Cryogenic Graphene-Based Phase Modulators for Quantum Information Processing

Electro-optic modulators are key components for photonic quantum computing, particularly in fully cryovenic integrated platforms where low loss and compactness are critical. We present a systematic theoretical investigation of compact dual-layer graphene (DSLG) electro-optic phase modulators integrated on silicon nitride waveguides, with emphasis on cryogenic operation. By combining electromagnetic simulations with a physically consistent description of graphene conductivity based on the Kybo formalism, we analyze the interplay between electrostatic tuning, optical mode confinement, and material-dependent losses. We show that cryogenic operation enhances device performance by sharpening the Fermi-Dirac distribution, enabling access to the Pauli-blocking regime at lower Fermi levels and reducing the required modulation length. Through optimization of the waveguide geometry, dielectric spacer thickness and permittivity, and graphene quality, we identify regimes that simultaneously minimize insertion loss and device footprint under realistic voltage constraints. The optimized designs achieve near-pure phase modulation with insertion losses below 0.3 dB and modulation lengths below 50 um at 10 K, while maintaining GHz-scale bandwidths. These results provide quantitative design guidelines for low-loss, compact, cryogenic graphene phase modulators for scalable integrated quantum photonics.