## 3 Results and Discussion  
When the coupling laser frequency is scanned over the \(5P_{3/2}-57D_{5/2}\) transition and the probe laser frequency resonates at the hyperfine transition of \(5S_{1/2}(F=3)-5P_{3/2}(F^{\prime}=4)\), a typical EIT signal, corresponding to \(5P_{3/2}(F^{\prime}=4)-57D_{5/2}\) transition with the full width at half maximum (FWHM) about 7.36 MHz, appears in Figure 2a (blue dots). The powers of the probe and coupling lasers are 15 \(\upmu\)W and 23 mW, respectively. A microwave E-field, with the frequency at 11.36 GHz and the power at \(-22\) dBm, resonates with the adjacent Rydberg \(57D_{5/2}-58P_{3/2}\) transition and results in a resonant dark state with all of the population in the ground state (the AT splitting) as shown in black dots of Figure 2a. The AT splitting interval gradually decreases when the microwave E-field power reduces; Figure 2b shows the AT splitting spectrum with a microwave field of \(-26\) dBm, which is close to the indistinguishable intensity. In Figure 2c, the AT splitting peaks becomes more difficult to identify when the microwave power is \(-28\) dBm. Figure 1: (**a**) illustration of a four-level system of \({}^{85}\)Rb; (**b**) sketch of the experiment setup. MW, microwave source; BB, beam block; BS, beam splitter; \(\lambda/2\), half-wave plate; PBS, polarizing beam splitter; M, mirror; DM, dichroic mirror; Lock-in, lock-in amplifier; OSC, oscilloscope; AM, amplitude modulation; FM, frequency modulation. The microwave frequency detuning is introduced to realize the reappearance of the AT splitting even in the case of low microwave E-field power. Compared with the resonant transition, the AT splitting peaks are non-symmetric, the left peak is higher than the right if the microwave frequency is blue detuning; otherwise, it is the opposite. The AT splitting interval \(\Delta f_{d}\) of the two peaks can be given by [24]:  
\[\Delta f_{d}=\sqrt{(\Delta_{M})^{2}+(\Delta f_{0})^{2}} \tag{1}\]  
where \(\Delta_{M}\) is the frequency detuning of the microwave E-field (\(\Delta_{M}=f_{Md}-f_{M0}\), \(f_{M0}\) is the on-resonance frequency, \(f_{Md}\) is the actual frequency of the microwave E-field), and \(\Delta f_{0}\) is the splitting interval induced by the resonant microwave E-field. We measured the AT splitting interval \(\Delta f_{d}\) with different microwave frequency detunings \(\Delta_{M}\). It can be found that the relative intensity ratio of two AT splitting peaks increase as the \(\Delta_{M}\) increases. Additionally, the change of the AT splitting interval \(\Delta f_{d}\) versus \(\Delta_{M}\) has similar trend. The intensity ratio of two AT splitting peaks is optimal for measurement when the microwave frequency blue detuning is 20 MHz. Figure 2d-f show the AT splitting spectra in this case; meanwhile, the microwave E-field powers remain consistent in Figure 2a-c. It can be found that the distinguishing ability is significantly improved with frequency detuning compared to that of the resonance frequency, which is obviously observed with a weak microwave E-field power of \(-28\) dBm. From Figure 2e, we can find that the spectral SNR is relatively low, but the resolution of AT splitting interval is determined by the identification of the right transmission peak. As the microwave E-field power continues to decrease, the right transmission peak is gradually difficult to distinguish. We adopt the MCM scheme, which is composed by FM and AM, to improve the measurement sensitivity. Figure 3 shows the right transmission peaks recorded under different modulation schemes when the microwave E-field power  
Figure 2: (**a–c**) are the AT splitting spectra as a function of the coupling laser frequency detuning \(\Delta_{c}\) with microwave E-field powers of \(-22\) dBm, \(-26\) dBm, \(-28\) dBm, respectively. The microwave E-field frequency is resonance with the \(57\mathcal{D}_{5/2}\)–\(58\mathcal{P}_{3/2}\) transition. The blue dots in Figure 2a is the EIT spectrum without the microwave E-field.