## 1 Introduction  
With the development of frequency-stabilization techniques [1; 2; 3] and laser cooling and trapping techniques [4], two-photon spectroscopy has developed fast in recent years. For its high accuracy and stability, two-photon spectroscopy has many practical applications in many fields, such as fiber communication [5; 6], precision measurement [7; 8; 9; 10; 11; 12; 13; 14; 15], detection of macromolecules [16], and Doppler laser cooling [17; 18]. Among this, the Rubidium (Rb) 5S\({}_{1/2}\)-5D\({}_{5/2}\) two-photon transition (TPT) has unique advantages, such as narrow linewidth and low sensitivity to environment [19]. The relevant energy levels of Rb ladder type two-photon transition is shown in Figure 1. In addition, the 778 nm transition can be easily excited by frequency doubling the communication band lasers at the C band (an infrared communication band from 1530 to 1565 nm). For these reasons, it is suitable for optical communication frequency standard. The stability of the Rb two-photon frequency standard has reached \(10^{-13}\)[20]. Because of many natural advantages of optical frequency comb (compact scheme, wide spectrum bandwidth and high peak intensity), the direct frequency comb spectroscopy (DFCS) on the TPIs is the research focus of two-photon spectroscopy [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Compared to a narrow-linewidth continuous wave (CW) laser, the linewidth of each optical comb teeth is easier to be realized and adjusted to sub-hertz [21]. Moreover, for its higher instantaneous power and higher conversion efficiency in the deep ultraviolet (122 nm or 200 nm) [18], optical frequency comb has the potential to demonstrate the TPT excitations of the C, H, N, and O atoms in organic chemistry that are not available for CW laser [18]. The two-photon spectroscopy using optical frequency combs was first proposed for observation of the 1s-2s transition of hydrogen atoms [7]. In addition, a coherent control method, which uses optical frequency comb to directly excite TPT, was proposed in recent years [8]. This method, which is called Direct Frequency Comb Spectroscopy (DFCS), is widely used for TPT spectroscopy of molecules and ions [5; 6; 9; 10; 11; 12; 13; 14; 15]. In the previous work, we explore a simplified scheme to obtain the DFCS of Rb two-photon transition [5; 6]. In contrast to the conventional scheme, this scheme utilizes an Erbium-fiber-based frequency comb to excite the two-photon transition. The natural advantages of Erbium (Er) optical frequency make the whole scheme more simplified and robust.  
In order to implement accuracy and stability of the system, we eliminate the Doppler-broadening, which is the main line broadening. The laser cooling technologies, such as magneto optical trap [4] and molasses, can eliminate most of the Doppler-broadening background. However, the number of atoms in the magneto-optical trap is much lower than the number of atoms in a normal gas cell.. Cold Rb TPT transition intensity is weak for establishing frequency standard or Doppler laser cooling. Therefore, following the previous research [5; 6], we try to optimize repetition frequency of optical frequency comb to achieve higher transition intensity with the same average probe laser power. As the result of measurement, transition intensity is improved threefold.