A Floquet ladder lattice (FLL) is created by introducing ultrastrong temporal modulation into a gain-embedded cavity magnonics platform. In contrast to conventional atomic lattices, the FLL is a synthetic polariton lattice manifested in the frequency dimension, embodying light-matter interaction, temporal diffraction, and gain-driven nonequilibrium dynamics. Distinct lattice phenomena—including bistability-enabled exfoliation, edge singularities, compact edge localization, and Floquet band gaps—are experimentally observed and theoretically analyzed. Benefiting from its highly flexible lattice architecture, the FLL enables a superior microwave frequency comb with on-demand engineering capabilities.

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• Cavity magnonics
• Lattice dynamics
• Light-matter interaction
• Localization
• Magnons
• Optical & microwave phenomena
• Polaritons
• Floquet systems
• Bloch-Floquet theorem