We design phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a megahertz radio frequency (rf) field and recombines them into FEIT bands. The FEIT bands act as screens to present the interference between paths with different phases, which are transitions between the sidebands and excited states. This interferometry can measure the phase of a megahertz rf field without a local rf reference field. A phase reference is supplied to the atoms via a periodic electrical signal in the FEIT. We demonstrate that the megahertz rf phase can be resolved over the full $2\pi$ range with a theoretical accuracy of ${10}^{-4}$ rad. Moreover, the rf amplitude can also be resolved with higher accuracy than with the traditional EIT-based scheme.

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• Atom interferometry
• Electromagnetically induced transparency
• Light-matter interaction
• Rydberg gases
• Atomic gases
• Floquet systems
• Rydberg atoms & molecules
• Semiclassical methods