## 3 Analysis and Discussions
The blue solid circles in the figure are Rydberg level shifts obtained under seven temperature conditions in Figure 3c; the black squares show the calculated mean electric fields. Laser beams with different frequencies will interact with atoms of different velocity groups [29,30]. We can change the frequency detuning of the coupling laser \(\Delta_{C}=-\Delta_{P}\cdot\lambda_{P}/\lambda_{C}\) by controlling the frequency detuning of the probe laser \(\Delta_{P}\), as the Rydberg level shift can also react to the frequency detuning of the probe laser. Therefore, according to the theoretical simulation, we find \(\Delta_{S}\approx-\Delta_{P,max}\cdot\lambda_{P}/\lambda_{C}\), where \(\Delta_{P,max}\) is the 852-nm probe detuning of the maximum EIT signal intensity. Therefore, Rydberg level shift \(\Delta_{S}\) is caused by the mean electric field generated by the collisions induced ionization, such that the probe laser is in resonance with the Cs \(6S_{1/2}(F=4)\to 6P_{3/2}(F^{\prime}=5)\)transition, while the coupling laser is in resonance with the Cs \(6P_{3/2}(F^{\prime}=5)\to 50S_{1/2}\) Rydberg transition, satisfying the two-photon resonance condition, the intensity of EIT signal is the strongest under this condition. Figure 4: **(a)** The densities of charged particles and Cs 50S\({}_{1/2}\)Rydberg atoms. The blue squares indicate the densities of charged particles, while the red solid circles indicate Rydberg atomic densities; **(b)** Rydberg level shift due to Rydberg dipole–dipole interaction of Cs atoms for 50S\({}_{1/2}\) state versus the calculated Rydberg atomic density; **(c)** Rydberg level shift versus \(N_{C}\) for Cs 50S\({}_{1/2}\) Rydberg state. The blue solid circles are Rydberg level shifts caused by the calculated density of charged particles, according to seven temperature conditions of Figure 3c, while the blue solid line shows Equation (3). The black squares indicate the mean electric fields based on the calculated density of charged particles. We study the relationship between the Rydberg level shift and detuning of the probe laser that produces the EIT signal of maximum intensity multiplied by the Doppler mismatch factor, as shown in Figure 5. The blue solid circles indicate the change of Rydberg level shift \(\Delta_{S}\) with density of charged particles, while the red squares indicate the change of probe laser detuning multiplied by the Doppler mismatch factor with density of charged particles, that is, how \(-\Delta_{P,max}\cdot\lambda_{P}/\lambda_{C}\) varied with density of charged particles. It can be seen that, with the change of density of charged particles, Rydberg level shift and detuning of probe laser multiplied by the Doppler mismatch factor are approximately equal. The solid black line is the fitting of the change of \(-\Delta_{P,max}\cdot\lambda_{P}/\lambda_{C}\) with the density of charged particles by using Equation (3). In our experimental system, the main deviation is inaccuracy of the temperature control of the atomic vapor cell. For the red detuning for Rydberg state \(50S_{1/2}\), there is also an energy shift and maximum intensity of Rydberg EIT signal. For the case of the Cs \(6P_{3/2}(F^{\prime}=5)\to 50S_{1/2}\) Rydberg transition, the red detuning of \(\sim\)500 MHz is corresponding to the blue detuning of the Cs \(6P_{3/2}(F^{\prime}=3)\to 50S_{1/2}\)Rydberg transition. With Rydberg EIT spectra, it is difficult to eliminate the influence of hyperfine folds in \(6P_{3/2}\) state. Therefore, the detailed discussion is not performed on the red detuning case for \(50S_{1/2}\)Rydberg state.