Sensitive detection of radio-frequency field phase with interacting dark states in Rydberg atoms

An efficient scheme of phase measurement of a radio-frequency (RF) field is proposed by interacting dark states. Under the condition of electromagnetically induced transparency (EIT), the four-level Rydberg atom exhibits two windows. Compared with the transmission spectrum on resonance, the linewidths of absorption peaks off resonance are very narrow due to the interaction of double dark states. It is interesting to find that the distance of absorption peaks shifts approximately linearly with the phase of an RF field, which can be used to measure the RF field phase. Simulation results show that the linewidth of an absorption peak can be narrowed by more than one order of magnitude, and a narrow linewidth improves the detectable minimum phase difference by more than six times. It helps to reduce analyzation complexity and increase sensing resilience. The dependence of phase measurement on the control field and RF field is also investigated.