# Precise Measurement of Hyperfine Structure of Cesium 7S\({}_{1/2}\) Excited State
## 3 Results
### Electromagnetically Induced Spectroscopy  
In EIS experiments, a probe (coupling) laser has a power of 3 \(\mu\)W (16 \(\mu\)W) and a beam waist of \(\omega_{852}\simeq 100\)\(\mu\)m (\(\omega_{1470}\simeq 150\)\(\mu\)m). The weak power of probe (coupling) laser results in a negligible line broadening. The coupling and probe beams are linear polarized along the vertical direction. The probe transmission is detected as a function of the coupling laser detuning \(\Delta_{c}\). In Figure 3, we display EIS spectra for the probe laser frequency locked to the \(|6S_{1/2}(F=4)\rangle\rightarrow|6P_{3/2}(F^{\prime}=3,4,5)\rangle\) hyperfine transitions, while coupling laser scanned cover the \(|6P_{3/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition. The spectra demonstrate some EIT or EIA peaks corresponding to the possible transitions labeled in Figure 1. To analyze and measure the hyperfine splitting of \(|7S_{1/2}\rangle\) state from EIS spectra, we defined the EIS peak of 4-5-4 as the zero-detuning point and calibrate coupling laser detuning, \(\Delta_{c}\), with the space between EIS 4-5-4 and 4-4-4 peaks due to the accurate hyperfine splitting of \(|6P_{3/2}\rangle\) state [14]. Considering the Doppler factor, the EIS peak distance between 4-5-4 and 4-4-4 peaks is \(251.09\times(1-852/1470)\) = 105.56 MHz and 4-4-4 peak is located on the blue side. Besides, we calibrated the coupling laser detuning using high order side band of EOM to decrease the effect of the nonlinearity of coupling frequency during the laser scanning. Moreover, we used Lorentz function to fit each peak to extract the peak positions and further the hyperfine structure splitting of \(|7S_{1/2}\rangle\) state. Figure 3: (color online) EIS spectroscopy for the probe laser locked to the transitions: \(F=4-F^{\prime}=5\) (**a**); \(F=4-F^{\prime}=4\) (**b**); and \(F=4-F^{\prime}=3\) (**c**). The coupling laser scanned cover the \(|6P_{3/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition. Solid lines display the Lorentz fittings to EIS spectra for extracting the position of EIS peaks and further the hyperfine splitting. The bottom curves display the residuals, \(R\), of the Lorentzian fit and spectrum. The label \(R_{FV}\) at the bottom of (**c**) displays the residuals of the Fano–Vogit fit and the spectrum. Figure 3 presents the EIS spectroscopies for the probe laser locking to the indicated hyperfine transitions. Figure 3 shows that the EIS spectra present different profiles for probe frequency locked to different hyperfine transitions. Among three cases of probe frequency, only the 4-5-4 peak displays the decrease of probe absorption, i.e., EIT spectrum, because the 4-5-4 configuration constitutes the cycling transition. The 4-5-4 peak displays strong EIT signal when the probe laser resonantly interacts with the \(F=4-F^{\prime}=5\) hyperfine transition (see Figure 3a) and shows decreased EIT when probe laser locked to \(F=4-F^{\prime}=4\) hyperfine transition due to the detuned interaction of probe for the 4-5-4 configuration (see Figure 3b). The 4-5-4 peak displays the smallest EIT signal when the probe frequency is locked to the \(F=4-F^{\prime}=3\) hyperfine transition due to larger detuning for the 4-5-4 configuration (see Figure 3c). All other EIS peaks show increase of the probe absorption, i.e., EIA spectrum, as the other four configurations are non-cycling transition and a large population leakage occurs via spontaneous emission decays from the excited state to the other ground states [15]. We take the case of probe locked to \(F=4-F^{\prime}=4\) (Figure 3b) as an example to illustrate how we obtained the hyperfine splitting of excited \(|\mathcal{7}S_{1/2}\rangle\) state. The spectrum of probe locked to \(F=4-F^{\prime}=4\) clearly shows the five indicated transition signals, where one of them is an EIT signal of the 4-5-4 cycling transition and the others are EIA signals of non-cycling transitions.