Sensitivity of RF electric field sensor based on Rydberg AC-Stark effect

Rydberg atoms hold particular appeal for applications in electrometry due to their large transition electric dipole moments and huge polarizability, which lead to a strong atomic response to electric fields. In radio-frequency (RF) fields, the Rydberg levels are AC stark shift and splitting, which can realize the study of high-sensitivity electric field sensor of Rydberg atoms. In this work, we use the simpler Shirley's time-independent Floquet Hamiltonian model to calculate the AC Stark energy spectrum of Cs Rydberg atoms. This model can reduce the basis of Hamiltonian to only include those Rydberg states that have direct dipole-allowed transitions with the target state, significantly improving the speed of computation. The accuracy of the calculation is proved by fitting with the calculated frequency shift of DC Stark energy levels in the weak fields, and the polarizability of 60D_5/2 and 70D_5/2 Rydberg atomic states is obtained by fitting with the measured ion spectra of DC Stark Cs ultra-cold Rydberg atoms in magneto-optical trap. In addition, we calculate the AC Stark shift of Cs Rydberg atom |60D_5/2,m_j=1/2> state in different frequency electric fields with ε = 100 mV/m. Rydberg atom provide a structured spectrum of sensitivity to electric fields due to strong resonant and off-resonant interactions with many dipole-allowed transitions to nearby Rydberg states. This structure of the frequency response has important implications for a wideband sensor. And we calculate the sensitivity and the scaling of the signal-to-noise ratio, β, varying with detuning from the |60D_5/2>→|61P_3/2> transition. The value of β allows one to use the results for any Rydberg state sensor to determine the SNR for any E in a 1s measurement. Therefrom, Rydberg sensor can preferentially detect many RF frequencies spread across its carrier spectral range without modification while effectively rejecting large portions where the atom response is significantly weaker, and the signal depends primarily on the detuning of the RF field to the nearest resonance which does not convey the RF frequency directly.