# Experimental Evaluation of the Blackbody Radiation Shift in the Cesium Atomic Fountain Clock
## 2 Theoretical Research on the Blackbody Radiation (BBR) Shift
### Temperature Measurement Research of Atomic Flight Zone  
To improve the spatial uniformity of the temperature in the atomic flight zone, it was necessary not only to design the system to make the temperature distribution of the resonant cavity and the free flight zone as stable and uniform as possible but also to accurately measure the temperature at each point. According to Formula (8), the uncertainty of BBR shift is strongly correlated to the uncertainty of the temperature measurement. A platinum resistance temperature sensor was used to measure the temperature at each point in real time. Heat conduction is a problem that needs to be addressed in temperature measurement. Among the current methods for dealing with the thermal conductivity of temperature sensors is the use of glue or a screw to attach the temperature sensor to  
Figure 3: Physical system temperature measurement: (**a**) before adding the insulation layer; (**b**) after adding the insulation layer.  
the surface of the device in question. However, since the side wall of the vacuum metal cavity is a curved structure, there will be a gap if the sensor is attached directly to the wall. Because the thermal conductivity of air is only 0.024 W/(m\(\cdot\)K), it is a poor conductor of heat, which increases the contact thermal resistance and significantly hinders the conduction of heat; this makes the temperature measurement inaccurate. In this study, we chose to use indium metal, which has a lower hardness and higher thermal conductivity, as the thermally conductive material in the experiment.  
The specific solution for temperature measurement was the following: a temperature-measuring platinum resistor was arranged between two indium sheets, which were fixed to the outer wall of the vacuum chamber using an oxygen-free copper band. The indium sheet had a low hardness at room temperature and was able to achieve close contact with the temperature-measuring resistor and the metal cylinder. The heat-conducting property was greatly improved as a result. In addition, a copper band was used to fix the indium sheet. The copper band had good thermal conductivity, was not easily deformable, and prevented the generation of a magnetic field in the system environment.  
The thermometer was a FLUKE-1529 series four-channel thermometer, the sensors were PT100 platinum resistors, a four-wire connection method was adopted, and the influence of cable resistance fluctuation on the temperature measurement was eliminated. We matched and connected the four-channel thermometer with the sensors and carried out a calibration. The calibration results are shown in Table 1. The deviation between the displayed measured value and the actual standard temperature value can be deducted in the calculation; thereafter, we obtain the accurate temperature distribution result.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nominal Temperature (\({}^{\circ}\)C)** & **18** & **22** & **26** & **30** \\ \hline
**Standard Values (\({}^{\circ}\)C)** & **17.995** & **21.992** & **25.997** & **30.023** \\ \hline
**Channel Number** & \multicolumn{4}{c}{**Displayed Value (\({}^{\circ}\)C)**} \\ \hline
**Ch1** & 18.0081 & 22.0117 & 26.0184 & 30.0461 \\
**Ch2** & 18.0707 & 22.0743 & 26.0780 & 30.1074 \\
**Ch3** & 17.9890 & 21.9931 & 26.0001 & 30.0247 \\
**Ch4** & 18.0153 & 22.0205 & 26.0272 & 30.0565 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermometer calibration results.  
Figure 4: Distribution of temperature measurement points of the system.