## 3 Results and Discussion
We note that the calculations show agreement well with measurements at a large \(\Omega_{MW}\) region for two coupling Rabi frequency cases; whereas at a weak \(\Omega_{MW}\) region, the calculated \(f_{AT}\) display a nonlinear dependence, but measurements for the small Rabi frequency (\(\Omega_{c2}\)) is closer to the calculations than the large (\(\Omega_{c1}\)) case. Furthermore, the calculated \(f_{AT}\) is almost the same at an interested \(\Omega_{MW}\) range for two \(\Omega_{c}\) cases, this is attributed to the coupling-laser induced EIT line broadening that is not taken into account in our calculations. To verify the assumption of EIT line broadening, we keep microwave \(\Omega_{MW}\) fixed and vary the probe/coupling laser Rabi frequency and do a series of measurements of \(f_{AT}\). In Figure 4, we display the \(f_{AT}\) dependence on \(\Omega_{p}\) in Figure 4a and \(\Omega_{c}\) in Figure 4b with \(\Omega_{MW}=2\pi\times 7.61\) MHz (corresponding to \(E_{MW}=0.46\) V/m) and \(\Omega_{MW}=2\pi\times 9.48\) MHz (\(E_{MW}=0.57\) V/m). It is seen that the \(f_{AT}\) shows different value as \(\Omega_{c}\) or \(\Omega_{p}\) varies. For the range \(\Omega_{c}\) and \(\Omega_{p}\) we used in Figure 4, microwave-free EIT linewidth \(\gamma_{EIT}\lesssim 2\pi\times 6.5\) MHz. The \(f_{AT}\) is located in the nonlinear region due to microwave \(\Omega_{MW}=2\pi\times 7.61\) MHz (9.48 MHz) that is smaller than \(3\gamma_{EIT}\), which result in \(f_{AT}\) less than \(\Omega_{MW}\). The error bars in Figure 4 display the standard error of four times measurements. The error bar of Figure 4a is less than \(\pm 0.18\) for \(\Omega_{p}/2\pi<4\) MHz, and increases with \(\Omega_{p}\), this is because the large probe Rabi frequency leads to an EIT linewidth that approaches to \(\Omega_{MW}\). The \(f_{AT}\) fluctuation below \(\Omega_{p}/2\pi=4\) MHz may due to the inhomogeneous of the microwave field in the cell. In Figure 4b, the error bar decrease with coupling Rabi frequency, which is attributed to the large \(\Omega_{c}\) yielding enhanced EIT-AT spectrum. The deviations coming from the nonlinear behavior for the cases in Figures 3 and 4 would result in a measurement uncertainty. In order to investigate how the probe/coupling laser affect the microwave electric field measurement for \(f_{AT}\) at a linear and nonlinear regions, we do the measurements and analysis the field-measurements uncertainty. In Figure 5, we present four-time averaged EIT-AT spectra for the \(f_{AT}\) at a linear region with \(\Omega_{MW}=2\pi\times 30.71\) MHz (Figure 5a,b) and a nonlinear region with \(\Omega_{MW}=2\pi\times 7.73\) MHz (Figure 5c-e) and indicated coupling \(\Omega_{c}\). For comparison, we also plot the calculations based on the four-level model, see solid lines in Figure 5. The microwave Rabi frequency \(\Omega_{MW}\) used in calculations are same as \(f_{AT}\) for linear regime in Figure 5a,b, the calculations reproduce the EIT-AT spectra well. The small difference at shoulder of the AT peak is due to the inhomogeneous of MW field in the cell that yields the AT line broaden [23]. In Figure 5c-e, the microwave Rabi frequency \(\Omega_{MW}\) in calculations has a tiny difference with the measured \(f_{AT}\). Below we analysis the relative deviation, \(D_{Err}\), that is defined as the ratio \((f_{AT}-\Omega_{MW})/\Omega_{MW}\). In the linear region, the measured \(f_{AT}\approx\Omega_{MW}\) and independent of the coupling Rabi frequency. The extracted \(D_{Err}\) is \(-0.52\%\) and \(0.88\%\), see Figure 5a,b, which are smaller than \(1\%\). However, in the nonlinear region, for the same microwave field the measured \(f_{AT}\) display different value and varies with the coupling laser Rabi frequency leading to large deviations of field measurements. The resultant uncertainty \(D_{Err}\) in Figure 5c-e are \(-11.38\%\), \(0.52\%\) and \(9.31\%\) for \(\Omega_{c}/2\pi=3.56\) MHz, \(2.06\) MHz and \(1.13\) MHz, respectively. The results of Figures 4 and 5 provide experimental evidence for the theoretical simulations in Ref. [12].