The effect of the Doppler mismatch in microwave electrometry using Rydberg electromagnetically induced transparency and Autler–Townes splitting

Abstract

Abstract We have systematically investigated the influence of the gas temperature (T), the Rabi frequencies of the probe laser (Ωp), the coupling laser (Ωc) and the radio-frequency (RF) (ΩRF) on the Rydberg electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting (Δf) by defining a general Doppler mismatch factor D g = ΩRF/Δf in the Rydberg atom-based microwave electrometry. The effect of T on D g is studied in detail from 0 to 1000 K, the results show that D g is insensitive to T when T < 10 μK or T > 10 K, while D g changes significantly with 10 K \,T > 10\enspace \mu K$?> > T > 10 μ K . Then the effects of Ωp, Ωc and ΩRF on factor D g at T = 300 K (typical room temperature) and T = 10 μK (typical temperature of cold atom by laser cooling) are studied in detail, respectively. The results show that the linewidth of Rydberg EIT (ΓEIT) can be used as a key parameter to characterize the dependence of D g on Ωp and Ωc in both cases. D g is insensitive to T, Ωp and Ωc when ΩRF > 3ΓEIT which means that ΓEIT determines the lower limit of the linear region of the RF electric field strength measured by EIT–AT splitting. More interesting, the range where D g is insensitive to Ωp and Ωc can be greatly expanded by lowering the gas temperature to 10 μK. The ranges of parameters where D g is insensitive to T, Ωp, Ωc and ΩRF are given, and such relationship can be easily scaled to other atomic systems. The results can help the selection of various parameters in the experiments and specific applications to ensure the accuracy of measuring the RF electric field.