# Precise Measurement of Hyperfine Structure of Cesium 7S\({}_{1/2}\) Excited State
## 2 Experimental Setup  
We considered a three-level cesium atomic system with a ladder-type level configuration, as shown in Figure 1. An 852 nm laser coupled the ground state \(|6S_{1/2}\rangle\) and intermediate state \(|6P_{3/2}\rangle\), and a 1470 nm laser coupled state \(|6P_{3/2}\rangle\) and an excited state \(|7S_{1/2}\rangle\). Figure 1 (right) displays the hyperfine levels and relative splittings of \(|6S_{1/2}\rangle\) and \(|6P_{3/2}\rangle\) referring to the work of [PERSON] [14]. Considering the nuclear spin of Cs atom I=7/2, the \(|S_{1/2}\rangle\) state splits into hyperfine doublets, and the \(|6P_{3/2}\rangle\) level splits into four hyperfine levels, displayed with the quantum number \(F\). According to the selection rule, five transitions from the ground hyperfine level \(|6S_{1/2}(F=4)\rangle\) are allowed, which are indicated by arrows on the right-hand side of Figure 1. For simplicity, we denote the transition by hyperfine quantum number, i.e., the transition \(|6S_{1/2}(F=4)\rangle\rightarrow|6P_{3/2}(F^{\prime}=3)\rangle\rightarrow|7S _{1/2}(F^{\prime\prime}=4)\rangle\) is denoted as \(F=4-F^{\prime}=3-F^{\prime\prime}=4\) or simply 4-3-4.  
The experiments were performed in a room temperature cesium vapor cell with diameter 25 mm and length 75 mm. The cell is made of silica glass. The related apparatus is shown in Figure 2. Two lasers, \(\lambda_{p}\) = 852 nm and \(\lambda_{c}\) = 1470 nm, were used to couple the lower and upper transitions. The 852 nm laser was provided by a diode laser (DL pro, Toptica); the related frequency was locked  
Figure 1: (color online) Three-level energy scheme. An 852 nm laser couples the transition of \(|6S_{1/2}\rangle\rightarrow|6P_{3/2}\rangle\), while 1470 nm laser drives \(|6P_{3/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition. The right panel displays the hyperfine levels. The hyperfine level intervals of the ground and intermediate state refer to Steck [14]. The arrows display possible transitions of \(|6S_{1/2}(F=4)\rangle\) ground hyperfine level.  
to the first side band of an electro-optic modulator (EOM) employing PDH (Pound-Drever-Hall) method with an ultra-stable Fabry-Perot (FP) cavity of a finesse 15,000. The frequency was then tuned to the resonant hyperfine transition of \(|6S_{1/2}(F)\rangle\rightarrow|6P_{3/2}(F^{\prime})\rangle\) by changing the radio-frequency that was applied to an EOM, monitored with a wavelength meter (WS-U,HighFinesse GmbH). The 1470 nm laser, provided from the other DLpro diode laser, was scanned over the \(|6P_{3/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition, calibrated with a FP cavity (SA200-12B, Thorlabs). Two lasers were lined and overlapped in a counter-propagating geometry inside two separated cesium vapor cells. The purple square in Figure 2 indicates the experimental setup for an EIS measurement, while the red square denotes the setup for an OODR measurement. For the EIS measurement, the 852 nm beam probe was passed through a dichroic mirror (DM1) and detected with a photodiode (PD1). For the OODR measurement, the 1470 nm beam was detected with a balanced photodiode detector (BPD). The PD2 was employed to monitor the 1470-nm laser power.