# Precise Measurement of Hyperfine Structure of Cesium 7S\({}_{1/2}\) Excited State
## 1 Introduction  
With fast development of high-resolution spectroscopy and laser technique, fundamentally important atom-based precise measurements, such as electric field and basic physical constant, are receiving growing attention in the communities of quantum optics, quantum information, and atomic physics. Atom-based metrology has had a tremendous impact on science, technology, and everyday life. Seminal advances include optical atomic clocks [1, 2], the Global Positioning System, and highly sensitive, position-resolved magnetometers. Atom-based measurements have clear advantages due to the invariance of atomic properties. Therefore, precise measurements of atomic hyperfine structures play an important role in better understanding the atomic structure and its characteristics. Hyperfine structures are caused by the interaction between the nuclear spin and electron angular momentum. Due to having one outermost electron that is similar to hydrogen, alkali metals are one of the most popular groups of elements to study in both theory and experiment. This feature provides theorists with tractable calculations and experimentalists access to the atom's structure through optical and microwave sources. The study of hyperfine structures has great influences on parity non-conservation [3, 4], laser cooling and trapping of atoms [5], high-resolution spectroscopy [6], and frequency reference [7, 8]. Precise measurements of atomic hyperfine structure can: (i) inspect the accuracy of fundamental physics issues theoretically; and (ii) provide a more precise frequency reference experimentally.  
The investigation of the hyperfine structure for alkali metal atoms is always attractive in atomic physics. Before preceding, we note that a few groups have carried out experiments on the hyperfinestructure of the alkali metal atoms. [PERSON] et al. [9] investigated the hyperfine structure of Cs \(|7S_{1/2}\rangle\) state by laser excitation of \(|6S_{1/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition within the electric field. [PERSON] et al. [10] measured the absolute frequencies and the hyperfine coupling constant of Cs atoms by using a femtosecond frequency comb. [PERSON] et al. [11] measured the hyperfine splitting of Cs \(|9S_{1/2}\rangle\) using Doppler-free two-photon fluorescence spectroscopy. [PERSON] et al. [12] determined the hyperfine coupling constant of Cs \(|7S_{1/2}\rangle\) state by optical-optical double-resonance spectroscopy (OODR).  
Different from the previous studies [9; 10; 11; 12], we investigated the hyperfine splitting of cesium \(|7S_{1/2}\rangle\) state by using electromagnetically induced spectroscopy (EIS) in the three-level cascade atomic system, consisting of \(|6S_{1/2}\rangle,|6P_{3/2}\rangle\), and \(|7S_{1/2}\rangle\) states, where the probe laser couples the \(|6S_{1/2}\rangle\rightarrow|6P_{3/2}\rangle\) transition and coupling laser drives the \(|6P_{3/2}\rangle\rightarrow|7S_{1/2}\rangle\) transition. We used the hyperfine level interval of \(|6P_{3/2}\rangle\) state, which is well known, as a standard frequency reference to determine the \(|7S_{1/2}\rangle\) hyperfine structure. Furthermore, we present the measurement by OODR spectroscopy. Both EIS and OODR are shown to be in excellent agreement with the previous measurements [10; 12] and the theoretical calculations [13].