# Precise Measurement of Hyperfine Structure of Cesium 7S\({}_{1/2}\) Excited State
## 4 Discussions and Conclusions  
We used EIS and OODR spectra to investigate the hyperfine structure of cesium \(|7S_{1/2}\rangle\) excited state. The measured hyperfine splitting is displayed in Table 1. To compare with the previous results, we also display the calculated and measured hyperfine splittings mentioned in [9; 12; 13; 20]. The measured hyperfine splitting is 2183.61 \(\pm\) 0.50 MHz by EIS and 2183.48 \(\pm\) 0.04 MHz by OODR in this work, showing a good agreement with the previous experimental measurements in [9; 12] and the calculation by [PERSON] [13]. We found that the two methods can obtain the same results. One can see that the EIS measurement has three obvious advantages: (i) EIS spectroscopy is a quantum effect that needs weak probe laser power; (ii) the probe frequency locking to hyperfine transition leads to the Doppler-free narrow linewidth signal; and (iii) the weak probe could decrease the atomic population at intermediate \(|6P_{3/2}\rangle\) level, therefore the radiation decay effect on the EIS can be effectively compressed. Figure 4: (color online) Measurements of OODR spectroscopy for first step laser locked to the hyperfine transitions: \(F=4-F^{\prime}=5\) (**a**); \(F=4-F^{\prime}=4\) (**b**); and \(F=4-F^{\prime}=3\) (**c**). The spectroscopy displays five indicated double resonant peaks, labeled with arrows in Figure 1. The solid lines are Lorentz fittings to the double resonant peaks. The bottom curves show the residuals, \(R\), of the Lorentz fits and spectra. We finally discuss the error of measurements, which might be contributed by the following reasons. (i) The main reason causing the error is nonlinearity of the coupling laser frequency scanning. To measure hyperfine splitting of 75\({}_{1/2}\) state, the 1470 nm laser needs to scan over \(\gtrsim\)2.3 GHz and the minor nonlinearity of frequency scanning could lead to error. (ii) The error could also come from the frequency calibration of 1470 nm laser. We used hyperfine splitting of cesium \(|6P_{3/2}\rangle\) in EIS or OODR spectrum and another wavelength meter (WS-6, HighFinesse GmbH) to calibrate the 1470-nm laser. A saturated absorption spectra and the wavelength meter (WS-U, HighFinesse GmbH) were used to calibrate the 852 nm frequency. (iii) Moreover, the error could come from fitting to signal peak. We used Lorentz fittings to EIS or OODR peaks and extracted the peak position. For the EIS measurements, the fittings to the spectra would yield a systematic error (see the residuals in Figure 3). This kind of error can be further decreased by modeling the measurement using a density matrix formalism [16; 17] and the corresponding accuracy is expected to be further improved. (iv) The laser power broadening and shift may also induce an error, which would be negligible due to very smaller laser power used in our study. In summary, we measured hyperfine splitting of cesium \(|7S_{1/2}\rangle\) state using EIS spectroscopy employing the \(6S_{1/2}-6P_{3/2}-7S_{1/2}\) cascade transitions in a room temperature vapor cell. EIS spectrum was attained by detecting a weak probe laser that was locked to the lower hyperfine transition. This kind of spectra is Doppler-free and with narrow linewidth. The \(|7S_{1/2}\rangle\) state hyperfine splitting we measured by electromagnetic induced spectrum is 2183.61 \(\pm\) 0.50 MHz, while the OODR measurement is 2183.48 MHz \(\pm\) 0.04 MHz. The measurements are in good agreements with theoretical calculations [13] and previous experiments. In the future, we will model the measured spectrum using a density matrix formalism to decrease the systematic error and use a high finesse cavity for calibrating the up transition laser to realize precise measurement of the excited state. Conceptualization, [PERSON] and J.Z. ; investigation, [PERSON], [PERSON], and Y.J. ; software, [PERSON], J.F. ; validation, [PERSON], [PERSON], and J.F. ; formal analysis, [PERSON], J.F., and L.H. ; Writing--original draft, [PERSON]; writing--review and editing, [PERSON]; project administration, [PERSON] and Y.J.