Phase-sensitive Rydberg-atom interferometry with Floquet electromagnetically induced transparency

We design a phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a MHz 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 MHz 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 MHz RF phase is measured over a full range of $2\pi$, and $10^{-4}$ rad accuracy is achieved. Moreover, the RF amplitude can also be measured with higher accuracy than the traditional EIT-based scheme.