# Lifetime Measurement of Cesium Atoms Using a Cold Rydberg Gas
## 4 Conclusions  
We have measured the lifetime of cesium Rydberg atoms in the high state (\(60\leq n\leq 83\)) and found that the blackbody radiation and Rydberg interaction would strongly enhance  
Figure 4: (Color online) (**a**) The measurements (red circles) and calculations (black squares) of \(|nS_{1/2}\rangle\) atomic lifetimes as a function of the principal quantum number \(n\). Error bars of data display the standard error of five independent measurements. The calculations of Equation (4) reproduce the experiments well. For comparison, we also present calculations of spontaneous radiation lifetime \(\tau_{sp}\) (blue stars) and BBR lifetime \(\tau_{BBR}\) (pink triangles). The red solid (black dashed) line indicates the fitting of the measured (calculated) lifetime with the function \(\tau=a\times(n-\delta_{L})^{b}\), with \(b\) displaying the scaling law. \(b_{exp}\) = 2.30 \(\pm\) 0.01 and \(b_{theor}\) = 2.27 \(\pm\) 0.01. (**b**) The same measurements and calculations as in (**a**) for \(|nD_{5/2}\rangle\) state. \(b_{exp}\) = 2.55 \(\pm\) 0.02 and \(b_{theor}\) = 2.50 \(\pm\) 0.02. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lifetime** & **State** & **\(n\)-Range** & **\(b\)** \\ \hline \(\tau_{sp}\)[5] & \(nD_{5/2}\) & 10 \(\leq n\leq\) 80 & 3.00 \\  & \(nS_{1/2}\) & & 2.99 \\ \hline \(\tau_{eff}\)[5] & \(nD_{5/2}\) & 10 \(\leq n\leq\) 80 & 2.56 \\  & \(nS_{1/2}\) & & 2.39 \\ \hline \(\tau_{exp}\)[15] & \(nD_{5/2}\) & 50 \(\leq n\leq\) 75 & 2.45 \\ \hline \(\tau_{eff}\) & \(nD_{5/2}\) & 60 \(\leq n\leq\) 83 & 2.50 \(\pm\) 0.02 \\ (this work) & \(nS_{1/2}\) & & 2.27 \(\pm\) 0.01 \\ \hline \(\tau_{exp}\) & \(nD_{5/2}\) & 60 \(\leq n\leq\) 83 & 2.55 \(\pm\) 0.02 \\ (this work) & \(nS_{1/2}\) & & 2.30 \(\pm\) 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of measurements and calculations of \(n\)-scaling magnitude \(b\) of cesium Rydberg lifetime. the decay rate and shorten the lifetime of the given Rydberg state. For lower Rydberg atomic density, the measured lifetime shows a good agreement with the calculated effective lifetime \(\tau_{eff}\). The cross section can be extracted by fitting the measurement of decay rate as a function of the Rydberg atomic density, which is closer to the Rydberg geometric collision section. The calculated spontaneous lifetime displays \(n^{3}\) scaling law [1,5]. However, the scaling \(b\) of lifetime measurement is \(b_{exp}\) = 2.55 (2.30) for \(|nD_{5/2}\rangle\) (\(|nS_{1/2}\rangle\)) that is less than that of the spontaneous lifetime. The reduction of the scaling magnitude of \(b\) can be attributed to the BBR induced decay that enhances the decay rate of the Rydberg state. The results here demonstrate that the lifetimes are affected by the room temperature BBR radiation and the interaction between Rydberg atoms. In this work, we have measured the lifetime of \(|nS_{1/2}\rangle\) and \(|nD_{5/2}\rangle\) for \(n\) = 60-83. The agreement between the measurement and calculation of Rydberg lifetime displays that the calculation of effective lifetime accounting BBR in Ref. [5] can be extend to \(n\) = 83. It is noted that the superradiation effect has a negligible effect on the lifetime measurement in this work. When the Rydberg density is larger than \(\sim\)10\({}^{10}\) cm\({}^{-3}\), the superradiation will strongly accelerate the decay rate and modify the lifetime of Rydberg state [4,25]. The high precision measurement of the lifetime provides a powerful tool for investigating the cross section for the quenching collision and also has a significant correction to quantum defects. Conceptualization, J.Z., Y.J. and R.S. ; investigation, J.Z., Y.J., J.B. and R.S. ; software, Y.J., J.B. and R.S. ; validation, R.S. and J.B.; formal analysis, R.S. and J.B.; Writing--original draft, R.S. ; writing--review and editing, J.Z. ; project administration, J.Z. ; Y.J. and S.J. ; funding acquisition, J.Z. and Y.J. All authors have read and agreed to the published version of the manuscript.