We have systematically investigated the influence of the gas temperature (T), the Rabi frequencies of the probe laser (Ω_p), the coupling laser (Ω_c) and the radio-frequency (RF) (Ω_RF) on the Rydberg electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting (Δ_f) by defining a general Doppler mismatch factor D _g = Ω_RF/Δ_f 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>10μK . Then the effects of Ω_p, Ω_c and Ω_RF 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 (Γ_EIT) can be used as a key parameter to characterize the dependence of D _g on Ω_p and Ω_c in both cases. D _g is insensitive to T, Ω_p and Ω_c when Ω_RF > 3Γ_EIT which means that Γ_EIT 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 Ω_p and Ω_c can be greatly expanded by lowering the gas temperature to 10 μK. The ranges of parameters where D _g is insensitive to T, Ω_p, Ω_c and Ω_RF 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.

中文翻译：

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使用 Rydberg 电磁感应透明和 Autler-Townes 分裂的微波静电计中多普勒失配的影响

我们系统地研究了气体温度的影响（吨)、探测激光 (Ω _p )、耦合激光 (Ω _c ) 和射频 (RF) (Ω _RF ) 对里德堡电磁感应透明 (EIT) 和 Autler–Townes (AT) 分裂的Rabi 频率(Δ _f ) 通过定义一般的多普勒失配因子丁 _g = Ω _RF /Δ _f在基于里德伯原子的微波静电计中。的效果吨在丁 _{从0到1000 K对g}进行了详细研究，结果表明丁 _g不敏感吨什么时候吨< 10μ或吨> 10 K，而丁 _g随 10 K 显着变化 \,T > 10\enspace \mu K$?> >吨>10μ钾 . _{那么 Ω p}、Ω _c和 Ω _RF对因子的影响丁 _克在吨= 300 K（典型室温）和吨= 10 μ分别详细研究了 K（激光冷却冷原子的典型温度）。结果表明，里德堡 EIT 的线宽 (Γ _EIT ) 可以作为关键参数来表征对丁 _g在 Ω _p和 Ω _c两种情况下。丁 _g不敏感吨, Ω _p和Ω _c当Ω _RF > 3Γ _EIT即Γ _EIT决定了EIT-AT分束测得的射频电场强度线性区域的下限。更有趣的是，范围丁 _{g对 Ω p}不敏感，Ω _c可以通过将气体温度降低到 10 来大大扩展μK. 参数范围丁 _g不敏感吨, Ω _p , Ω _c和 Ω _RF是给定的，这种关系可以很容易地扩展到其他原子系统。研究结果有助于实验和具体应用中各种参数的选择，保证射频电场测量的准确性。