency channel. The principal challenge is resonator birefringence: because horizontally and vertically polarized light resonate at slightly different frequencies, the selected frequency can reveal the photon's polarization state and weaken the quantum correlation between the photon pair. We solve this problem by adding a small lithium-niobate tuning element controlled with a single applied voltage. The voltage shifts the resonator so that it responds almost identically to horizontally and vertically polarized light, reducing the remaining mismatch to only 0.286 optical linewidths across nine frequency channels. The photons remain strongly entangled after passing through the device, with a concurrence of C = 0.969, a Bell-state fidelity of F = 0.981, and a Bell parameter of S_max = 2.785. If the relative timing between the frequency channels is also controlled, the same device can generate a nine-channel polarization-frequency hyperentangled state with an effective dimension of K = 8.97. This computational design provides a compact, electrically tunable bridge between polarization-entangled photon sources and future high-capacity quantum photonic systems.