Rydberg Superatom Interface for Topological Microwave-to-Optical Photon Conversion in Fock-State Lattices

Microwave-to-optical conversion (MTOC) of single photons plays a pivotal role in bridging quantum devices across different frequency domains, but faces challenges in maintaining efficiency and robustness against fluctuations and dissipation in hybrid quantum systems. Here, we propose a topologically protected MTOC scheme mediated by a Rydberg superatom to address these limitations. By constructing cross-linked Fock-state lattices (FSLs) through a dual-mode Jaynes-Cummings (JC) architecture, we map the effective hybrid system onto an extended Su-Schrieffer-Heeger~(SSH) model with tunable hopping rates. Photon-number--dependent property of hopping rates triggers a topological phase transition in the extended SSH chain, converting the defect mode into a topological channel that directionally pumps photons between microwave and optical cavities. This mechanism leverages Rydberg blockade-enhanced photon-superatom couplings to establish a robust energy transfer channel, achieving high-efficiency photon conversion under realistic decoherence. Our theoretical framework demonstrates how topological protection synergizes with Rydberg-mediated light-matter interactions to realize a robust quantum transducer, providing a scalable platform for noise-resilient quantum networks and frequency-multiplexed quantum interfaces.