Vacuum metrology based on refractive index of gas
Authors: Xu Yu-Rong , Liu Yang-Yang , Wang Jin , Sun Yu , Xi Zhen-Hua , Li De-Tian , Hu Shui-Ming ,   Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, China,   CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China,   Science and Technology on Vacuum Technology and Physics Laboratory, Lanzhou Institute of Physics, Lanzhou 730000, China
Published: December 2020

With the development of vacuum technology, subject to the influence of directional flow and uneven temperature, the thermodynamic equilibrium state is destroyed. In this case, the pressure reference is not suitable for characterizing the vacuum state. To ensure the long-term stability and reproducibility of the measurement system, vacuum metrology will be characterized by gas density. The precisive measurement of gas refractive index based on a Fabry-Perot cavity can be used to derive the gas density. This kind of an optical measurement of vacuum links macroscopic dielectric constants of gases with microscopic polarization parameters of atoms and molecules. It replaces the physical standard based on the mercury pressure gauge with the quantum standard. In this paper, we discuss the reverse process from refractive index to gas pressure, and use the laser-locked Fabry-Perot cavity method to measure the refractive index of argon gas. The contribution of related parameters to the uncertainty of determined gas pressure is analyzed. The influences of material parameters and experimental parameters such as gas molar susceptibility, molar susceptibility, dielectric second Virial coefficient and temperature on gas pressure accuracy are analyzed. The result shows that the uncertainty in our measurement of argon within 1 atm is <inline-formula><tex-math id="M2">\begin{document}$u = \sqrt {{{(6\;{\rm{mPa}})}^2} + {{(73 \times {{10}^{ - 6}}p)}^2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200706_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200706_M2.png"/></alternatives></inline-formula>. Currently, the uncertainty mainly comes from the measurement deviation of gas temperature inside the cavity. After repeating the measurement a few times, the results show that the statistical uncertainty of refractive index is within 100 ppm, which is limited by the accuracy of the pressure gauge used here. In addition, we compare the dipole calculated by the <i>ab initio</i> method with that by the DOSD method. The results show that the dynamic polarizability obtained by the <i>ab initio</i> method is consistent with our experimental results. In conclusion, these experimental results show that the measurement of gas pressure based on the gas refractive index has high repeatability and accuracy. If the temperature control and corresponding measurement accuracy of the gas are further improved, this method can also be used to obtain high-precision microscopic parameters such as the polarizabilities of atoms and molecules. In the future work, we will focus on improving the temperature control and the design of the cavity to reduce cavity leakage and deflation. It is possible that the measurement accuracy of the gas pressure will be increased to 10 ppm level, which is the same level as the current standard pressure gauge and will become a new standard for pressure measurement in the future.